Question

1. (Put-call parity) A stock currently costs So per share. In each time period, the value of the stock will either increase or decrease by u and d respectively, and the risk-free interest rate is r. Let Sn be the price of the stock at t-n, for O < n < N, and consider three derivatives which expire at t - V, a cal option Voll-(SN-K)+, a put option VNut-(X-Sy)+, and a forward option VN(SN contract FN SN N) , and a forwar -K The forward price is the strike and K-(1 + r)So, then Fo 0. price such that the price of the forward contract is Fo = 0, Show that if N = 1 (one-period binomial model), a) (b) Show that if N 1 (one-period binomial model), and K = (1 +r)So, en (c) Explain why in the general N-period model, for any strike price K, FN+Vvut. That is, if you buy at t 0 a forward contract and a put option, and hold them until expiration, the payoff you receive is the same as the payoff of a call o prices of these three options at t 0? ption. What can you

Answer 1

A stock currently costs s_0 pet share. In each time period, the value of the stock will either increase of decrease by u and d respectively and the risk-free interest rate is t Abs - given that a) if N = 1, F_1 = s_1 - k where k = (1 + r) so If we sell the Asset for so to buy back again affect time N = 1 or l = (1 + r) so under the forward contract and lend the money so received from selling at rate of interest r then affect time N = 1 we receive so (1 + r) and use this money to buy the Asset back at (1 + r) so under the forward contract so that the net cash flow at time t = N = 1 is so (1 + r) received from lending at r - (1 + r) so from buying the asset under the forward contract = 0