Consider a one-year futures contract for 1 share of a dividend paying stock. The current stock price is $50 and the risk-free interest rate is 10% p.a. It is also known that the stock will pay a $3 dividend at the end of year 1. The current settlement price for the futures contract is $51. Set up a strategy for an arbitrage profit. What are the initial and terminal cash flows from the strategy? Assume that investors can short-sell or buy the stock on margin and that they can borrow and lend at the risk-free rate. There are no margin requirements, transactions costs, or taxes.
Consider a stock that pays no dividends on which a futures contract, a call option and a put option trade. The maturity date for all three contracts is T, the exercise price of the put and the call are both X, and the futures price is F. Show that if X = F, then the call price equals the put price assuming that spot-futures parity and put-call parity conditions hold. Assume that interest is continuously compounded (i.e., use the spot-futures parity with continuously compounded interest).