9) A European call option and a European put option on a stock both have a strik

Question

9)

A European call option and a European put option on a stock both have a strike price of $45 and expire in 6 months. Currently, the call price is $10 and the put price is $5 in the market. The risk-free rate is 2% per annum, and the current stock price is $50. Identify the arbitrage opportunity open to the trader. All the interest rates are with continuous compounding.

a) Buy call, sell put, sell stock

b) Buy call, sell put, buy stock

c) Sell call, buy put, buy stock

d) Sell call, buy put, sell stock

a) Buy call, sell put, sell stock

b) Buy call, sell put, buy stock

c) Sell call, buy put, buy stock

d) Sell call, buy put, sell stock

Explanation / Answer

a) Trader will buy call at a Price of $10 and sell a Put for $5. So a total Loss of $5. Than he sell stock at $50. Now if Price goes up say, $53, than he will exercise his Call Option and make a Gain of $8 (53 - 45). But in that case he has to face a loss of $3 on the stock he sold. So, net gain is zero. But the money he got from sell of stock can be invested at risk free rate. That interest will be the gain of Trader.

If the Price go down say, $47 than he will excercise his Call option and make a gain of $2 (47 - 45). Put option will not be exercised in that case. His net gain would be Zero, because there is a Profit and loss of $5. But the money he got from sell of stock can be invested at risk free rate. That interest will be the gain of Trader.

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