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Could you please explain to me what delta and gamma mean in relation to the BSOP model in P4. In my study text, the following was written but I didn’t understand what it means:
(a) Delta – measures the rate of change of option value with
respect to changes in the underlying asset’s price.b) Gamma – measures the rate of change in the delta with
respect to changes in the underlying price. Gamma is the
second derivative of the value function with respect to the
underlying price.The Greeks are explained in both our free Lecture Notes and the lectures that go with the notes!
The point is that although we can calculate an option price at one point in time, using the Black Scholes formula, if we were to calculate the price again a week later then all of the variables in the equation stand to have changed. For example, the share price is likely to have changed, the time to expiry will certainly have changed (it will be one week less), and so on for all of them.
Dealers therefore need to change their position with regard to options if they want to maintain a delta hedge. They use measures such as delta and gamma (along with theta, vega etc.) to help them – they measure to what extent the option price will change as the variables (such as the share price) change.
You cannot be asked to calculate any of the Greeks (except for delta, which is N(d1)) – you can only be asked what they measure.
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