You are a trader who trades both puts and calls on Procter and Gamble. Informati
ID: 2714255 • Letter: Y
Question
You are a trader who trades both puts and calls on Procter and Gamble. Information about current market conditions is displayed below.
Stock Price Exercise Price Expiration Date Call Price Put Price
88 90 1/12th of a year 3.447 5
88 95 1/12th of a year 2.131 8
The annualized continuously-compounded risk-free rate is .06 (6%).
1. Given the information above, are there any arbitrage opportunities?
2. If no, explain why. If yes, describe one set of trades you could make now to exploit the arbitrage opportunity. Show that this strategy generates an arbitrage profit.
Explanation / Answer
Given the risk free rate at 6% means the stock price 1 year hence with most certainity will be at 6% higher than the present value or more given normal market conditions.
So This case, considering risk free return the stock a year hence will be at least at $88 * 1.06 = 93.28. In most probability it will be higher than this. Hence taking a call option in the first case would be a better approach.
If the stock makes a slightly higer return than the risk free return, the call option would be in the money
So in order to make money on the call option, the strike price should be at least 90 + 3.447( Call option price). Hence the price should be greater than 93.447 to make prfit and exercise the call option. SInce the price of the stock is expected to be definetly above the risk free return and the economy is not in recession, we can use the 1st option which would be more conservative.
The customer can take a put option in the 2nd Trade and the put option will be in the money if the stock price trades below 87 (95- 8). This would be a contaraian bet if the economy falls int recession
Hence in this method the customer would be in profit is the stock trades above 93.447 or below 87 in about 1 year
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