For our friend Johnny, crunching numbers is tougher than crunching nails of iron. Thankfully, last week while talking about option pricing Johnny had no need to worry about number crunching. Could it really be like that? If you don’t have to go to Mexico to eat a Mexican banana, what could be better than that? It is time for our friends to resume their chat.
Johnny: Last week you had left our discussion in the middle.
Jinny: I think last week you had raised a question: What if the strike price of a call option is higher than the current market price of the underlying asset? By now I hope you would have figured out that in such a situation your option would have no intrinsic value. In fact, if you subtract the strike price from the current market price, you would get a result in the negative. But as I had said, an option having negative intrinsic value is only as bad as an option having zero intrinsic value. In both situations the option would end up without being exercised and the likely loss to the option buyer is the premium that he has paid for buying the option.
An option having negative intrinsic value is also called an “out of money” option and an option having zero intrinsic value is called “at the money” option. In respect of at the money options, the strike price of the underlying asset is equal to the current market price.
Johnny: That was all about call options. But how can we know whether a put option is “in the money” or “out of money”?
Jinny: The basic formula in respect of put options is the same but the situations are opposite. The strike price of the underlying asset for an “in the money” put option is higher than its current market price whereas the strike price would be low if the option is “out of money”. In other words, if you can make money by exercising your put option then it is “in the money”, and if you can’t make money, then your option could be either “at the money”, or “out of money”.
Suppose you hold an American put option for selling a single share of Company X at a strike price of Rs100 per share before the expiry date and the same share is presently trading at a lower price of Rs80.
Illustration: Jayachandran / Mint
You can get the intrinsic value of your option by subtracting the current market price from the strike price of your put option, which in the present case is Rs20.
Johnny: I got the point, Jinny. So far you have explained how intrinsic value is determined, but I was just wondering what role time value plays in deciding the value of an option premium.
Jinny: As I had said, the price of an option revolves around both its “intrinsic value” and its “time value”.
The intrinsic value of an option keeps fluctuating depending on the current price of the underlying asset. To start with, your option may be “at the money” but as the days pass, your option may get “in the money” or "out of money" depending on the direction of current price movements.
This upward or downward movement of the intrinsic value will keep on going till the expiry of your option.
To decide the option premium you need to take into account the present intrinsic value of an option and how much that intrinsic value is likely to change over time.
However, the role of intrinsic value in fixing the premium differs for European options and American options.I will briefly explain the reasons.
Johnny: Yes, Jinny. It would be better if you could explain.
Jinny: As you know, American options can be exercised on or before the expiry date, which means that while deciding the premium for American options you need to not only take into account the present intrinsic value but also the likely changes in the intrinsic value over each day in the entire life of the option. To make such a calculation, the Binomial option pricing model is very useful.
So, the premium of the American option is always higher than its present intrinsic value so that the buyer is not able to earn any profit by immediately exercising it.
You may buy an American option that is “in the money” right at the beginning but you can make profit only when the intrinsic value of your option further increases during the remaining term. But that’s not all.
To take care of further increase in the intrinsic value, the option seller also includes the “time value” in the option premium. You can instantly know how much time value the option seller is charging by subtracting the intrinsic value at the beginning of the option term from the total option premium.
So, if you are paying Rs30 for an option enjoying Rs20 intrinsic value, then Rs10 is the time value of your option.
The chat on this will continue next week.
What: The pricing of an option has to take into account both its “intrinsic value” and “time value”.
Why: The price of an American option is always higher than its present intrinsic value because such options can be exercised before the expiry date.
How: The binomial option pricing model is very useful for pricing American options.
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 email@example.com