# Question: Let r 0 08 S 100 0

Let r = 0.08, S = $100, δ = 0, and σ = 0.30. Using the risk-neutral distribution, simulate 1/S1. What is E(1/S1)? What is the forward price for a contract paying 1/S1?

## Relevant Questions

Suppose S0 = 100, r = 0.06, σS = 0.4 and δ = 0. Use Monte Carlo to compute prices for claims that pay the following: a. S21 b.√S1 c. S1-2 The formula for an infinitely lived call is given in equation (12.18). Suppose that S follows equation (20.20), with α replaced by r, and that E* (dV ) = rV dt. Use Itˆo’s Lemma to verify that the value of the call, V ...Use Itˆo’s Lemma to evaluate d(√S). For the following four problems, use Itˆo’s Lemma to determine the process followed by the specified equation, assuming that S(t) follows (a) Arithmetic Brownian motion, equation ...What is the value of a claim paying Q(T )2S(T )? Check your answer using Proposition 20.4. Use the answers to the previous two problems to verify that the Black-Scholes formula, equation (12.1), satisfies the Black-Scholes equation. Verify that the boundary condition V [S(T), T ]= max[0, S(T ) − K] is satisfied.Post your question