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Jul
31
To refresh your memory about the Greek, Vega, she is the goddess who tells us exactly how much the price of an option will move in sympathy with a change in volatility. She also doesn’t care if you buy a call or a put….its all the same to her. Vertically speaking, all she cares about is the strike price. Moreover, if we want to locate the highest Vega for a given month, we know right where to find her….at-the-money. But Vega is different when it comes to the horizontal.
When we look over time, Vega is most likely to increase. What does that mean for traders? Well, it means that Vega becomes more sensitive to volatility in the out months. As Ron Ianieri of Options University explains, “We don’t trade from the future backward; we trade from now toward the future. We need to see and understand that if we buy an option, especially an out-month option, as it gets closer and closer to expiration its volatility sensitivity decreases. The option becomes less and less sensitive to movements in implied volatility; you need bigger movements to move the value of the option as expiration gets closer and closer. In other words, as our option approaches expiration, it takes more and more implied volatility to change the price of the option. From a Vega point of view, if price changes become less sensitive in the front months it implies that Vega is more sensitive in the out months.
Suppose you want to move an option price 17.5 cents. You do it in July where the Vega’s only 4.7 cents, you would need to have a volatility move of four ticks to get the same 17.5 cent movement in one tick of an option four months further out. So, you need to know that as options get closer to expiration their Vega component dwindles; they become less sensitive to tick movements in volatility. This fact is important because if we want to play volatility we might want to go out a little further where volatility movements may have a greater affect on price.
So, speaking vertically, Vega is highest at-the-money and decreases in both directions. Horizontally, however, Vega sensitivity increases in the out-months and lowers in the front months. And, although a bit counter-intuitive, as you approach expiration, volatility lessens and as a result, you need more Vega to move price per tick.
Another interesting thing about Vega is that spreads have their own Vega. For spreads where you are selling one leg of an option and buying the other, you’re looking at the difference between the Vega’s of the two option components and that will equal the spread’s Vega. However, if you are buying both options, you need to add the two Vega’s together.
When using a strategy using multiple options, you must first use the Vega to equalize the volatility levels of the two options. For example, if one leg has a volatility of 32 and the other leg has 30, you either take the 32-volatility option, using its Vega, to recalculate it for 30-volatility and then you’ll have two options at 30-volatility and then go ahead and balance it out. Or, you can take the 30-volatility option and recalculate that using its Vega to get the theoretical value of the option at 32-volatility. This is how most spread volatility is figured out.
Because Vega is the first relationship between movement in volatility and the price of your option, it’s important to have an idea of how Vega is affected by time and changing volatility.
For more information on Vega and all the other Greeks, contact Options University at www.optionsuniversity.com and check out the current online courses to help boost your knowledge in the dynamic study of stock options.
Jul
31
Table 2-5: JNPR Quotes Taken on Expiration Day
insert tav
I noticed that the stock was bidding $83 5/8, which means that his calls should be worth $83-5/8 - $50 strike = $33-5/8 rather than the $32-1/4 they were bidding. They were missing $1-3/8, or $1.375 worth of intrinsic value! What do you suppose we did? Hopefully you said short the stock and exercise the calls. Doing so brought in an additional 20 contracts * $1.375 * 100 shares per contract = $2,750 less some commissions for shorting the stock and exercising the call.
As you start trading options, you’ll find that 20-cent (or greater) discrepancies occur all the time near expiration. You’ll even find lesser, but still viable, discrepancies with as much as a week until expiration.
To capture this missing intrinsic value, some of the newer, more progressive firms have an order called “exercise and cover,” which automatically uses the technique we are describing. It allows you to quickly submit an order to sell the shares and then immediately exercise in order to capture any missing intrinsic value on your option. If you are trading even a few option contracts, this method of capturing intrinsic value near expiration day can be quite profitable. Depending on the commissions you’re paying and the number of contracts you’re closing, it pays to check what your difference will be between the outright sale of the option versus trying to capture any missing intrinsic value. In many cases, you’ll find that it is worth paying the extra commissions. Serious money can be hiding there, and you now have the tools to reclaim it.
Pricing Principle #4:
Prior to Expiration, All Call Options Must Be Worth At Least the Stock Price Minus the Present Value of the Exercise Price, or S – Pv (E). Put Options Must Be Worth More Than the Exercise Price – Stock Price, or E – S.
The previous pricing relationship stated that all options must be worth either zero or their intrinsic value at expiration. Is there anything we can specifically say about option prices prior to expiration? The answer is yes. Bear in mind that our previous pricing principle also applies prior to expiration and all options must be worth at least their intrinsic value. If not, arbitrage would be carried out exactly the same way as discussed for Principle #3. However, Principle #4 shows that prior to expiration we can make a stronger claim as to the minimum value. The strength of our claim depends on whether we’re dealing with calls or puts. Let’s start with call options.
Pricing Principle #4 tells us that all call options must be worth at least the stock price minus the present value of the exercise price. This may sound a little complicated, but it’s not so difficult once you understand what we mean by the present value. To do so, we to talk about the financial concept of the time value of money.
The Time Value of Money
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Review of transactions
If call option is below intrinsic value:
1) Short the stock
2) Exercise the call
If the put option is below intrinsic value:
1) Buy the stock
2) Exercise the put
In either case, these actions provide the necessary funds to purchase the stock. You do not need to have any cash in the account.
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One of the most important fundamental financial concepts is called the time value of money. Simply put, the time value of money states that a dollar today is worth more than a dollar tomorrow. This originates from the simple fact that a dollar today can be invested and earns the risk-free rate of interest. If someone owes you $10,000 in one year and offers to either pay you today or in one year, you’d rather have it today because you could invest that money at the risk-free rate and have more money in one year. The two payments are not the same. If $10,000 today is worth more in one year then it follows that $10,000 in one year must be worth less today. How much less? That depends on the risk-free interest rate.
Let’s say you deposit $10,000 into an account that pays 5% interest. You will have $10,000 * (1.05) = $10,500 in one year. We call this the future value of money. The future value of money shows us how much a dollar today will be worth in the future at a stated interest rate. In this example, the future value of $10,000 in one year is $10,500 if interest rates are 5%.
Now let’s work the same problem backwards. If someone owes you $10,500 one year from now and interest rates are 5% then you should be willing to accept $10,500/(1.05) = $10,000 today. In this example, we say that the present value of $10,500 due in one year is $10,000 if the risk-free rate of interest is 5%. The present value of money shows us how much a future payment is worth today at a stated interest rate.
In other words, it should make no difference to you to wait one year and receive $10,500 or collect $10,000 today. The reason is that you can take the $10,000 today, invest it at 5% for one year, and still have $10,500 a year from now. No matter which choice you take, you’d end up with $10,500 in one year. The two choices are identical and it is the time value of money that allows us to line up the different cash flows at different points in time and arrive at that conclusion.
It’s important to understand that if we are using the risk-free rate then we must be dealing with guaranteed future payments. You would be indifferent between taking $10,000 today and $10,500 in one year assuming the $10,500 payment in one year was guaranteed. If the person owing you the money is financially unstable and on the verge of bankruptcy, you would probably be willing to take substantially less than $10,000 today to settle the debt.
Another way of expressing the present value concept is to say that $10,500 discounted at 5% for one year is $10,000. So the discount value and the present value express the same idea. Sometimes, as a simple notation, you might see Pv ($10,500) = $10,000, where “Pv” is used to denote the present value. We will use this notation throughout the book.[1]
If the $10,500 were due in two years, then we must discount by 1.05 twice. Mathematically, we could go straight to the answer by dividing $10,500 by (1.05 * 1.05), which is 1.052. Doing so, we find that $10,500/1.052 = $9,523.80. To check the answer, $9,523.80 invested for one year at 5% is $10,000. If we invest $10,000 for another year at 5% we end up with $10,000 * 1.05 = $10,500. Therefore, if you are guaranteed to receive $10,500 in two years then you should be indifferent between that or accepting $9,523.80 today.
We can use the time value of money concept to place even tighter restrictions on our call option prices prior to expiration and the fourth pricing principle shows us how to do just that. If there is time remaining on the option then the call option’s price must be worth at least the stock price minus the present value of the exercise price, or S – Pv (E).
This formula is probably best understood by considering the previous principle that showed us an in-the-money call option must be worth exactly S – E at expiration. In other words, if the call is in-the-money at expiration, the call holder could receive the stock (+S) by exercising and paying the strike (-E). Therefore the value of the call must be S – E. However, prior to expiration that same exercise price must have a value of Pv (E) since the exercise will not take place until the future. The value of the call today must therefore be at least S – Pv (E).
The formula S – Pv (E) defines a minimum value for all call options and not just in-the-money calls. Let’s run through some examples using in-the-money, at-the-money, and out-of-the-money to be sure you understand how this formula affects option prices. We’ll begin by considering the in-the-money call.
Assume you are looking at a one-year $50 call option with the stock trading for $55. You know there is $5 intrinsic value, so the option must be worth at least $5 (Principle #3). But because there is time remaining we know there is a higher minimum that it must be worth (Principle #4). Because you have the $50 call, you do not need to exercise it until the very end in one year, which means you can hang on to your $50 cash for one year and earn $50 * .05 = $2.50 interest. If you could earn an additional $2.50 in guaranteed interest in one year then that must have a value today of $2.50/1.05 = $2.38. This means that our $50 call has $5 intrinsic value ($55 stock - $50 strike) but it also has an additional value today of $2.38 (the present value of the interest that is earned), which means the $50 call value today must be worth at least $5 + $2.38 = $7.38.
In some texts, you may see the notation Ee-rt to denote the present value of the exercise price, where E = exercise price, e = the mathematical constant 2.7183…, r = rate, and t = time. The use of the mathematical constant e is just a way to accounting for continuously compounded interest and doesn’t make a big difference in the calculations. To keep things simple and more understandable, we’re going to use Pv (E) to mean the same thing.
To be continued…
[1] In some texts, you may see the notation Ee-rt to denote the present value of the exercise price, where E = exercise price, e = the mathematical constant 2.7183…, r = rate, and t = time. The use of the mathematical constant e is just a way to accounting for continuously compounded interest and doesn’t make a big difference in the calculations. To keep things simple and more understandable, we’re going to use Pv (E) to mean the same thing.
Jul
30
The essence of an option is the extrinsic value and the biggest component of extrinsic value is volatility. Understanding volatility brings on the importance of Vega because Vega shows us the exact direct affect of movements in volatility to an option price. It is a one step direct link.
Vega is given as cents just like Theta and tells us how much the option price is going to change when volatility increases or decreases. Ron Ianieri of Options University (www.optionsuniversity.com) states in his Options Mastery Course, “Vega is probably the source of most of the losses in the options market for new options traders”. He uses the example of a stock that is going up and currently trading at $46. You look at the $50 strike price for a call that is selling at only .80 or .90 cents. You look three weeks later and the even though the stock went up, the price for the $50 call has gone down-the reverse of what one might think. Why didn’t the option price also increase along with the rising stock?
Most likely what probably happened is that Vega took a bite out of the price. What happened was that the stock traded up in a nice steady fashion and as a result, the implied volatility decreased by the amount of Vega. This becomes particularly important when using a stock replacement strategy for an option play. Why?
Under certain situations, Vega and Theta can work against you and this is not uncommon to see on a regular basis. The stock may go up but not the corresponding call option. You see, Vega beat Delta and Theta (time decay) conspired to erode the option price. As a matter of fact, according to Ron, if you talk to any floor trader and you ask them, over the course of their career did they make more money trading Delta, stock direction, Vega (volatility direction), just about every trader would tell you that their money was made through Vega; that’s how important Vega is. Vega allows an option trader to anticipate what the price of the option will be in the future with the movement in volatility.
An important thing about Vega-as well as with Gamma and Theta-is that these three Greeks don’t discriminate between put and call. They just react to month and strike price. So, Vega-as well as the other two-will be the same for put and call at the same strike. For example if the June 70 Strike has a Vega of .053, that means that both the call and put will move 5.3 cents with a one tick change in volatility. So, if the volatility of the June 70 strike is currently at 40 and it moves up to 41, the price of the option will move up 5.3 cents. If volatility goes down, so will the price of the option as a factor of Vega for the particular strike. If Volatility in our example moves up 3 ticks, the option price will move up about 16 cents. The reverse holds true for a 3 tick decline; the option price will decrease about 16 cents.
So, if a trader is making a directional play, they need to make sure that Vega won’t become a surprise if volatility starts to drop. Therefore, we look specifically for options that are not very sensitive to volatility. We look for options with low Vega’s and it makes it a heck of a lot easier when we know that Vega is highest at the money and moves down on either side. So, to compare Vegas, look for at-the-money options.
For more information about all aspects of stock options, contact Options University at www.optionsuniversity.com and find out about their online courses, webinars and mentoring programs.
Jul
30
Expiration Values for Put Options
At expiration, put options must be worth either zero or their intrinsic value, which is found by taking the exercise price minus the stock price, or E - S. For example, assume the stock is $53. The $60 put must be trading for $60 - $53 = $7 at expiration. If the stock is above $60 at expiration, the put will expire worthless since there is no reason to exercise a put and collect $60 when you can just sell the stock in the open market for more money.
If a put option is in-the-money (stock is below the strike price) at expiration and not trading for the intrinsic value then arbitrage is possible. Assume the stock is $53 but that the $60 put is trading for only $5 thus there is $2 of intrinsic value missing. Arbitrageurs would buy the stock and buy the put for a net cash outlay of $58:
Buy stock = -$53
Buy $60 put = -$5
Net debit = -$58
The arbitrageur would then immediately exercise the put and receive the $60 strike price thus making an immediate, guaranteed minimum profit of $2 for no cash outlay, which is exactly the amount of missing intrinsic value. The missing intrinsic value can only be restored if the stock price rises to $55 or if the put price rises to $7 or some combination of the two. Notice that the above transactions (buying stock, buying puts) will place buying pressure on the stock and the $60 put, which are the forces necessary to restore intrinsic value.
So at expiration, options can only be one of two values: zero or intrinsic value. Now you see why all in-the-money options must retain intrinsic value at expiration. It is not a matter of courtesy or tradition by the market makers; it is forced through the process of arbitrage.
All options must be worth either zero or intrinsic value at expiration.
Theory Versus Reality
Okay, hopefully you’re convinced that an option must always trade for at least its intrinsic value. Arbitrage is the theory that supports that conviction. However, the reality is that there are really two prices for an option – the bid and ask. The theory holds only for the asking price and not for the bid. For instance, assume that a $50 call option is close to expiration with the stock at $55. Because the option’s price is approaching a pure intrinsic value of exactly $5, the market maker will not bid $5 for it. Instead, the market maker may bid $4.80 so that he can sell it for the $5 intrinsic value and make a 20-cent profit. If you sell this $50 call at the bid, there is 20 cents worth of missing intrinsic value. Most traders have observed this near expiration and just accept it as part of the way the system works. However, there is a way to get it back and it is similar to how the arbitrageurs do it.
Here’s how to do it: If you are ever selling a call option that is bidding below intrinsic value, all you have to do is short the stock and then immediately exercise the option. Since you already own the call, you do not need to purchase it like the arbitrageurs do. However, the idea is the same. By selling the stock and exercising the option, you can gain back the missing intrinsic value.
Using our example, let’s say you wish to sell 10 contracts of the $50 call that is bidding $4.80. If you sell at the bid, you’ll receive $4,800. But if you short the stock and exercise the call, you’ll get a net credit of $5,000:
Short stock = +$55,000
Exercise call = -$50,000
Net credit = $5,000
This represents a $200 difference from selling at the bid price of $4.80. The reason is that the bid price is missing 20 cents worth of intrinsic value, which equals 0.20 * 10 contracts * 100 shares per contract = $200. So in this example, for the commission of shorting the stock, you can pick up an extra $200.
You’re probably thinking that this sounds good but with one problem. What if you don’t have the $50,000 to exercise the call? The answer is you do have it. You’ll get it from the $55,000 credit you’ll receive from shorting the stock. The fact that there is intrinsic value in the option tells us that the value of the stock must be greater than the strike. Therefore, shorting the stock will always provide enough funds to pay for the exercise.
Also, there is no margin requirement on the short stock position since you own a long call with a lower strike price, which protects you from any upside movement in the stock. The point is that there is absolutely no reason to not grab the extra $200. For two small commissions – one to short the stock and another to exercise the option – you can restore your intrinsic value in the call option. Most firms today charge very low commissions to buy or sell stock but charge significantly higher commissions to buy or sell options. In most cases, you’ll find that commission to short the stock and exercise the option will still be cheaper than the commission charged for selling the call. Exercising an option is normally charged as a regular stock transaction so it is usually worth your while to short the stock and then exercise the call to collect the missing intrinsic value.
If you have a put option with missing intrinsic value, you simply buy the stock and then exercise the put. For example, assume you have 10 $50 puts with the stock at $45 near expiration. The market maker might only bid $4.80 for this put even though it is theoretically worth $5. You can capture the missing 20 cents of intrinsic value by purchasing the stock and then immediately exercising the put:
Buy stock = -$45,000
Exercise put = +$50,000
Net credit = $5,000
By exercising the put, you collect the exercise price of $50. And because you only paid $45 for the stock, your net gain is the $5 difference. Once again, you may be wondering where you’ll get the money to pay $45,000 for the stock. The answer is that you will receive it once you exercise the put. Because the OCC guarantees that the transaction will go through, there is no reason for your broker to not allow it. In this example, for one small commission to buy the stock, you picked up an extra $200 for closing your $50 puts.
In the previous two examples, we assumed there was 20 cents worth of missing intrinsic value. How realistic is this figure? It’s actually quite common, and sometimes you’ll find the options are missing much more. For example, Table 2-4 shows Cyberonics (CYBX) call and put quotes taken on expiration day June 18, 2004:
Table 2-4: CYBX Quotes Taken on Expiration Day
insert table2-4
Now look at the June $40 puts. With the stock at $37.60, these should be worth $2.40 at expiration but they are only bidding $2.25, which means they are missing 15 cents of intrinsic value. As with the calls, the $2.70 asking price more than reflects the intrinsic value, so you cannot arbitrage these prices. But if you already own the put, you can buy the stock and immediately exercise the put to collect the full intrinsic value.
How bad can these discrepancies get? One day in 1999 while working on an active option trader’s team, a client called in to sell 20 of his Juniper Networks (JNPR) Feb $50 calls. Table 2-5 shows the quotes and you can see that the Feb $50 calls were bidding $32-1/4 (this is when stocks and options were still quoted in fractions).
To be continued…..
Jul
29
Theta is the Greek that produces time decay in stock options. It’s a bit depressing but true; each day you own a stock option, you lose a certain amount of money due to time decay. Moreover, every option has a different rate of time decay. According to Ron Ianieri of the Options University, quite often Theta is going to play an important part in choosing which strategy or option a trader may choose.
Every day that goes by, an option has to either perform for us because it decays. This usually that each day it hurts us just a little bit. It can get to the point that if we wait too long for an option to perform, any gains we might make from the movement may be offset by the loss in value we had already accrued in time decay.
It’s also very important for option traders to realize that when talking about option prices, premium or price consists of two types of values. Value number one is intrinsic value; the amount by which an option is in-the-money. In-the-money options are the only options with intrinsic value and intrinsic value does not decay.
The other value component of option premium price is extrinsic value, and this element of value is all about time decay. An in-the-money option can have both intrinsic and extrinsic value at the same time. At-the-money options have just a little intrinsic and a lot of extrinsic value. Out-of-the-money options are all extrinsic value and its extrinsic value that decays to zero over the period of the option.
If a trader is short an option or wants to sell an option to try to take advantage of premium collection, the trader needs to understand Theta. The trader needs to know and be aware of which options are going to have the most amount of extrinsic value and which options are going to decay the fastest. If an option trader is collecting premium, they want to try to collect as much premium and then have the value of the option decay as fast as possible. What tells us that? Theta tells us that. But what exactly does Theta tell us?
If you have a Theta of .032, for example, this means that extrinsic value will decay 3.2 cents a day-everyday until approaching expiration. It is also very important to know that Theta does not decay in linear fashion. When within about 20 days of expiration, the rate of decay starts to accelerate. For example, the 3.2 cent per day decay might move up to 5 cents per day and the slope of the decay chart starts to “roll over” as each day the rate of decay increases and the extrinsic value starts to evaporate rapidly and reaches zero at the end of expiration day; that is, the option no longer has worth once it has expired.
Option traders need to keep in mind that most out-month options have little time decay until approaching the last two weeks or so before expiration. That means that selling out-month options is not a good strategy for premium collection. Traders want to collect the premium and then have the option premium race to zero as fast as possible. So, sell the front-month if you’re interested in premium collection.
The key concept to remember is: the front-month option decays much more dramatically than an out-month option. So, if we’re going to be a premium collector, if we’re going to sell options to collect premium, which is a great idea, we want to make sure that we’re selling the optimal option and that is always the front month at-the-money.
For more information on all aspects of stock option trading, contact the Options University at www.optionsuniversity.com.
Jul
29
Put options are also more valuable with additional time. The reason is that stock prices are equally likely to rise and fall. A $50 stock, for example, is equally likely to rise or fall by $5. Because put options act like all options but in the opposite direction, puts must also be more valuable with additional time.
Will longer-term options always be more expensive than short-term options? The answer is yes and the reason is arbitrage. Let’s assume the July $32.50 call is $4.90 but that the August $32.50 call is $4.75. In other words, a longer-term option is trading below that of a shorter-term option, which is something we said should not happen. Arbitrageurs would sell the July $32.50 call and receive a $4.90 credit, and then use $4.75 of that credit to buy the August $32.50 call, thus taking in a credit of 15 cents:
Sell July $32.50 = +$4.90
Buy August $32.50 = -$4.75
Net credit = 15 cents
Now think about their rights and obligations. They have the right to buy stock for $32.50 and may have to sell it for $32.50, which is a wash. If that happens, the arbitrageurs keep the 15-cent credit. However, it is also possible that the July contract expires worthless (the stock falls below $32.50) and the arbitrageur still owns the August contract, which could rise in value after July. This means that the arbitrageur is guaranteed to make at least 15 cents and could potentially make much more. This is a riskless opportunity for which the arbitrageur paid no money. As the arbitrageur buys the August calls and sells the July calls, he will put buying pressure on August and selling pressure on July, eventually making August more expensive than July. At that point, the arbitrage opportunity disappears. A similar set of transactions occurs for put options.
With all else being equal, more time to expiration means higher option prices.
As before, you don’t need to understand this arbitrage process to trade options. Just understand that there is a very real force that assures us that longer-term options (calls or puts) will cost more than the shorter-term ones assuming all other factors are the same (same underlying stock and same strike price). That part you do need to understand.
Square-Root Rule
While options get more expensive with increases in time, there is another mathematical boundary that option prices closely follow. That is, it takes about four times the amount of time in order to double the at-the-money option’s price. For example, if a one-month at-the-money option is trading for $1 then the four-month at-the-money option will be roughly $2. While it may seem that doubling time will double the option’s price it actually takes a quadrupling of time. If you get more into the mathematics of option pricing, you will find that option prices are proportional to the square root of time. If time increases by a factor of four then the option’s price doubles – a factor that is exactly the square root of four. If you double the time on an option, then the option’s price will rise by the square root of two, or about 1.41 times. If the one-month at-the-money option is worth $1 then the two-month at-the-money option is worth $1.41.
This means that if you are a buyer of an option, it is a progressively better deal for you to buy time. While options get more expensive over time, they get cheaper per unit of time. In our example, the one-month option costs $1 per month. The four-month option costs $2 for four months of time, or 50 cents per month. So while the four-month option is more expensive in total dollars, it is actually cheaper per unit of time. Think of it like buying soft drinks by the case at the grocery store. A case of Coke will cost more in terms of total dollars but is cheaper per can (per unit). The square-root rule implies that buyers should buy more time as they become progressively a better deal. Sellers should sell short-term options. With all else being equal, buyers are better off buying one four-month option rather than four one-month options. The opposite is true for sellers.
Exercise:
Go to www.cboe.com and check out option quotes on several stocks. Are longer-term options always more expensive than shorter-term options? Explain in your own words why this happens.
Principle #3:
At Expiration, All Options Must Be Worth Either Zero orTheir Intrinsic Value.
At the end of the first chapter, we said that any intrinsic value must remain with an option at expiration. This means that if an option is in-the-money at expiration the price must be the difference between the stock price and the exercise price, or S – E. For example, if the stock closes at $53 at expiration, the $50 call must be worth exactly $3 since there is $3 worth of intrinsic value and no time value left. Because a long option cannot have negative value then all at-the-money and out-of-the-money calls expire worthless.
To restate it differently, a call option can only be worth one of two values at expiration: It is either worth the intrinsic value (intrinsic value + zero time value) or it is worth nothing (zero intrinsic value + zero time value).
Using our previous example, if the stock is $53, then how can we be sure the $50 call must be worth $53 - $50 = $3 at expiration? Once again, the answer is arbitrage. In order to understand the basics of the arbitrage, think back to the pizza coupons. Imagine that pizza coupons do have value and are traded in the streets (the marketplace). Now assume that pizzas are $15 and a $10 coupon is available, which means the coupon has $5 intrinsic value. However, let’s assume the coupon is trading for only $4. Can anything be done to capitalize on the missing $1 intrinsic value? The answer is yes. The way the market corrects for this missing value is that enterprising individuals would buy the pizza coupon for $4 and then take it to the store and buy the pizza for $10. They would have spent a total of $14 to get the pizza ($4 for the coupon + $10 for the pizza). Then they’d walk out in the street and sell the pizza for $15, thus making a $1 guaranteed profit. This $1 profit is exactly the amount of the missing intrinsic value. As individuals figure this out, they will compete in the market for these coupons thus raising its price. At what point will the competition for coupons stop? When the price of the coupon reaches $5 (or more), which means that the full intrinsic value is now reflected in the price of the coupon.
At expiration, all in-the-money options must trade for their intrinsic value; otherwise a similar set of transactions would take place in the market by arbitrageurs. For instance, assume that the stock is $53 and the $50 call is trading for $2 in the final minutes of trading, which means there is $1missing from the intrinsic value. An arbitrageur would short the stock and buy the call for a net credit of $51 to his account:
Short stock = +$53
Buy $50 call = -$2
Net credit = $51
Because he’s shorted the stock, he has an obligation to buy it back and can do so by exercising the call and paying $50 out of the $51 credit he received. This leaves him with a guaranteed minimum profit of $1 for no out-of-pocket expense, which is exactly the amount of missing intrinsic value. Of course, if the stock price falls below $50, the arbitrageur would just let the call expire worthless and buy the stock in the open market to close out the short position. This would result in a profit greater than one dollar. So whether the stock price rises or falls, the arbitrageur is guaranteed a minimum profit of one dollar. As with all arbitrages, the arbitrageurs’ actions restore the proper pricing relationship. In this example, the above transactions (shorting the stock, buying the call) will put selling pressure on the stock and buying pressure on the call until the full $3 intrinsic value is restored.
To be continued….
Jul
28
It’s never been something that’s caught on in the retail market until recently and that’s because the brokerage prices have come down so much and the spreads of trading stocks have gone from eighths to pennies and that something is called Gamma trading.
Ron Ianieri, in his popular course “Gamma Trading” presented by Options University, explains that Gamma trading can be a way of using the Gamma positions of options to trade stock back and forth when Gamma makes you either long or short Delta. According to Ianieri, the beauty of this strategy is its ability to allow day traders to take an overnight position and help make a winning trade with very high probability.
One of the most difficult things about being a day trader is making that first winning trade of the day. By using Gamma, all a day trader has to do is let Gamma make the decision on the first trade. As you may recall, when the stock moves, either a trader will be long or short Deltas and Gamma will let the trader know whether to acquire short or long Deltas and how much to buy or sell. Moreover, if Delta neutral, a trader is also hedged and can carry positions overnight.
Gamma traders have the benefit of being able to use the Gamma as a hedge or to use it offensively. So a Gamma trader can be a passive one letting the Gamma trade for him/her or the Gamma trader can be an aggressive one using the Gamma as a hedge. Just exactly how to do that can’t be covered in this short article and that is why Options University (www.optionsuniversity.com) offers this special course given by one of the industry’s leading authorities on stock options.
Gamma trading also allows an option trader to trade the same side of the market more than once; typically, the moment a day trade purchase is made, the trader is looking to make a sale. The moment they make the sale, the trader is looking to make a purchase. With Gamma trading, traders can stay on the same side of the market. How does that happen? Once again, that is not within the scope of this article but to let the reader know that it can be done. These kinds of little known tidbits are what make stock options so exciting and challenging. Compared to trading stocks, options are much more sophisticated and complex but if done properly, the effort can be rewarded handsomely.
To find out more about the world of stock options, online courses and live webinars, contact the Options University.
Jul
28
We’ve shown in two ways that lower strike calls and higher strike puts must always be the more expensive strikes. That’s a pretty bold statement to make. While it may make sense as a practical argument, will these relationships always hold? The answer is yes. The reason is due to a process called arbitrage. Arbitrage is a process where “free” money can be made, and that is a powerful incentive to keep a watchful eye on prices. Traders who search for these opportunities are called arbitrageurs (or arbs, for short). How does arbitrage work? Assume for a moment that the $32.50 call in Table 2-1 is $4.90 but that the $35 call is, instead, priced at $5.00. In other words, the $35 call is priced higher than the $32.50 call, which is something we said cannot be possible in the real markets. This is the perfect setup for an arbitrage opportunity since the more valuable call ($32.50) is cheaper than the less valuable one ($35).
In order to exploit this situation, arbitrageurs generally buy the underpriced option and simultaneously sell the higher-priced option. Although simply buying the underpriced option or selling the overpriced one individually will provide a theoretical edge, it is not enough to complete the arbitrage. In this example, the $32.50 call is a cheaper relative to the $35 call; however, just buying the $32.50 call does not guarantee a profit because that option could still lose if the stock’s price falls below $32.50 at expiration.
In order to capitalize on the mispricing, arbitrageurs would buy the $32.50 call and spend $4.90. Then they would immediately sell the $35 call and receive $5.00 for a net credit of 10 cents to their account:
Buy $32.50 call = - $4.90
Sell $35 call = +$5.00
Net credit = 10 cents
A net credit of 10 cents may not seem like a lot of money but arbitrageurs do things on a very big scale. They may send hundreds of thousands or even millions of dollars worth of trades to take advantage of such a discrepancy. The sale of the $35 call more than pays for the $32.50 call so the arbitrageur has zero money invested. In other words, the sale of the $35 call more than financed his purchase of the $32.50 call. In fact, he was even paid 10 cents to take this trade. Now think about the arbitrageur’s rights and obligations.
The arbitrageur now has the right to buy stock for $32.50 (since he bought the $32.50 call) and may have the obligation to sell for $35 (since he sold the $35 call), which means he could potentially make a $2.50 profit. But because he got paid 10 cents to execute the trade, his maximum gain is $2.60, which occurs if the stock price is greater than $35 at expiration. However, it’s also possible for the stock price to fall below $32.50 at expiration so that both options expire worthless. That’s okay too since the arbitrageur always keeps the 10-cent credit. (Remember, when you sell an option, the money you take in from the sale is yours to keep no matter what happens to the stock or option.) He might make as much as $2.60 but cannot earn less than the 10-cent credit. If the stock price closes somewhere between $32.50 and $35 at expiration then the arbitrageur’s profit will fall somewhere between 10 cents and $2.60.
The arbitrageur cannot lose and has therefore capitalized on a trade that resulted in a guaranteed profit for no out-of-pocket expense – and that’s the definition of arbitrage. We must include the phrase “for no out-of-pocket expense” otherwise the purchase of a government bond would qualify as arbitrage since it produces a guaranteed return. The difference between arbitrage and a bond purchase is that you must spend money on the bond and wait in order to get that guaranteed return. With arbitrage, you are paid to take the guaranteed trade.
Arbitrageurs will continue to execute the above trades – buy the $32.50 call and simultaneously sell the $35 call – as long as the opportunity is there. Unfortunately for the arbitrageur, their actions also guarantee that the opportunity will eventually disappear. As they buy the $32.50 calls they put upward pressure on its price. As they sell the $35 calls they put downward pressure on its price. Eventually the $32.50 calls will be more expensive than the $35 calls and that’s when the opportunity disappears. It is the arbitrageurs who guarantee that lower strike calls will always be more valuable than higher strike calls (and that higher strike puts will be more valuable than lower strike puts).
With all else being equal, LOWER strike calls and HIGHER strike puts must be more valuable.
Arbitrage is a high-stakes game involving computerized programs that search and execute the proper trades to exploit any mispricings. As a retail investor, you will never be able to participate in arbitrage. The speed at which arbitrage is carried out is too fast and complex for the tools and software that retail investors have to work with. In addition, the arbitrage opportunities that do arise are usually for pennies and retail investors pay too high of a commission to make arbitrage worthwhile. The big brokerage houses such as Merrill Lynch, Solomon Brothers, and JP Morgan are the ones doing the arbitraging. In fact, around 1995 there was an article in the Wall Street Journal about a Japanese firm engaged in triangular arbitrage. Triangular arbitrage is a currency arbitrage that is executed by purchasing one currency, converting it to another, and then immediately converting it back to the original currency. The speed at which these transactions is lightning fast and the article went on to say that this firm paid $23 million dollars to gain one second quicker access time to currency quotes. That’s how big the stakes are and how fast the game is played. (So don’t get any ideas of logging into your brokerage account and participating in arbitrage.)
There are many who feel that arbitrage is “unfair” because there’s something that doesn’t seem right about being able to make free money from the market. But the arbitrageurs provide an important economic function in that they make sure the relative prices stay fair for the rest of us. You don’t need to understand the process of arbitrage to trade options. However, you do need to understand that lower strike calls and higher strike puts will always be more expensive. That’s a big key to understanding many strategies.
Exercise
Go to www.cboe.com and check out option quotes on several stocks. Are lower strike calls always more expensive than higher strikes? Are higher strike puts always more expensive than lower strikes? What about for different expiration months? Explain in your own words why this happens.
Principle #2:
More Time Means More Money
Another principle of option trading is that longer-term options will be more expensive than shorter term ones. As before, this assumes that all other factors remain constant; we must be talking about the same underlying stock and strike price.
Take a look at Table 2-3, which shows the July and August call options from Table 1-1. Notice that the July calls are more expensive that the August calls. Why are the August calls more expensive? (Hint: For any strike, think about which is more desirable.)
Table 2-3
|
Call Options
|
||
|
Strike
|
July
|
August
|
|
$32.50
|
$4.90
|
$5.50
|
|
$35
|
$2.70
|
$3.60
|
|
$37.50
|
$1.05
|
$2.10
|
|
$40
|
$0.35
|
$1.10
|
You guessed it. The markets realize there is an advantage in having time on your side since the price of the option has a better chance of increasing in value. Think about stock prices. If you buy a stock today for $50, is there a better chance for price appreciation after one day or after one month? Obviously, you have a better chance for the stock to increase in value over a one-month period. That’s all this principle is saying. The market realizes that there is a better chance for the August $32.50 call to rise in value when compared to the July $32.50 call and so will place a higher value on it.
Since all other factors between the two calls are the same, the only difference between the July call for $4.90 and August call for $5.50 is the value of the additional time. Why 60 cents extra value? That’s a question for which we will never know the answer. That is up to the market to decide; it’s up to people like you and me. Every day we place orders to buy and sell options, we’re either putting upward or downward pressure on their prices. At the time these quotes were taken, the market was placing 60 cents extra value on the August $32.50 call over the July $32.50 call. We can be sure that longer-term options will always cost more than shorter-term options but we cannot be sure by how much. All we can be sure of is that with all else constant (same underlying stock and strike price), longer-term options will cost you more money.
To be continued….
Jul
27
How to Calculate Good and Bad Gamma When Trading Stock Options
Filed Under Advanced Options Trading | Leave a Comment
One of the barriers that keep many stock traders from becoming successful option traders is understanding the importance of the Greeks. These are important variables spun out as part of the calculations of the Option Pricing Model. One of them causes particular confusion because it is a second derivative of its important litter mate-Delta. Gamma, the second derivative of Delta, discloses what will happen to Delta if the underlying stock moves $1. For instance, if the Gamma of a certain strike price is 10 and Delta is 55, that means if the underlying stock moves up $1, the option’s Delta will move 10 points to 65. But this rather simple relationship becomes more complicated as one delves deeper into Gamma. For example, there is an anecdotal classification of Gamma into bad Gamma and good Gamma.
Long calls and long puts both always have positive gamma. Short calls and short puts both always have negative Gamma. When we talk of short Gamma (negative gamma), that appears to be the reason some call it “bad Gamma”. Some important characteristics of short Gamma are:
With a short Gamma position, as the stock trades down, we need to get longer. That means we’ve got to sell, which is equivalent to selling low.
Conversely, if the stock goes up when we are short Gamma, we’re getting shorter forcing us to buy more stock to stay flat. This means we are buying high.
The above sell-low and buy-high situation is the formula for losing money and has prompted the naming of short Gamma as Bad Gamma.
On the other hand, long Gamma is “good Gamma” because you get to buy low and sell high. This can be confusing so to reiterate, when hedging and with long Delta, if the underlying price goes up, we’re going to get longer Delta to stay Delta neutral. If the price goes down, we’re going to get shorter Delta. On the other hand, when short Delta, as the stock trades up we’re going to acquire shorter Delta. As the stock trades down, we’re going to get longer Delta (close out positions). Because of the buy-high sell-low conundrum, most traders stay away from taking up a short Gamma positions. But hold on. If only it were that simple. You see, another Greek, Theta also plays an important part as we get closer to expiration, the time decay of Theta also comes into play by affecting Gamma.
When using stock options to hedge a long stock position, it is important to understand how you’re total position is going to change as the stock moves. Gamma is going to tell you that ahead of time from the standpoint of what Delta will become when the underlying stock moves up or down.
But that’s not all that Gamma is good for. As a matter of fact, trading Gamma is a specialized trading strategy for making short term swing trades. But that‘s a subject for another day.
To find out about the extensive list of online courses, webinars and workshops, contact Options University at www.optionsuniversity.com
Jul
27
Chapter Two
Option Pricing Principles
We’ve just been introduced to real call and put options and now understand how to interpret their prices when looking at quotes. But did you notice in Table 1-1 that some options are more expensive than others? Why is that? And is there a pattern we should understand? This chapter takes you through some of the most important pricing principles of options. Understanding these principles is essential for mastering option strategies.
Principle #1:
Lower Strike Calls (and Higher Strike Puts) Must Be More Expensive
If you look at the prices in Table 1-1, you’ll notice that the lower strike calls are more expensive than the higher strikes. This will always be true assuming, of course, that all other factors are the same. That is, we must be looking at strikes on the same underlying stock and expiration month. For example, Table 2-1 shows the call prices for July from Table 1-1. Why do the prices get cheaper as we move to higher strikes?
Table 2-1
|
July Call Options
|
|
|
Strike
|
Price
|
|
$32.50
|
$4.90
|
|
$35
|
$2.70
|
|
$37.50
|
$1.05
|
|
$40
|
$0.35
|
There are many mathematical reasons why this relationship must hold and we’ll look at one shortly. However, you already know enough to figure it out intuitively by thinking back to the pizza coupon analogy. Imagine that you walked in to buy a pizza and found the following two coupons lying on the counter:
insert pizza1 insert pizza2
Notice that both coupons control exactly the same thing (one large three-topping pizza) and have the same expiration date. The only difference is that the coupon on the left allows you to buy the pizza for $10.00 while the one on the right gives you the right to buy it for $20.00. If both pizza coupons allow you to do exactly the same thing but one just allows you to do it for a cheaper price, then obviously you would choose to pay the cheaper price. You should pick up the coupon that gives you the right to buy the pizza for $10.00.
The same thought process occurs in the options markets. For example, both the $32.50 call and the $35 call in Table 2-1 allow the trader to buy 100 shares of eBay, so there are absolutely no differences in what those two coupons allow you to buy. However, the $32.50 allows you to buy the 100 shares for less money. Traders realize the benefit in paying $32.50 rather than $35, so they will compete in the market for that coupon. It is a more desirable coupon, so traders and investors will bid its price higher than the $35 coupon. The same process happens all the way up the line. Each successively lower strike is bid to a higher price. Or conversely, each higher strike is bid lower than the strike below it. When you get into strategies, there will be times when you need to figure out which call option is more valuable. You can always find the answer by asking yourself which is more desirable. The answer to that question is the one that has the lower strike price. As our first Pricing Principle states: Lower strike calls must be more valuable.
This same reasoning drives many decisions in the financial markets. If it is more desirable then it must cost more with all other factors constant. Consider government bonds. Why are government bond yields lower when compared to the same face amount and maturity as a corporate bond? The reason is that government bonds are guaranteed; corporate bonds are not. So if a government bond and corporate bond both mature to $10,000 at the same time, which would you rather have? Again, there is no difference in what either of these bonds promise. Both promise $10,000 to be delivered to you at the same time. However, there is a big difference in the ability to carry out that promise. The government bond is far more secure so it is more desirable to investors. Investors will therefore pay a higher price for the government bond. And when bond prices rise, yields fall. That’s why government bonds will always have a lower yield than corporate bonds of the same face value and maturity.
When first attempting to understand option prices, you must remember that “more desirable” equates to more money with all other factors the same. If you do, you’ll understand many aspects of strategies that many traders must memorize
Now let’s take a look at why higher strike puts are more expensive. Table 2-2 is a listing of the July put options from Table 1-1:
Table 2-2
|
July Put Options
|
|
|
Strike
|
Price
|
|
$32.50
|
$0.20
|
|
$35
|
$0.50
|
|
$37.50
|
$1.40
|
|
$40
|
$3.20
|
With the put options, the reverse appears to be true and the higher strike puts are more expensive. Why does this pattern occur? The reasoning is similar as it is for calls but you must remember that put options allow you to sell stock. If all prices were the same, which put option would you rather have? In other words, which strike price is more desirable? Obviously, it is more desirable to sell your shares for $40 than for $37.50, so traders will bid the prices of the $40 puts higher than that of the $37.50 puts and the $37.50 puts will be bid higher than the $35 puts and so on down the line. Higher strike puts will always be more expensive than lower strike puts with all other factors the same (same underlying stock and expiration).
To better understand the relationship between put strikes and price, think about insurance. If you have a $30,000 car and want to insure it for the full value, you will pay a certain premium. However, if you accept a $500 deductible and only want insurance for the remaining value, you will pay a lower premium. If you accept a $1,000 deductible, you will pay even less. In exchange for assuming some of the risk, you will pay a lower premium. In other words, the higher the value of your car insurance, the higher the premium you will pay.
This same relationship holds for put options. In Table 2-2, if a trader owns 100 shares of eBay and buys the July $37.50 put, he is attempting to insure the stock for more than its current value of $37.11. For that coverage he will pay $1.40 premium. However, if he chooses to assume some of the risk, he can pay a lower premium. How can he assume some risk? He can choose lower coverage by selecting a lower strike price. For instance, if he chooses the July $35 put, he will pay on 50 cents for the coverage. But in exchange for that lower premium, he is assuming the first $2.11 in damage since the protection on his stock does not start until a stock price of $35.
As we’ve written before, put options can be thought of as a form of insurance. If you want high coverage (high strike prices) you will pay a larger premium for that. If you choose to accept some risk (lower strike prices) you will pay a lower premium. In other words, high strike puts cost more than low strike puts.
There’s another way to understand why lower strike calls and higher strike puts must be more valuable. We can do so by looking at different strikes from a probability standpoint. Let’s assume that a stock can only move between $0 and $100 with all prices equally likely at expiration. If you own a $50 call, then there is a 50% chance that you will have intrinsic value at expiration. In other words, the $50 call acts as an asset to “catch” all stock prices to the right of the strike. Obviously, the more prices it can catch, the greater the value of the call. What can we do if we want to catch more strikes? We can shift to a lower strike price such as the $25 strike as shown in the following diagram:
insert diagram14-1
If we lower the strike from $50 to $25, you can see that we have far more area to the right for the stock price to land at expiration as shown by the white arrows. This shows that the $25 call must be more valuable than the $50 call because it allows the trader to potentially catch more intrinsic value. The reverse reasoning shows that higher strike puts must be more valuable since they catch more stock prices to the left of the strike price.
Stick with whichever method helps you to understand or visualize why lower strike calls and higher strike puts must be more valuable.
To be continued…
Jul
26
Ron Ianieri, one of the founders of Options University used to be a floor trader and market maker and he has mentioned that as the “insiders” on the trading floor were replaced by computer trading, something the traders used to do is starting to become more popular with the retail traders…. something called Gamma trading.
The subject is a bit complex and has spawned a special 8 hour course on Gamma Trading presented by Options University. But to give you some taste of how Gamma is used, we will try to give you an idea of how it works.
Gamma trading is a way of setting up using options, a Gamma position and then flipping the stock back and forth when the Gamma makes you long Delta or when the Gamma makes you short Delta. The beauty of this is it’s great for day traders because day traders could now flip the stock back and forth in a hedged fashion. Remember that Gamma is a key in forecasting Delta and its effect on option pricing.
Another cool thing about Gamma trading is the resolution of one of the toughest things about being a day trader- getting off on the right foot, to make that first correct trade. If an option trader is unsure or doesn’t have a good feel about the first trade, they can step aside and let Gamma make the first trade. Remember as soon as the stock moves the Gamma position is either going to buy you or sell you Deltas to keep you properly hedged. The beauty of it is Gamma is never wrong so your first trade will always be a winner if you let Gamma make the first trade.
If you’ve done day trading, you normally never hold a position overnight. Too much can happen. However, because you have Gamma you can also be properly hedged. As a result, a day trader can carry overnight positions that are hedged. Ron Ianieri, designer of Opt