Question

2. Consider a stock that pays no dividend trading at $100. Suppose one-year call options with strike prices of $95, $100, $105, and $110 can be bought for a premiums of $16.41, $12, $9, and $7.24 respectively. Suppose the annual effective interest rate is 5% (i.e., a $100 bond pays $105 one year from now).

a) What are the values of one-year puts with strike prices corresponding to those listed for the call options above?

b) Suppose you wished to enter into a short one-year forward position on the stock. What is the fair forward price?

c) Suppose a dealer offers to take the other side of your forward at a price of $106 (i.e., she agrees to buy the stock from you for $106 in one year). Is this a fair priced offer according to arbitrage pricing theory (assume that you can borrow and lend at an annual effective interest rate of 5%; and that you can buy and short the stock without transaction costs)? If not, what payment now (either from you to the dealer, or from the dealer to you) would make it fair? Specify in your answer the amount and who makes the payment and who receives it.

d) Suppose that you cannot find a counterparty for your desired short forward position. Using only the calls and puts described above, how would you synthesize a short (on market) forward position?

e) Suppose you had a long position in the stock and wished to hedge in such a way that your payoff would never be below $100. How could you accomplish this using the options (both the calls, and the puts) described above without incurring any net out of pocket cost? Assume there are no transactions costs.

Answer 1

a). By using call put parity equation:-

C + PV(x) = P + S

Where

C = price of the call option

PV(x) = the present value of the strike price (x), discounted from the value on the expiration date at the risk-free rate

P = price of the Put

S = spot price or the current market value of the underlying asset

b).

C). synthetic forward contract uses call and put options with the same strike price and time to expiry to create an offsetting forward position. An investor can buy/sell a call option and sell/buy a put option with the same strike price and expiration date with the intent being to mimic a regular forward contract.

D). To create this strategy we need to buy protected put and sell a covered call.

I.e. we will but a put @$100 strike price which will have cash outflow of $7 and sell call @$110 strike price which will have cash inflow of $7.