The strike price for a European call and put option is $56 and the expiration date for the call and the put is in 9 months. Assume the call sells for $6, while the put sells for $7. The price of the stock underlying the call and the put is $55 and the risk free rate is 3% per annum based on continuous compounding. Identify any arbitrage opportunity and explain what the trader should do to capitalize on that opportunity. In the event you determine an arbitrage opportunity exists, calculate possible payoffs from the arbitrage strategy.
First calculate call option price given data for put option:
Using put call parity formula:
Put option = Call option - Stock price + Strike price*exp(- risk free rate * time)
Call option = 7 + 55 - 56*EXP(-3%* 9/12)
Put option = $7.25
As calculated call option is $7.25 and given Call option price is $6 which means in market call is under price.
If put call parity holds, traders should buy Call options in market for $6 and in future when market recognize the put call parity the price of call options will go up to $7.25 and it will give a pay off of $1.25 i.e. 7.25-6 = 1.25
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