Put Call Parity
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A European call option and put option on a stock both have a strike price of $30 and an expiration date in three months. Both sell for $5. The risk-free interest rate is 6% per annum, the current stock price is $28 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 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? What are your net profits in 2 months and at the expiration?
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Solution Summary
Determines option price using Put Call Parity and investigates whether there is mispricing and arbitrage opportunity.
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Please see the attached file for answers and explanations:
A European call option and put option on a stock both have a strike price of $30 and an expiration date in three months. Both sell for $5. The risk-free interest rate is 6% per annum, the current stock price is $28 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 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 Price= S= $28.00
Exercise price = X= $30.00
Value of call= c= $5.00
Time to expiration = ...
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