How option prices are affected by the exercise price and the time to expiration? We first discuss how option values are affected by strike prices and then discuss how they are affected by time to expiration. Strike prices Call option premiums are negatively related to their strike prices. This makes sense because a call option with a lower strike price allows us to buy the underlying stock for a lower price. Thus, it will be more valuable than a call option with a higher strike price (assuming these options are the same in every other way). Suppose there are two American call options: one with a strike price of $20 and another with a strike price of $30. Suppose the underlying stock is trading for $100. It is clear that the call option with the lower strike price is more valuable. If we exercise it immediately, we get a payoff of $100-$20 = $80. The other American call option with a strike price of $30 will only give us a payoff of $70 ($100-$30). Put option premiums are positively related to their strike prices. This is true because a put option with a higher strike price allows us to sell the underlying stock for a higher price. Thus, it will be more valuable than a put option with a lower strike price (assuming these options are the same in every other way). Consider two American put options: one with a strike price of $30 and another with a strike price of $20. Suppose the underlying stock price has gone down to $0. It is clear that the put option with the higher strike price is more valuable. If we exercise it immediately, we get a payoff of $30-$0 = $30. The other American put option with a strike price of $20 will only give us a payoff of $20 ($20-$0). Time to expiration All options (except European puts) with a longer time to expiration are worth at least as much as their equivalent options that have a shorter time to expiration. For example, suppose there are two American call options that are alike in all respects except time to expiration. One of them expires in one year and the other expires in two years. We would expect the two-year call option to sell for no less than what the one year call option is selling for. This is intuitive: the two-year option can do everything that the one year option can do + it expires one year later. Further, a longer time frame provides more opportunity for the underlying stock price to move in a favorable direction. The exception to the above explanation is European puts. It is possible for a European put option with a longer time to expiration to be worth less than a European put option with a shorter time to expiration. Suppose the strike price of two European put options is $20 and the underlying stock price is $0. One of them expires today and the other expires in one year from now. We can exercise the first European put option today, receive $20 and invest the proceeds to generate interest income. With the other European put option, we will receive $20 one year from now. Thus, we are foregoing interest income on this $20. This would result in the European put option expiring in one year to be worth less than the European put option expiring today. However, European put options with a longer time to expiration can be worth more than their counterparts with a shorter time to expiration. This would occur when the underlying stock price is quite volatile and interest rates are low.
Posted on: Mon, 24 Nov 2014 00:51:03 +0000
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