8. (10 points) Recall the Black-Scholes PDE and Euro call payoff C(S, T) = =0, S<1. if 0 C(S, t) satisfies a) By differentiating with respect to S, show that u b) The v above is a Greek. Which...
4. (10 marks) (Black-Scholes) Fill in the details of L9.24. Specifically, a. (3 marks) Assume that C(S, t) satisfies the first PDE of L9.24 (Black-Scholes). Show that U(z,T) satisfies the second PDE of L9.24 (the heat/diffusion equation b. (5 marks) Using L9.23, solve for U Write your final answer using the standard normal CDF N Hint: Replace the lower limit of integration (the -o) with a correctly chosen quantity that lets you get rid of the "positive-part function" in the...
Problem 5.4 (10 points) Let (Sn)n-01. be a simple, symmetric random walk with starting value So-s e R. (a) Show that ES for alln0 b) Show that ElSn+1 Sn] Sn for 0. (c)Suppose that (Sn)n-0,12,. . denotes the profit and loss from $1 bets of a gambler with initial capital So-s who is repeatedly playing a fair game with 50% chances to win or lose her stake. What are the interpretations of the results in (a) and (b)?
Problem 5.4...
Suppose a plane passes through the points O(0,0,0). B(1,2,2) and C(-1,-1,2) and u -OB and v-OC. (See figure below.) The vector equation of the plane is:x-sutv Choose... s=0, t=0 s-1, t-1 (5,8,2) s--3, t--1.5 (2,5,8) s 3, t-1 s-3, t--2 What values of s and t correspond to point O? What values of s and t correspond to point D? What values of s and t correspond to point B? what values of s and t correspond to point C?...