Ask Mint | The time value component of options decreases exponentially

Ask Mint | The time value component of options decreases exponentially
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First Published: Mon, Jan 26 2009. 01 02 AM IST

Updated: Mon, Jan 26 2009. 01 02 AM IST
The “intrinsic value” and the “time value” of an option are like two sides of the same coin. Together they give us the true worth of an option. But the real challenge lies in finding out the time value. So, is there really a simple way to explain how the time value of an option is determined without going into the nitty-gritty of complex models? Let’s find out.
Johnny: Last week, you talked about American options. Tell me, how do the sellers of European options look at the intrinsic value and the time value?
Jinny: Well, European options, as you know, can be exercised only on the expiry date. A seller of European options knows that he is not immediately going to lose anything by selling an “in the money” option. What matters more to him is whether or not the option remains in the money on the expiry date. So, while deciding the premium of European options, we are bothered more about what the intrinsic value of the option on the expiry date would be. But that doesn’t mean that we can completely ignore the present intrinsic value of the options. The current price of the underlying asset as well as the strike price under the option are used as valuable inputs in the Black Scholes model that is most commonly used for the pricing of European options. An option deep in the money enjoys a better chance of remaining in the money at the expiry date whereas an option deeply “out of money” may have no hope. The greater an option is in the money or out of money, the greater the movement in the price required to influence its intrinsic value. You would generally find that when all other factors are equal, the premium of an out of money option is less than an option “at the money”, which in turn is less than an option in the money. So, the present intrinsic value of an option in one way or the other is always connected with the time value. In fact, all option pricing models take into account both the intrinsic value and the time value while fixing the price of an option.
Johnny: You have repeatedly talked about the time value. It would be better if you could explain it.
Jinny: All options remain valid for a particular length of time, which could be a few weeks, a month or even longer, depending on the need of the parties. This length of time is like a running taxi meter—the longer the drive, the more money you pay. The length of time has a similar effect on the option premium. The greater the length of time of an option, the higher the premium. But, you may ask, why is an option having less time to expire cheaper than an option having a longer time?
Illustration: Jayachandran / Mint
This is so because in the longer run the chance of an option ending in the money greatly increases. This is so because even a slow price momentum may put an option in the money over a long time but as the length of time decreases, greater movement in the price is required for the same amount of change. Think of this in terms of running a long distance. If you have to run 20km in 20 days, then even a kilometre a day is enough to see you through, but if you have to run 20km in just one day, then you need to draw on all your strength. An out of money option having just one day to expire may need to pull out all stops to get in the money. No doubt a tsunami that lasts just one day is enough to change the scene but thankfully, such events do not happen every day.
Our option pricing models make use of the historical data of price volatility to find out how much the price of an asset is likely to move over a period of, say, one month or a week or even a single day. With each passing day, the time value of your option decreases. But interestingly, this decrease in time value is not uniform throughout the entire life of an option. The time value component of an option premium decreases exponentially. This means that in the beginning the rate of decrease of the time value is slow but as the option approaches the expiry date the rate of decrease increases.
Again, think of a long-distance run. You run at a leisurely pace in the beginning but as you start running out of time, you increase your speed. As a rule of thumb, we can say that an option may lose one-third of its time value during the first half of its life and two-thirds of its value during the remaining half of its life. This is how we arrive at the time value, which helps us in determining the price of an option.
Johnny: Thanks, Jinny. I think we can keep on talking about options. But let’s stop now. I will ask you about something new next week.
What:The time value of an option decreases exponentially with the decrease in the length of time for which an option is valid.
Why: This is so because over a short period, greater movement in price is required to make the change in the intrinsic value.
How much: An option may lose one-third of its time value during the first half of its life and two-thirds of its value during the remaining half of its life.
Shailaja and Manoj K. Singh have important day jobs with an important bank. But Jinny and Johnny have plenty of time for your suggestions and ideas for their weekly chat. You can write to both of them at realsimple@livemint.com
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First Published: Mon, Jan 26 2009. 01 02 AM IST