Suppose that the stock price follows a jump diffusion process as outlined in Section 20 7 Let the jump intensity be 0 75, the expected jump exp(J), with J 0 15, and let the jump volatility be J 0 25 You can simulate the behavior of the martingale St Pt as xt h 1 kh hZt h J(Y 1) xt where k exp(J) 1,...

abc You need to follow the simulation strategies of Chapter 19 Monte Car ...

Suppose that the stock price follows a jump-diffusion process as outlined in Section 20.7. Let the jump

Question:

Suppose that the stock price follows a jump-diffusion process as outlined in Section 20.7. Let the jump intensity be λ = 0.75, the expected jump exp(αJ), with αJ = −0.15, and let the jump volatility be σJ = 0.25. You can simulate the behavior of the martingale St/Pt as
xt+h = [1− λkh + σ √ hZt+h + J(Y − 1)] xt
where k = exp(αJ) − 1, J = 1 indicates a jump and J = 0 otherwise, and Y = eαJ−0.5σ2J +σJWt, with Wt standard normal. Let h be approximately 1 day.
a. Evaluate P0EST /PT (T, T) > K.
b. Compute the mean and standard deviation of the difference xT − x0. Verify that you have simulated a martingale.
c. Verify that the result is approximately the same as the price of a cash-or nothing call ($0.5865 for the above parameters).