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Advanced Options Trading - Time Spread Volatility

Filed Under Advanced Options Trading 

Time Spread Volatility
Often, when people do spreads, they want to know what the volatility of the spread is. They want to know what the implied volatility of each option in the spread is. Traders will say something like “I sold 34 volatility, I bought 32 volatility, so it’s like I have a combined volatility of 33. That statement is incorrect.
 
At the Options University, they point out that you can’t just take the two options and average them. When you average something you normally are making a simple assumption that both values are weighted equally. But in the case of spreads, it’s a bit different. When you’re doing a spread and trying to figure out the volatility of the spread, you need to understand that implied volatility in the front month and implied volatility of the out month are not weighted equally. Why? Because of Vega- the amount that the price of an option changes compared to a 1% change in volatility- is what weights volatility sensitivity and we know that the front month is not going to have the same Vega as this out month.
 
Before we can determine the actual volatility of the spread, we must first equalize the volatility of both options. Perhaps the best way to explain it is do an actual example. Suppose I bought the 34 volatility for $3 and I sold the 32 for $2. The option that’s at 34 volatility is trading at a volatility level that’s two ticks higher than the 32 volatility option and we know this option’s Vega is 8 cents. We know that the 32 volatility option is trading for $2, we know that we can bring this option up to the 34 volatility option’s level very easily. At 32 volatility it’s worth $2 and we know that Vega is 8 cents. So, if we move up from 32 volatility to 34 volatility we would move up 2 ticks times 8 cents. At volatility 34, the Vega would have the value at $3.16.
 
Now that we have brought the theoretical value of this option up to a volatility level that matches both options, we can figure out that at 34 volatility this spread should be worth $3.16 minus $2, or $1.16. This spread is worth $1.16 at 34 volatility.
 
The underlying idea is that we take 32 volatility up to 34 volatility. If you aren’t confused yet, try this one on: We found out that the spread is worth $1.16, but now we traded it at $1.20. How do we figure out what volatility we traded the option at? Now that we’ve got it equalized we can use the spread’s Vega to compute the difference between the two values. We did a spread at $1.16 and as we said it’s a 34 volatility and now we need to figure out what $1.20 volatility is. Both have their own Vega and we are long one and short the other. If I know that the Vega difference between the two options is 3 cents, this gives us a spread Vega of 3 cents. If I take volatility up one tick to 35 volatility it’s going to take this value up 3 cents making it $1.19 which is right around $1.20. The implied volatility of this spread is 35.
 
Whenever you’re doing two options with different strikes, different Vega values you can’t just sit there and average them out. Where this becomes important, especially is when a trader is trying to hedge their volatility exposure. But that story is for another time.
 
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