Mark,
When there is no put/call skew (all options trading at same volatility like on your sheets) you will find that you can choose any options you want to use. They will all be effectively equal in terms of equivalent stock price. Remember, the synthetic stock position formula has you buying one option, selling the corresponding. If the volatility is equal, then extrinsic value is equal and thus the two options extrinsic value, one positive, one negative, cancel each other out. All that is now left is the intrinsic value of the one option that is ITM.
So, that being said, when the volatility is the same, you can create synthetic stock at any strike and it will be effectively equal. For example, buying long synthetic stock in the 50 strike for a stock trading at $58 will cost $8. Buying long synthetic stock at the 45 strike will cost you $18. Buying long synthetic stock at the 55 strike will cost you $3. Meanwhile, buying long synthetic stock at the 60 strike will give you a $2 credit and if you chose the 65 strike, you would also receive a credit...this time a $7 credit.
So, advantage is created when there are proper skews in place. You have an advantage in buying stock when there are negative skews. Why? Because you buy call and sell put to create synthetic long stock. If the call is priced effectively lower than the put in terms of volatility, then the put will carry a higher, not equal, amount of extrinsic value over the call which will create a small extrinsic value credit to you which will lower your effective stock purchase price possibly to a point where you are buying synthetic stock lower than where the actual stock is trading. This only happens when you are buying synthetic stock in a negative put/call skew scenario.
The opposite is true also in the case of selling synthetic stock in a positive put/call skew scenario. Here, you gain advantage because the call you are selling has a higher level of extrinsic value due to its higher volatility level. In the same way as above, the additional extrinsic value you are selling creates an additional credit which allows you to synthetically sell the stock at a effective price that is higher than the actual current stock price.
So, the general rule of thumb will be that when buying synthetic stock, only do so in a negative put/call skew scenario and look for the strike with the biggest dollar differential as created by vega.....it will provide the biggest extrinsic value credit. When selling synthetic stock, only do so in a positive put call skew scenario and again, look for the strike with the biggest dollar differential as created by vega.....it will provide the biggest extrinsic value credit allowing you to sell synthetic stock at an effectively higher price than the actual stock is trading.
Hope this helps!
