# How and Why Interest Rates Affect Options

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Changes in interest rates have an effect on the general economy, stock market, bond market, and other financial markets, as well as macroeconomic issues. Changes in interest rates also have an influence on option valuation, which is a complicated job including several considerations such as the underlying asset price, exercise or strike price, time to expiration, risk-free rate of return (interest rate), volatility, and dividend yield. Except for the exercise price, all other components are unknown variables that may vary until the option expires.

## Which Interest Rate for Pricing Options?

It is critical to determine the appropriate maturity interest rates for use in pricing options. The majority of option valuation models, such as Black-Scholes, employ annualized interest rates.

If an interest-bearing account pays 1% each month, the annual interest rate is 12%. Correct?

No! Converting interest rates across multiple time periods behaves differently than a straightforward up- (or down-) scaling multiplication (or division) of the time durations. Assume you have a monthly interest rate of 1%. How do you calculate the yearly rate? Time multiple = 12 months/1 month = 12 in this case:

1. Subtract the monthly interest rate from 100. (to get 0.01)
2. Add 1 to it (to get 1.01)
3. Increase it to the power of the time multiple (for example, 1.0112 = 1.1268).
4. Take 1 away from it (to get 0.1268)
5. Multiply that by 100 to get the yearly interest rate (12.68%).

This is the annualized interest rate to employ in any interest rate valuation model. The risk-free one-year Treasury rates are utilized in a conventional option pricing model such as Black-Scholes.

It is crucial to remember that interest rate increases are uncommon and of little scale (typically in increments of 0.25%, or 25 basis points). Other elements used to determine option pricing (such as the underlying asset price, time to expiration, volatility, and dividend yield) vary more often and in greater magnitudes, having a disproportionately higher influence on option prices than changes in interest rates.

### Key Takeaways

• Changes in interest rates have a direct impact on option pricing, which is calculated using a number of complicated criteria.
• The risk-free annualized Treasury interest rate is utilized in typical option pricing models such as Black-Scholes.
• When interest rates rise, call option prices rise, while put option prices fall.

## How Interest Rates Affect Call and Put Option Prices

A comparison of stock purchases and analogous options purchases will be important in understanding the theory underlying the effect of interest rate fluctuations. We suppose a skilled trader trades long positions with interest-bearing lent money and short positions with interest-earning money.

### Interest Advantage in Call Options

Buying 100 shares of a company for \$100 will cost \$10,000, which, if a trader borrows money for trading, will result in interest payments. Buying the \$12 call option in a lot of 100 contracts will cost you merely \$1,200. However, the profit potential will be the same as with a long stock investment.

Effectively, the \$8,800 difference saves the incoming interest payment on the borrowed money. Alternatively, the \$8,800 saved may be invested in an interest-bearing account, generating \$440 in interest income over the course of a year.

Thus, a rise in interest rates will result in either less outgoing interest on the lent money or more interest income on the savings account. Both will benefit this call position and save money. The price of a call option rises to reflect the advantage of rising interest rates.

### Interest Disadvantage in Put Options

In theory, shorting a stock in order to profit on a price decrease will generate cash for the short seller. Buying a put provides a comparable gain from price drops, but comes at a penalty in the form of a put option premium. There are two options in this case: cash obtained by shorting a stock may generate interest for the trader, while cash spent on purchasing puts is interest payable (assuming the trader is borrowing money to buy puts).

Shorting stock becomes more advantageous than purchasing puts when interest rates rise, since the former provides revenue while the latter does not. As a result, rising interest rates have a negative influence on put option values.

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## The Rho Greek

Rho is a typical Greek that calculates the effect of interest rate changes on option prices. It shows how much the option price changes for every 1% change in interest rates. Assume a call option with a rho value of 0.25 is presently priced at \$5. If interest rates rise by 1%, the call option price rises by \$0.25 (to \$5.25) or by the amount of the rho value. Similarly, the price of the put option will fall by the amount of its rho value.

Because interest rate fluctuations are rare and generally in 0.25% increments, rho is not regarded a key Greek because it has little influence on option pricing when compared to other variables (or Greeks like delta, gamma, vega, or theta).

## How a Change in Interest Rates Affects Call and Put Option Prices?

Using the Black-Scholes model, the call price for a European-style in-the-money (ITM) call option on an underlying trading at \$100 is \$12.3092, with an exercise price of \$100, one year to expiration, a volatility of 25%, and an interest rate of 5%. A put option with comparable parameters costs \$7.4828, and the put rho value is -0.4482. (Case 1).

Source: Chicago Board Options Exchange (CBOE)

Let us now raise the interest rate from 5% to 6% while keeping the other parameters constant.

The call price has risen to \$12.7977 (up \$0.4885), while the put price has fallen to \$7.0610 (down \$-0.4218). The call and put prices have changed by about the same amount as the previously calculated call rho (0.5035) and put rho (-0.4482) values. (The fractional discrepancy is caused by the BS model calculation process and is insignificant.)

In actuality, interest rates are frequently changed in 0.25% increments. To provide a practical example, let’s reduce the interest rate from 5% to 5.25%. The other values are identical to those in Case 1.

The call price has risen to \$12.4309, while the put price has fallen to \$7.3753 (a change of \$0.1217 for the call price and -\$0.1075 for the put price).

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As can be seen, the changes in call and put option prices are insignificant following a 0.25% shift in interest rates.

Interest rates may fluctuate four times in one year (4 * 0.25% = 1% rise), i.e. till the expiration date. Nonetheless, the effect of such interest rate fluctuations may be minor (only around \$0.5 on an ITM call option price of \$12 and an ITM put option price of \$7). Other variables may shift with considerably greater magnitudes during the course of the year, having a major influence on option pricing.

Similar calculations for out-of-the-money (OTM) and in-the-money (ITM) options provide similar findings, with only fractional changes in option prices seen following interest rate increases.

## Arbitrage Opportunities

Is it feasible to profit from projected rate fluctuations via arbitrage? Typically, markets are thought to be efficient, and the pricing of options contracts are supposed to be inclusive of any such anticipated changes.

Furthermore, changes in interest rates often have an inverse effect on stock values, which has a far higher influence on option pricing. Overall, arbitrage gains are difficult to capitalize on owing to the modest relative change in option price due to interest rate movements.

## The Bottom Line

Option pricing is a complicated process that is ever evolving, despite the fact that famous models such as Black-Scholes have been employed for decades. Multiple variables influence option value, resulting in extremely large changes in option pricing in the near term. Interest rate changes have an inverse effect on call and put option premiums. However, the influence on option prices is marginal; changes in other input factors, such as underlying price, volatility, time to expiration, and dividend yield, have a greater impact on option pricing.

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