By Jake Bernstein
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Extra info for Dearborn Market Masters-How Successful Traders Think, Trade and Invest Jake Bernstein
This will allow us to focus our attention on what happens at option expiration. 1 below) should help illustrate the concept of asymmetry. If we purchased a one-year call option on IBM with a strike price of $100, we would only choose to exercise the call option if the price of IBM was above the $100 strike price (in the money) on the expiration date. If the price of IBM was $110 on the expiration date, the payoff would be $10. The payoff is also called the intrinsic value and represents the value of exercising an in-the-money option at expiration.
Gamma reflects the curvature of the option price function. More specifically, Gamma equals the change in Delta for an instantaneous $1 increase in the price of the underlying security, holding all of the other variables constant. While that is the definition of Gamma, it is not very intuitive, which is why I refer to the curvature or convexity of the option price function instead. All long option positions have positive Gamma, which means they benefit from realized changes in the price of the underlying security.
Finally, I will include numerical examples, for those of you who would like to verify that you are applying the formula correctly. For this example, we will assume that the annualized earnings volatility equals 180% and the annualized normal volatility equals 30%. Why the huge disparity between earnings volatility and normal volatility? As I explained earlier, the BSOPM assumes that price changes are continuous, which implies that the distribution of information that affects stock prices is also released continuously.