We are examining the price of a European put option on a share of stock GG with one period to expiration. No dividend is expected prior to expiration. The current stock price is $130, the exercise price is $135, the risk-free rate is 4%. The stock price of the next period is either $175.5 or $84.5. Using replicating portfolio approach, what is the value of the put option?

We are examining the price of a European call option on a share of stock GG with one period to expiration. No dividend is expected prior to expiration. The current stock price is $130, the exercise price is $135, the risk-free rate is 4%. The stock price of the next period is either $175.5 or $84.5. What is the risk-neutral probability of the up state?

Which of the following statements is NOT correct?

When there is no dividend payment prior to expiration, two otherwise identical call options, one European style and the other American style, should have same prices.

When a call option on a share of stock is exercised, the payoff to the owner is equal to the current stock price (S) minus the exercise price (X); when a put option is exercised, the payoff to the owner is equal to the exercise price minus the current stock price. Thus, when the stock price is below the exercise price, the call option owner will never exercise the option; when the stock price is higher than the exercise price, the put option owner will never exercise the option.

For an American put option, it is possible that it is optimal for the owner to exercise the option prior to expiration. Thus, American put option can be worth more than an otherwise identical but European put option.

We are looking at an American put option and an American call option written on the same underlying asset, same exercise price and same time to expiration. When there is no dividend paid prior to expiration, the American put and American call should satisfy the put-call parity.