# Question: Assume S0 50 r 0 05 0 50

Assume S0 = $50, r = 0.05, σ = 0.50, and δ = 0. The Black-Scholes price for a 2-year at-the-money put is $10.906. Suppose that the stock price is lognormal but can also jump, with the number of jumps Poisson-distributed. Assume α = 0.05 (the expected return to the stock is equal to the risk-free rate), σ = 0.50, λ = 2, αJ =−0.04, σJ = 0.08.

a. Using 2000 simulations incorporating jumps, simulate the 2-year price and draw a histogram of continuously compounded returns.

b. Using Monte Carlo incorporating jumps, value a 2-year at-the-money put. Is this value significantly different from the Black-Scholes value?

a. Using 2000 simulations incorporating jumps, simulate the 2-year price and draw a histogram of continuously compounded returns.

b. Using Monte Carlo incorporating jumps, value a 2-year at-the-money put. Is this value significantly different from the Black-Scholes value?

**View Solution:**## Answer to relevant Questions

Let ui ∼ U (0, 1). Compute _12 i=1 ui − 6, 1000 times. (This will use 12,000 random numbers.) Construct a histogram and compare it to a theoretical standard normal density. What are the mean and standard deviation? (This ...Suppose that ln(S) and ln(Q) have correlation ρ =−0.3 and that S0 = $100, Q0 =$100, r = 0.06, σS = 0.4, and σQ = 0.2. Neither stock pays dividends. Use Monte Carlo to find the price today of claims that pay the ...Suppose that S and Q follow equations (20.36) and (20.37). Derive the value of a claim paying S(T )aQ(T )b by each of the following methods: a. Compute the expected value of the claim and discounting at an appropriate rate. ...Suppose that ln(S) and ln(Q) have correlation ρ =−0.3 and that S(0) = $100, Q(0) = $100, r = 0.06, σS = 0.4, and σQ = 0.2. Neither stock pays dividends. Use equation (20.38) to find the price today of claims that pay a. ...Use the Black-Scholes equation to verify the solution in Chapter 20, given by Proposition 20.3, for the value of a claim paying Sa.Post your question