This practice problem reinforces the concept of binomial option pricing model discussed in the following two posts

in a companion blog.

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**Practice Problems**

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 call option on the stock specifies an exercise price (strike price) of $55 and is set to expire at the end of one year. What is the fair price of this call option? Use the one-period binomial option model. What is the portfolio replicating the payoff of this call option?
- Consider a put 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 put option.
- Price the put option described in #2 using the binomial option model.

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**Answers**

- Replicating portfolio: 0.25 shares, -$9.512294245 (borrowing).

Call option price = = $2.9877

- Put option premium = $5.305324103
- Replicating portfolio: shares (short), $42.8053241 (lending).

Put option price = = $5.3053241

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