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What is the arbitrage opportunity with this European call option and put option?

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AD 9: A European call option and put option on a stock both have a strike price of $30 and an expiration date in six months. Both sell for $5. The risk-free interest rate is 7% per annum, the current stock price is $27.80 and a $1 dividend is expected in 2 months. Identify the arbitrage opportunity open to the trader.

Q1: To do this, take one of the option prices as correct and invoke the appropriate put-call parity relation to determine the arbitrage-free price of the other option.

Q2: Is the arbitrage-free price less than, greater than, or equal to the market price?

Q3: What strategy would lock in the gain from the apparent mispricing? Hint: Replicate Table 9.2 while remembering to discuss the impact of the dividend to be received in two months time.

Adapted from Fundamentals of Futures and Options Markets, 6th ed., John C. Hull. Chapter 9

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This solution provides calculations for and explains the arbitrage opportunity.

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AD 9: A European call option and put option on a stock both have a strike price of $30 and an expiration date in six months. Both sell for $5. The risk-free interest rate is 7% per annum, the current stock price is $27.80 and a $1 dividend is expected in 2 months. Identify the arbitrage opportunity open to the trader.

Q1: To do this, take one of the option prices as correct and invoke the appropriate put-call parity relation to determine the arbitrage-free price of the other option.

Let us take the value of call as correct
we will use put-call parity condition to arrive at the arbitrage free price of put option

Put call parity : c+ D+ Xe^-(rt) = p+S
where D is the Present Value (PV) of Dividend
Stock ...

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