Question

Suppose the call price is $14.2 and the put price is $9.3 for stock options, where the exercise price is $100, the risk-free interest rate is 5% (continuously compounded), and the time to expiration is one year.

a. Explain how you would create a synthetic stock position and identify the cost.
b. Suppose you observe a $100 stock price; identify any arbitrage opportunities.

A) a: Long call, Short put; b: No arbitrage opportunity
B) a: Short call, Long put; b: No arbitrage opportunity
C) a: Long call, Short put; b: Arbitrage opportunity
D) a: Short call, Long put; b: Arbitrage opportunity

Answer 1

To create a synthetic stock position, take a long call and short put option at the same strike price and expiration. The cost is the net of the call price minus the put price. Given the market data and using put-call parity, we find no significant arbitrage opportunities. The correct option is b.

Step-by-step explanation:

The question involves creating a synthetic stock position using options and identifying potential arbitrage opportunities given specific market conditions. A synthetic stock position can be created by a long call and short put at the same strike price and expiration date. The cost of this position would be the call price ($14.2) minus the put price ($9.3), resulting in a net cost of $4.9. If the stock price is $100 and the risk-free rate is 5%, we can use the put-call parity theorem to assess arbitrage opportunities.

The put-call parity equation is C - P = S - Xe-rt, where C is the call option price, P is the put option price, S is the stock price, and Xe-rt is the present value of the exercise price. Plugging in the values, we get $14.2 - $9.3 = $100 - $100e-0.05. After calculation, we find that the left side equals $4.9, and the right side approximately equals $4.88. Since these values are almost equal, there are no significant arbitrage opportunities present.