Question

Mrs Susan Martinson observes a $72 price for a non-dividend-paying stock. The
stock can go up by 35.6% or down by 45.9% in each of two binomial periods. The European
call option on this stock has two years to mature. The annual risk-free interest rate is 3%, and
the exercise price is $75. Mrs Susan asks you to:
• Find the value of the option today.
• Construct a hedge by combining a position in the stock with a position in the call.
Show that the return on the hedge is the risk-free rate regardless of the outcome over
both periods. You are also required to draw the tree with stock price, hedge ratio, value
of a call and a hedge portfolio showing at each node. Assume that the call sells for the
theoretical value.
• Advise what she would do if the call is overpriced and if it is underpriced?
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Answer 1

For Value of the option use binomial model.