Question

A stock price is currently $50. It is known that at the end of 3 months it will be either $50 or $48. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a 3-month European put option with a strike price of $49? How about a 6-month European call price? (Hint: 2 period binomial option pricing)

Answer 1

At the end of three months the value of the option $2(if the stock price is $50) or $0 (if the stock price is $48). Consider a portfolio consisting of:

+ : Shares

-1 : Option

The value of the portfolio is either 48 or 50 ?4 in three months. If

i.e. 48 = 53-4

   = 0.8

the value of the portfolio is certain to be 38.4. For this value of the portfolio is therefore riskless. The current value of the portfolio is:

0.80*50-F

where f is the value of the option. Since the portfolio must earn the risk-free rate of interest

(0.80*50-F)e^0.10*3/12=38.4

i.e F = 3.345

The value of the option is therefore $3.345.