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# Option Pricing using Binomial Model

1) Consider a stock currently selling for \$80. It can go up or down by 15% per period. The risk-free rate is 6%. Use a one period binomial model. You want to price a European call option with exercise price of \$84.
a. Determine the two possible stock prices at expiration.
b. Construct two portfolios with equivalent payoffs. One portfolio using a call the other the stock and a t-bill.
c. What is the value of the portfolios at expiration?
d. Compute the value of the call.

2) In problem 1 assume you find that the actual market price of the call is \$6. What arbitrage position should you take? Compute the profit you will earn from the position.

3) Assume that you want to price a one year American put option. The underlying stock is selling for \$40 and the option has a strike price of \$40. Standard deviation is 30% and the risk free rate is 6%. Use a one period binomial model.

a. Compute u and d using the formulas on page 322.
b. Compute p
c. Compute the value of the option.

4) Using the information from number 3 price a one year American call option with an exercise price of \$40 using a two-period binomial model.

5) Using the same information as in number 4 price a one year American put option with exercise price of \$40 using a two-period binomial model. Verify that put/call parity holds.

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#### Solution Summary

Find the value of an European call option using Binomial tree.

\$2.19