The common stock of Sternco is currently trading at $40 per share. Sternco is currently “in play” as a take-over target and is not expected to pay any dividends for the next 6 months. You believe that if management is successful at repelling all offers, the stock price will fall significantly, but if they are unsuccessful, the stock price will rise significantly. You want to profit from either outcome. The risk-free rate is 10% and a 6-month put option with an exercise price of $40 is selling at $4.
A dealer offers you a 6-month European call option with an exercise price of $40. What is a fair price for this option?
We can use put call parity to calculate the put.
S(0)=C 40,0.5(0)-P40,0.5(0)+40*e^(-0.5)0.1
P 40,0.5(0)=C 40,0.5(0)+ 40*e^(-0.5)0.1-S(0)
=4+38.05-40=2.05
Thus fair price is 2.05
Propose a strategy to take advantage of your beliefs that uses the above mentioned put and call options. That is the strategy that allows you to profit from both: the significant price increase and decrease. Your answer should include the payoff table and graph.
