This practice problem reinforces the concept of binomial option pricing model discussed in the following two posts
in a companion blog.
Suppose the stock of a certain company is currently selling for $50 per share. The price per share at the end of one year is expected to increase to $60 (20% increase) or to decrease to $40 (20% decrease). The stock pays no dividends during the next year. The annual risk-free interest rate is 5%. Assume all the options discussed here are European options.
- A put option on the stock specifies an exercise price (strike price) of $45 and is set to expire at the end of one year. What is the fair price of this put option? Use the one-period binomial option model. What is the portfolio replicating the payoff of this put option?
- Consider a call option on the same underlying stock and with the same strike price and the same time to expiration as the put option in #1. Use the put-call parity to derive the price of this call option.
- Price the call option described in #2 using the binomial option model.
- Replicating portfolio: -0.25 shares (short), $14.26844137 (lending).
Put option price = = $1.768441368
- Call option premium = $8.963117265
- Replicating portfolio: shares (long), -$28.53688274 (borrowing).
Call option price = = $8.96311726