Suppose you have call and put options of same maturity (4 months), same exercise

Question

Suppose you have call and put options of same maturity (4 months), same exercise price ($70), on the same stock that is selling at $75 now. The risk-free rate is 10% per year, the call is selling at $7, and the put is selling at $2. The stock does not pay any dividend. For these options, does the put-call parity condition hold? Use the put-call parity equation to numerically prove your answer. What arbitrage strategy would capture incorrect pricing - if any - and generate risk-free profit for you. Please describe your strategy without ambiguity and in detail. No need for a numerical answer.

Explanation / Answer

Answer:

Put call parity equation:

=>1st part = $7 + $70/(1+0.1)0.33 = 74.83

2nd part = $75 + 2 = $77

So the put call parity does not hold.

b) Create a synthetic call - Get into a long contarct to buy the stock at exercie price and go sort on the stock and put option

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