Suppose that you noticed the following prices: P=$48; S=$4; X=$50, for a one yea

Question

Suppose that you noticed the following prices: P=$48; S=$4; X=$50, for a one year European put option.

The simple risk-free interest rate is 10% per year. Is there an arbitrage profit opportunity here? Yes or no?

If yes, how would you exploit it? If no explain why not.

PS: In all questions above X = the exercise price of the options, C = call premium, P = put premium

plz show detailed answer

Explanation / Answer

In this case the present value of the strike price = 50e^-.10 =50*.90901=45.45 4 > (45.45- 48 00) hence buy a call option Buy the call option at c = 4. Sell the stock short at S0 = $48. Invest the proceeds 48 4 = 44 at r = 10%. At the expiration date, the arbitrage trader must close the short stock position. In other words, he/she needs to buy one share of the stock. To prove that the above position always makes a profit, we need to consider two cases If ST >50 : In this case, the trader buys the stock through his/her call optionThe payoff to the arbitrage position is given by44(1.10) + (ST 50) ST = $1.6> 0                                                            If ST < 50: In this case, the trader buys the stock directly in the market at ST . Call option is not exercised.The payoff to the arbitrage position is given by58 (1.10) ST = 48.4 ST > 0 for ST < 50.

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