Answer Happy

-10) SV21 1. The probability density function p.(S,t;S', t') for a risk neutral random walk is given by 1 (log(S'/S) - ( ro)(t' – t)) P(S, t; S', 1) = exp OS", 2(t' - t) 202('-t) In the binomial method, the value of the underlying is at time step mot and the value of the underlying at time step (m +1)&t is Sm+I. Assuming that the underlying asset follows a risk neutral continuous random walk evaluate E[(Sm+2)415"] = *(S")*pe(S", mốt; s', (m + 1)8t)dS showing all steps. You may assume that dr = 1 for all s > 0 2. Consider a put on a put compound option, where P has a expiry date T1 = 1 and exercise price Ej = 20 and P, has an expiry date T2 = 3 and exercise price E = 90 (a) What is the pay-off function of this compound option at its expiry date? (b) Assume that the current (at t = 0) price of the underlying is S(0) = 100. Apply the binomial method to determine the value of P at time t = 0. Use a time step of dt = 1. The interest rate is r = 0.05. Consider the case of p=1/2 with a = 0.25. 3. Consider the value V(C.P. t) of a chooser option where C = C(S. t) and P = P(S,t) depend on the same underlying asset S. The chooser option has an expiry date of t = T, with an exercise price E1. Both the call C and the put P have the same expiry date of t = T, and the same exercise price E2. Determine the value of the chooser option V(C, P,t) in the special case where T = T2. You may assume Es > E.