Do interest rates have any impact on options valuation?

Options are financial derivatives that give the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before a specific date. The most common types of options are call options, which confer the right to buy, and put options, which give the right to sell. Options valuation is the process of determining the fair price or theoretical value of an option based on various parameters.

The seminal Black-Scholes options pricing model, published in 1973, forms the basis for valuating options today. The Black-Scholes model takes into account variables like the stock price, strike price, volatility, time to expiry, and risk-free rate to calculate a theoretical fair value for an option. Among these variables, interest rates play a critical role in influencing option prices.

The role of Interest rates in Black-Scholes

The Black-Scholes formula includes risk-free interest rate as one of its key inputs. The risk-free rate represents the return that can be earned on a risk-free investment over the option’s time to expiry, such as a Treasury bill. It serves as a proxy for the time value of money.

Intuitively, investors evaluate returns on any investment relative to what they can earn risk-free. Thus, the prevailing risk-free rate, typically benchmarked to short-term government bond yields, factors into options valuation.

Interest rates impact option pricing in two ways under the Black-Scholes model. First, they influence the prices of underlying assets like stocks, which the option references. Rising interest rates affect the present value of future cash flows, making fixed income more attractive than equities, which can lead to a decline in the underlying asset's price. Second, interest rates adjust for the time value of money. The risk-free rate is used to discount the expected payoffs of the option at expiration to its present value today.

Impact on call option pricing

A call option provides the holder with the right to buy the underlying asset on expiry at the agreed strike price. When interest rates rise, the price of the call option declines.

The probability of the option finishing in-the-money reduces as higher interest rates tend to lower the expected price of the underlying stock. A lower stock price decreases the likelihood of the call option finishing in-the-money (i.e., for the stock price to exceed the strike price at expiration).

The declining time value of money also plays a role. Even if the call option finishes in-the-money at maturity, the discounted present value of the payoff is lower when interest rates are higher. Additionally, the cost of funding is higher in a rising interest rate environment. Buyers of call options must finance the option price today, and higher interest rates increase this cost, reducing the rational price they are willing to pay.

As a result, traders adjust their valuation models to factor in changes in the risk-free rate when pricing call options. All else being equal, an increase in interest rates reduces the theoretical fair value of call options, while a decline in rates increases their value.

Read more: Understanding How Call Options Work

Impact on put option pricing

Put options give the holder the right to sell the underlying asset at the strike price on expiry. Unlike call options, put pricing typically increases when interest rates rise.

A higher likelihood of finishing in-the-money arises because rising interest rates tend to reduce the expected price of the underlying stock. This makes it more likely for the put option to finish in-the-money, increasing its intrinsic value.

The gain from a lower stock price is also discounted less in a high-interest rate environment. Although the payoff occurs at expiration, the present value impact is reduced when rates are higher due to time value of money considerations.

Higher interest rates also benefit put holders in terms of funding costs. Since buyers of puts do not need to fund the purchase of the underlying asset, higher rates lower their overall financing costs for the trade.

Read more: What Is a Put Option? - Meaning, Benefits, Working and More

Magnitude of impact

While the directional relationship between interest rates and option prices is clear, the magnitude of the impact depends on several factors. These include the option's sensitivity to the underlying asset price (reflected in the Delta), the time to maturity (longer-tenor options see a greater impact), the degree of change in interest rates, and the initial level of interest rates (sensitivity is higher when rates are low).

For at-the-money options with relatively near-term expirations, a 0.25% or 0.50% change in interest rates may not significantly alter valuations. However, for deep out-of-the-money options with longer expiries, the impact can be more pronounced.

Traders use the Black-Scholes Greeks to measure the sensitivity of an option’s price to each pricing parameter. Metrics like Theta and Rho can help quantify the impact of interest rate changes. However, the overall impact of interest rates tends to be muted compared to other factors like implied volatility.

Practical implications

Understanding how interest rates influence options valuation allows traders to adjust their strategies accordingly. Traders may increase or decrease their position sizes depending on the prevailing rate environment. Hedging strategies may also need recalibration to account for changes in interest rates.

In a high-rate environment, traders may consider rolling or closing profitable trades earlier to benefit from Vega or Theta decay. Conversely, selling options as rates rise may require caution due to increased Theta risk.

Changes in interest rates can also create opportunities to capitalise on temporary mispricing in the options market. For example, traders may identify cheaper call or put options if pricing models lag behind changes in the risk-free rate.

Evaluating rate cycle trends becomes especially important in transitional rate environments. Monitoring these trends closely can help investors adjust expectations and refine their trading strategies.

Conclusion

Interest rates have a definitive impact on the valuation of call and put options under the Black-Scholes framework. An increase in interest rates reduces the theoretical value of call options while increasing the price of put options.

The key drivers of this relationship are the influence of interest rates on the underlying asset's price, the adjustment for the time value of money, and the effect on funding costs. While the directional relationship is clear, the magnitude of change depends on factors such as time to expiry, moneyness, Delta, Theta, Rho, and the degree of interest rate changes.