Question

The common stock of the Pat plc. corporation has been trading in a narrow range around £145 per share for months, and you believe it is going to stay in that range for the next 12 months. The price of a 12-month European put option with an exercise price of £145 is £8.19. i) If the risk-free interest rate is 9% per year, what must be the price of a 12-month call option on Pat plc. stock at an exercise price of £145 if it is at the money? (The stock pays no dividends). ii) What would be a straddle strategy using a European put and a European call to exploit your conviction about the stock price’s future movement? What is the most money you can make on this position? How far can the stock price move in either direction before you lose money?

Answer 1

Case 1: Risk free rate is compounded annually
1.
Using put call parity, Price of call=S+P-X/(1+r)^t=145+8.19-145/1.09^1=20.16247706

2.
Short Straddle, Sell 1 Call and Sell 1 Put
Maximum money=C+P=20.16247706+8.19=28.35247706

Stock moves in either direction=28.35247706

Case 2: Risk free rate is compounded continuously
1.
Using put call parity, Price of call=S+P-X*e^(-rt)=145+8.19-145*e^(-0.09*1)=20.66997814

2.
Short Straddle, Sell 1 Call and Sell 1 Put
Maximum money=C+P=20.66997814+8.19=28.85997814

Stock moves in either direction=28.85997814