Question

True or False: Consider 1 year European put and call options on XYZ stock with the same strike price. If the strike price is equal to the fair value price for the 1 year forward price on XYZ stock, the put premium and call premium must be equal, otherwise an arbitrage opportunity exists.

True or False: The maximum lose of a short stock position is equal to the price at which you enter the short position.

Answer 1

1). True - This is the basis for the put call parity. As per the put call parity,

C + PV(K) = P + S where C = call option premium; P = put option premium; S = current spot price; PV(K) = present value of strike price discounted at the risk-free rate

If K is the 1 year forward rate then it follows that PV(K) has to be the spot rate S. Under this condition, if C is not equal to P then there will be an arbitrage opportunity.

2). False - Theoretically, the maximum loss in a short stock position is infinite as the future stock price can see an unlimited increase.