e. option ple 18. Which one of the following statements is correct? a. The price
ID: 2805774 • Letter: E
Question
e. option ple 18. Which one of the following statements is correct? a. The price of an American put is equal to the stock price minus the exercise price according to the Black-Scholes option pricing model. b. The value of a European put is greater than the value of a comparable American put. c. The value of a put is equal to one minus the value of an equivalent call. d. The value of a put minus the value of a comparable call is equal to the value of the stock minus the exercise price e. The value of an American put will equal or exceed the value of a comparable European put.Explanation / Answer
Answer is option E.
According to the book of Hull, american and european calls on non-dividend paying stocks should have the same value. American puts, however, should be equals to, or more valuable than, european puts.
The reason for this is the time value of money. In a put, you get the option to sell a stock at a given strike price. If you exercise this option at t=0, you receive the strike price at t=0 and can invest it at the risk-free rate. Lets imagine the rf rate is 10% and the strike price is 10$. this means at t=1, you would get 11.0517$. If, on the other hand, you did'nt exercise the option early, at t=1 you would simply receive the strike price (10$). Basically, the strike price, which is your payoff for a put option, doesn't earn interest.
Another way to look at this is that an option is composed of two elements: The "insurance" element and the time value of the option. The insurance element is what you pay in order to have the option to buy a stock at a certain price. For put options, it is equals to the payout= max(K-S, 0) where K=Strike Price and St= Stock price. The time value of the option can be thought of as a risk-premium. It's difference between the value of the option and the insurance element.
If the benefits of exercising a put option early (i.e- earning the risk free rate on the proceeds) outweighs the time value of the put option, it should be exercised early.
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