Answer these questions. Please show your work step by step. Make sure your answers are correct.
Currently a share of Globex Industries trades for $50 per share. In one year, Globex's share price will be $60 with probability 0.55 or $40 with probability 0.45. A riskless bond also exists with a current price of $95. In one year, this bond pays $100 for certain. You can both lend and borrow using this bond. If you borrow one riskless bond, you will receive $95 today in exchange for the promise to repay $100 in one year. The stock and the bond have no other cash flows over the year.
In the problems that follow, you are asked to price by no arbitrage three common derivative securities. Approach these problems exactly like the bond examples we did in class. Start by finding a trading strategy in the stock and the bond that exactly matches the payoff of the derivative under all future contingencies (the stock price either rises or fall over the next year). By no arbitrage, the current value of this strategy is the value of the derivative security.
1. Pricing a European Call Option.
Consider a European call option on Globex Industries. This security gives the holder the right to buy a share of Globex in one year (the expiration date) for a pre-specified price X called the strike price.
Since the holder is given the right (not the obligation), they will only exercise the option (pay X in exchange for a share of stock in one year) when it is profitable for them. This implies the cash flow of a European call option in one year is max(S1 - X, 0) where S1 is the price of Globex in one year.
Consider a European call option which expires in one year and has a strike price of X = 48. What trading strategy in the stock and the bond today will exactly match the payoff of this call option in one year? By no arbitrage, what is the price today of this option?
2. Pricing a European Put Option.
Consider a European put option on Globex Industries. This security gives the holder the right to sell a share of Globex in one year (the expiration date) for a pre-specified price X called the strike price.
Since the holder is given the right (not the obligation), they will only exercise the option (receive X in exchange for selling a share of stock in one year) when it is profitable for them. This implies the cash flow of a European put option in one year is max(X - S1, 0) where S1 is the price of Globex in one year.
Consider a European put option which expires in one year and has a strike price of X = 48. What trading strategy in the stock and the bond today will exactly match the payoff of this put option in one year? By no arbitrage, what is the price today of this option?