Question

On February 1st, September call option with exercise price of $55 written on Aztec stock is sold for $4.375 per share and September put option with exercise price of $55 written on the same stock is sold for $6 per share. At the time, T-bills coming due in September are priced to yield 12%. Aztec stock is sold for $53 per share on February 1st. The time period between Feb 1st and expiration date of options is 8 months.
1. If the call option, Aztec stock, and T-bills are correctly priced, what is the appropriate value of a put option on February 1st? (1 point)
2. How to take advantage of this situation? Please show arbitrage profits using arbitrage table. (2 points)

Answer 1

1) Put-Call Parity
Stock + Put Option = Call Option + X/(1+Rf)n (where X = strike price)
53 + Put = 4.375 + 55/(1+0.12)(8/12)
53 + Put = 4.375 + 50.99770993
Put = 4.375 + 50.99770993 - 53
Put = $ 2.372709929

2) Put-Call Parity using the given info in the question
Stock + Put Option = Call Option + X/(1+Rf)n
53 + 6 = 4.375 + 50.998
59 is not equal to 55.373

Portfolio A = Stock + Put Option
Portfolio B = Call Option + X/(1+Rf)n

From the above equation we can see that Portfolio A is overvalued than Portfolio B. Hence, we will short Portfolio B and buy Portfolio A to do arbitrage profit

Arbitrage Profit = $ 3.6273