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# Market Put Price and Arbitrage-Free Put Price

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Chapter 10
A European call option and put option on a stock both have a strike price of \$60 and an expiration date in six months. Currently, call price is \$15 and put price is \$14. The risk-free interest rate is 7% per annum, the current stock price is \$57 and a \$1.50 dividend is expected in 4 months. Identify the arbitrage opportunity open to the trader. All the interest rates are continuous compounded.

Q1: To do this, take the call option prices as given and invoke the appropriate put-call parity relation (Eq. 10.10) to find the arbitrage-free theoretical price of the put option. This is not the market price given in the question.

Q2: Is the market put price greater or smaller than the arbitrage-free put price in Q1?

Q3: What strategy would lock in the gain from the apparent mispricing? What are your net cash flows now, in 4 months and at the expiration?

Hint: Replicate the arbitrage table in chat session while remembering to discuss the impact of the dividend to be received in four months time. If you are going to use the arbitrage table used in chat, then you need to add another column to account for dividend payout date (T = 4/12).

Note: If you buy a stock today and sell it in 6 months, the cashflow will be negative today but you will receive dividend in 4 months (positive cashflow) and also receive proceedings from sales in 6 months (positive cashflow).

#### Solution Summary

The solution discusses the market put price and the arbitrage-free put price.

\$2.19