Impact of interest rates on the intrinsic value of options

The intrinsic value of an option is the value of its premium related to changes in the underlying stock’s price compared to the option’s strike price. So the intrinsic value of a call option (IVco) is the difference between the market price of the underlying (U) and the strike (X) of the call option, while the intrinsic value of a put option (IVpo) is the difference between the strike (X) of the put option and the market price of the underlying (U). But an intrinsic value cannot be negative, since that would mean that its holder would lose money by exercising it, so we say in such instances that the option’s intrinsic value is nil or equal to zero.

IVco = max(U – X; 0)

IVpo = max(X – U; 0)

To make things simpler, we usually calculate intrinsic value as if the option had reached expiration.

For example, consider call options on shares in The Canadian National Railway Company (CNR), CNR 180119 C 90. These options expire on January 19, 2018 (in 354 days), have a strike of $90 and are worth $6.45, while shares in CNR are trading at a price of $91.51 on January 30, 2017. The options have an intrinsic value of $1.51:

IVco = max(U – X; 0) = max($91.51 – $90.00; 0) = $1.51

However, since we have not reached the call option’s expiration, which is 354 days away, we need to calculate the intrinsic value of the call option as of today.

Current intrinsic value of a call option: the impact of interest rates

To this end, we will need to find the current value* (see the capsule on current value at the end of this article) of the $90 strike and then calculate the intrinsic value using the market value of CNR stock.

Using an interest rate of 0.60% over a one-year period, the current value of the $90 strike is $89.48, for a current intrinsic value of $2.03.

Current IVco = max(U – X; 0) = max($91.51 – $89.48; 0) = $2.03

Now, if interest rates increase 1% in the near term, to 1.6%, the current value of the $90.00 strike will be $88.63, giving us a current intrinsic value of $2.88.

Current IVco = max(U – X; 0) = max($91.51 – $88.63; 0) = $2.88

So, if the price of CNR is unchanged at $91.51, the increase in interest rates will be profitable for the holder of the call options CNR 180119 C 90.

As you can see, holders of call options stand to profit when interest rates go up, but falling interest rates will work against them. We will not repeat this exercise for put options, but keep in mind that higher interest rates is a losing proposition for holders of put options, while lower interest rates work in their favour.

Even though changes in interest rates have a negligible impact during periods when rates are relatively stable, it is a factor that deserves careful consideration when central banks are making adjustments to monetary policy. With this in mind, it is very possible that an investor will buy a call option and then see the value of its premium decrease/increase, despite the fact that the value of the underlying has increased, if there has been a significant decrease/increase in interest rates.

In our next article we will discuss another variable that affects the intrinsic value of options: dividends.

* Current value

To understand the current value of a given amount, it is preferable to first understand the principle of capitalized value. A $100 investment bearing 10% interest will give us a capitalized value of $110 at the end of the year.

Capitalized value = current value + current value x interest rate = current value x (1 + interest rate) = 100 $ x 1.10 = $110

So, if I know the amount that I will receive in one year’s time, then in order to find the current value of this capitalized amount, I can perform the reverse calculation, i.e. I can divide the capitalized value by (1 + interest rate), or by 1.10% in our example.

Current value = capitalized value / (1 + interest rate) = $110 / 1.10 = $100

So if we divide the capitalized value of $110 by 1.10, we obtain the current value of $100.

Good luck in your trading, and have a good week!

The strategies presented in this blog are for information and training purposes only, and should not be interpreted as recommendations to buy or sell any security. As always, you should ensure that you are comfortable with the proposed scenarios and ready to assume all the risks before implementing an option strategy.