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We are aware that recently, US Treasury yields have been continuously rising, causing the prices of many financial assets to decline, such as stocks, bonds, funds, and non-US dollar exchange rates. However, the one asset class that is relatively less affected by this rise is options. In fact, to some extent, the increase in US Treasury yields has stimulated the increase in option prices. But why is this the case? What is the relationship between interest rates and option prices?

To understand this logic, let's first take a look at what Rho is for options."

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1. Understanding the Rho Value of Options

Rho value is a metric used to measure the sensitivity of option prices to changes in interest rates. Specifically, it represents the change in option price when the risk-free interest rate varies by 1%. The formula for Rho is expressed as Rho = Change in option price / Change in risk-free interest rate.

Let's first focus on the denominator, the risk-free interest rate, often considered with reference to the yield on U.S. Treasury bonds. How does the risk-free interest rate affect asset prices?

We know that the price of an asset is essentially the present value of a series of future cash flows.

For example, if A lends $100 to B at a 10% interest rate, B needs to repay $110 after one year. Conversely, if A holds a promissory note with a specified 20% interest rate, the note will be worth $120 when due. The present value of this promissory note is calculated by dividing $120 by 1 + 20%.

Therefore, whether it's stocks, bonds, or other assets generating future cash flows, their value is the present value of future cash flows discounted at the interest rate. As a result, when interest rates rise, the denominator increases, leading to a decline in the value of major asset classes. This is why the recent increase in U.S. Treasury yields (risk-free interest rates) has contributed to a sharp decline in the stock market.

Although interest rate hikes have a negative impact on various assets, options are an exception. Taking a call option as an example, if the strike price is $10, the expiration date is one year later, and the current price of the underlying asset is $20 with a risk-free interest rate of 10%, the current price of the call option should be【20*（1+10%）-5】/（1+10%）.

The underlying logic of this algorithm is that after one year, the price of the underlying asset naturally increases to $20*（1+10%）, allowing investors to profit $20*（1+10%）-5 by exercising the option. This future profit is equivalent to the present value of how much money today? It needs to be discounted at the rate of 10%, hence【20*（1+10%）-5】/（1+10%）. Simplifying further, it is 20-5/（1+10%）, which is the current price minus the present value of the strike price. The higher the discount rate, the smaller the present value of the strike price, and the higher the price of the call option.

Conversely, for a put option, the logic is reversed. Following the example, the value of a put option is equal to the present value of the strike price minus the current price of the underlying asset. Therefore, the higher the interest rate, the lower the price of the put option.

Hence, this explains why the Rho value for call options is always positive, while for put options, it is consistently negative.

2. How to Use Rho for Options Trading

Based on the characteristics of Rho, we can summarize the following trading techniques:

1. While an interest rate hike is generally favorable for long call options due to their positive Rho value, it's essential to note that such hikes can lead to a decrease in the underlying asset's price. Additionally, Rho has a relatively small impact on option prices. This means that the prices of long put options may increase, while long call options may decrease.

2. Rho values are more substantial for long-term options, and the Rho value for long put options is negative. Consequently, when interest rates rise, the increase in the price of longer-term long put options will be smaller than that of shorter-term long put options.

3. Rho values are relatively small in absolute terms, and in-the-money options have higher Rho values compared to at-the-money and out-of-the-money options. Furthermore, interest rate hikes are not a frequent occurrence in the capital market. Thus, compared to the other Greek values, Rho's impact is relatively minor, and it is not considered a highly significant factor.

That's it for today! In this episode of the Options Greek Series, we have covered all five Greek values for options: Delta, Gamma, Theta, Vega, and Rho. We introduced the basic meanings of these letters and how to use them when crafting option strategies. To recap:

Delta: How much an option's price changes for a one-unit change in the underlying asset's price.

Gamma: The rate of change of Delta in response to changes in the underlying asset.

Theta: The change in an option's price due to the passage of time, typically expressed as the daily decay.

Vega: The impact on an option's price due to a one-unit change in implied volatility.

Rho: How an option's price changes when the risk-free interest rate changes by 1%.

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