Simulate the tree in Problem 5. (Start with S = S₀ and randomly choose “up” with probability p or “down” with probability 1 − p, do this twice. Note the ending price S_T and note the payoff (S_T − K)⁺.) Answer the following by Monte Carlo. Letting C^' denote the actual price of the call, what is the expected gain to the option holder if C^' = C? If C^' = 3C/2? If C^' = C but p = 0.6?

Data in Problem 5

Let S₀ = 20, σ = 0.3, r = 0.06 and Δt = 1 week. Construct a 2-week binomial tree (2 steps), use the p = 1/2 method, and calculate the no-arbitrage call price C for K = 21. If the market price C_M were 3/2 times C, explain in detail how that could be exploited to make a risk-free profit.