Option Pricing Factors
Six factors influence the value of an option: current value of the underlying asset (stock); the strike price; the time to expiration of the option; the volatility of the stock price; the risk-free rate; and dividends.
With the exception of time to expiration, all of these factors affect European- and American-style options in the same way.
Upper And Lower Option Pricing Bounds
Call options cannot be worth more than the underlying security, and put options cannot be worth more than the strike price.
When the stock does not pay a dividend, European call options cannot be worth less than the difference between the current stock price and the present value of the strike price. European put options cannot be worth less than the difference between the present value of the strike price and the current stock price.
Computing Option Values Using Put-Call Parity
Put-call parity is a no-arbitrage relationship for European-style options with the same characteristics. It states that a portfolio consisting of a call option and a zero-coupon bond with a face value equal to the strike must have the same value as a portfolio consisting of the corresponding put option and the stock:
p + S0 = c + Xe–rT
American Call And Put Options
It is never optimal to exercise an American call option on nondividend-paying stock prior to expiration.
American put options on nondividend-paying stocks can be optimally exercised prior to expiration if the put is sufficiently in-the-money.
Call options are always worth more than corresponding put options prior to expiration when both are at-the-money.
The difference between prices of an American call and corresponding put is bounded below by the difference between the current stock price and strike price, and above by the difference between the current stock price and the present value of the strike price.
