5. (Computing Option Sensitivities I)

The goal of this exercise is twofold: based on the discussions in Section 12.5 we create a more user-friendly wrapper to compute option delta and gamma. We write code to compute the sensitivities in equation (12.11).

Answer the following questions:

a) Redesign the code in Section 12.5 to compute delta and gamma. We hide many of the details and write the new code as a black box. We start with the end in mind so that the desired output becomes a tuple whose elements are option price, delta and gamma.

The input is a struct containing option data, the kind of payoff and the number of steps NT in the binomial method.

b) Compare the accuracy of the output by comparing it with the exact Black–Scholes values for price, delta and gamma.

c) Determine how to make your code as reusable as possible, for example creating a repository of payoff functions and placing the new code in Level 3 of the Layers patterns.