Gamma of a far out-of-the-money call
Question
Approximately what gamma does a call option have when it is very far out of the money?
Short answer
Essentially . The option is almost certain to expire worthless, so its delta is pinned near and barely moves when the stock moves; gamma, the sensitivity of delta, is therefore close to zero.
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Open the worked solutionLessons behind this question
- Greeks and Numerical Sensitivities
- Derivation — From Binomial Trees to Black-Scholes in the Continuous Limit
- The Black-Scholes Formula Derived via Change of Measure
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