In the previous parts of the series on options trading, we have introduced a few Greek factors. As a rule, acquaintance with "Greek" ends with delta, gamma i theta. However, there are more Greek. In today's environment of rapidly changing interest rates, it's worth getting to know rho. Knowing it will allow you to control the risk of changes in the interest rate of the options portfolio.

READ NECESSARY: WHAT ARE THE OPTIONS? INTRODUCTION

What is Rho?

Rho is an indicator that tries to approximate how the option price will change when the risk-free rate changes. That is, thanks to this Greek coefficient you can estimate how the value of the options portfolio will change in the event of an increase or decrease in the interest rate. In other words, to estimate the risk of an interest rate change. 

Rho is calculated based on the option pricing model Black Scholes. According to this model, the impact of changing the interest rate on the option price is small. For this reason, rho is often considered a less important Greek indicator.

As with the other Greek factors, their effect on the option price depends on a number of factors. The most important in the case of rho are:

• Time until options expire
• Option strike prices

For a quick reminder, the options can be of three types:

• OTMs
• ATM
• ITM

OTM options

These are options whose strike price differs significantly from the market price of the underlying instrument. In the case of a call option, the OTM strike price is well above the current market price. In the case of a put option, the option exercise price is below the market price. This means that the option has no intrinsic value but only a time value. In this type of option, the value of rho is small.

At-the-Money (ATM)

ATM-style options have an exercise price that is the same as the current market price. Also, this type of option has no intrinsic value but has a much higher delta than the OTM type options. If the value of the underlying instrument changes, the rho of this type of option changes rapidly. 

In-the-Money (ITM)

ITM options have an intrinsic value. This means that in the case of a call option, the option strike price is lower than the market price. In the case of a put option, the option exercise price is higher than the market price. Options of this type have a high delta. The rho value for this option type is high (compared to ATM and OTM options).

The rho value is greater for in-the-money than out-the-money. It is not hard to guess that the longer the "life" of an option, the greater the impact of a change in the interest rate on the option price. For this reason LEAPS options have higher rho than short term options.

The options that are most sensitive to an interest rate change are at-the-money options with a very long expiry period.

Rho - practical application

The table below shows a breakdown of the rho depending on the option exercise price. Coca-Cola stock options that are expected to expire on June 17, 2022 were taken into account. The market price of Coca-Cola as of 27.05.2022/64,79/XNUMX was $ XNUMX. 

Having calculated the rho, it is very easy to estimate how the value of the option will change in the event of an increase in the risk-free interest rate. It is worth noting that call options have a positive or zero rho, while put options have a negative or zero rho. This means that the value of the call option rises as the risk-free interest rate rises and falls as the interest rates decrease in value. In the case of the put option, the change in the value of the option is inversely correlated with the change in interest rates. When the risk-free interest rate rises, the value of the option falls. In the previous examples, we talked about long positions in the case of call and put options.

The complete list of dependencies is below:

• Long call - positive rho value
• Short call - negative rho value
• Long put - negative rho value
• Short put - positive rho value

For example:

If call is 4 points and rho is 0.25. This means that if the risk-free interest rate increases by 100 basis points (e.g. from 3% to 4%), the value of this call option will increase to 4,25. The reverse is true for the put option. A put option of 4 points will drop to 3,75. 

Summation

Rho is a Greek coefficient that measures the sensitivity of an option portfolio to a change in the risk-free interest rate. The increase in the interest rate is favorable for holders of long positions in call options and short positions in put options. The rho value does not have a significant impact on the option price. This is because, as a rule, the level of the risk-free interest rate does not change too rapidly in developed economies. For this reason, the rho calculation is most often omitted in the calculations assessing the success of a strategy. The reason is that most of the trading is done on options with a short time to expiry. For this reason, rho has minimal impact on the success of a given investment in short-term options.  

Do you know that…?

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