Since we can only delta hedge at finite intervals due to transaction cost constraints, return distribution of an option trade is still relatively volatile. Expected return volatility can be expressed in quantitatively.
Getting a feel for return volatility
Here is an example 100 realized returns from a short option position, -$1,000vega, with the ending realized vol = implied so the EV~ 0, delta hedged once a week. (Volatility Trading, Sinclair)
We can see that even if the trader is correct with future realized vol, luck still plays a large factor without a large number of trades (Law of Large Numbers).
Quantitative estimate of return volatility
Derman and Kamal gave the answer in "When you can not hedge continuously..."
where
K = vega
N = number of delta hedges
Getting a feel for return volatility
Here is an example 100 realized returns from a short option position, -$1,000vega, with the ending realized vol = implied so the EV~ 0, delta hedged once a week. (Volatility Trading, Sinclair)
We can see that even if the trader is correct with future realized vol, luck still plays a large factor without a large number of trades (Law of Large Numbers).
Quantitative estimate of return volatility
Derman and Kamal gave the answer in "When you can not hedge continuously..."
K = vega
N = number of delta hedges
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