The stock price is currently at $50 per share. A European call option with 1 year to maturity and a strike price $60 is trading on this stock. Risk-free asset pays 5% interest rate per year. In one year, it is estimated that the stock price will either go up to $80 per share or go down to $31.25 per share.
1. Find the terminal payoffs of the call option in the “up” state and in the “down” state; that is, find cu and cd.
2. Find u, d, and R to plug into the binomial tree formula.
3. Use the binomial tree formula to find the risk-neutral probabilities and the call option premium today c.
4. Find the option delta
5. If you have written 100 call option contracts, what risk are you facing?
6. To hedge the risk, should you buy or short the stock? How many shares?
7. If you buy stock, how much do you borrow? If you sell, how much of the proceeds should you invest?