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Factors Affecting the Prices of Option Premiums

There are several interesting facts about how the premiums on option contracts are priced. The first fact is that when the strike (exercise) price for a contract is set at a higher level, the premium for the call option is lower and the premium for the put option is higher. For example, in going from a contract with a strike price of 112 to one with 115, the premium for a call option for the month of March might fall from 1 45/64 to 16/64, and the premium for the March put option might rise from 19/64 to 1 54/64.

Our understanding of the profit function for option contracts illustrated in Figure 1 helps explain this fact. As we saw in panel (a), a higher price for the underlying financial instrument (in this case a Treasury bond futures contract) relative to the option's exercise price results in higher profits on the call (buy) option. Thus, the lower the strike price, the higher the profits on the call option contract and the greater the premium that investors like Irving are willing to pay. Similarly, we saw in panel (b) that a higher price for the underlying financial instrument relative to the exercise price lowers profits on the put (sell) option, so that a higher strike price increases profits and thus causes the premium to increase.

The second fact is that as the period of time over which the option can be exercised (the term to expiration) gets longer, the premiums for both call and put options rise. For example, at a strike price of 112, the premium on a call option might increase from 1 45/64 in March to 1 50/64 in April and to 2 28/64 in May. Similarly, the premium on a put option might increase from 19/64 in March to 1 43/64 in April and to 2 22/64 in May. The fact that premiums increase with the term to expiration is also explained by the nonlinear profit function for option contracts. As the term to expiration lengthens, there is a greater chance that the price of the underlying financial instrument will be very high or very low by the expiration date. If the price becomes very high and goes well above the exercise price, the call (buy) option will yield a high profit; if the price becomes very low and goes well below the exercise price, the losses will be small because the owner of the call option will simply decide not to exercise the option. The possibility of greater variability of the underlying financial instrument as the term to expiration lengthens raises profits on average for the call option.

Similar reasoning tells us that the put (sell) option will become more valuable as the term to expiration increases, because the possibility of greater price variability of the underlying financial instrument increases as the term to expiration increases. The greater chance of a low price increases the chance that profits on the put option will be very high. But the greater chance of a high price does not produce substantial losses for the put option, because the owner will again just decide not to exercise the option.

Another way of thinking about this reasoning is to recognize that option contracts have an element of "Heads, I win; tails, I don't lose too badly." The greater variability of where the prices might be by the expiration date increases the value of both kinds of options. Because a longer term to the expiration date leads to greater variability of where the prices might be by the expiration date, a longer term to expiration raises the value of the option contract.

The reasoning that we have just developed also explains another important fact about option premiums. When the volatility of the price of the underlying instrument is great, the premiums for both call and put options will be higher. Higher volatility of prices means that for a given expiration date, there will again be greater variability of where the prices might be by the expiration date. The "Heads, I win; tails, I don't lose too badly" property of options then means that the greater variability of possible prices by the expiration date increases average profits for the option and thus increases the premium that investors are willing to pay.

Summary

Our analysis of how profits on options are affected by price movements for the underlying financial instrument leads to the following conclusions about the factors that determine the premium on an option contract:

1. The higher the strike price, everything else being equal, the lower the premium on call (buy) options and the higher the premium on put (sell) options.

2. The greater the term to expiration, everything else being equal, the higher the premiums for both call and put options.

3. The greater the volatility of prices of the underlying financial instrument, everything else being equal, the higher the premiums for both call and put options.

The results we have derived here appear in more formal models, such as the Black-Scholes model, which analyze how the premiums on options are priced. You might study such models in finance courses.

 
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