# How Interest Rate Movements Affect Options Prices

Option traders spend a lot of time teasing out how various factors influence the value of an option at any given time. The price of an option can reflect changes in the price of the underlying asset, its time to expiration, levels of market volatility, and adjustments to interest rates.

Of these metrics, interest rates—described by the Greek letter **rho**—typically gets the least attention. Although interest rates fluctuate along with everything else, they typically move much more slowly and with less regularity than the other factors. Also, many option traders trade options short term—expiring in one month or less. Some traders feel that the shorter the time to expiration, the less options respond to changes in interest rates.

Positive rho means the option increases in value when interest rates go up, while negative rho means the option decreases in value when rates go up. While rho may have less of an effect on options prices than the other greeks, the effect is real and may be important.

## The interest rate effect

In general, call options increase in value as interest rates increase, while put options decrease in value. This means call options have positive rho and put options have negative rho. The rho value itself gives theoretical change in dollars that would occur with a 1.00% change in rates. For example, if rho is –.30, then the price of the option would decline by $0.30 if interest rates increased from 4% to 5%. Higher interest rates mean potentially better returns from cash equivalents, such as short-term Treasury securities.

With all else equal, an increase in interest rates might drive up call premiums and cause put premiums to decrease. For example, if an option trader wants to buy $100,000 worth of stock on margin, the cost to use margin is three times higher when interest rates are at 6% instead of 2%. With a long call option, a trader can pursue a potential increase in the stock price without paying margin interest. Therefore, some traders may choose the increased risk needed to buy call options to avoid this increased cost. Call buyers may be willing to pay more when rates are relatively high. On the other hand, a covered call seller would receive more interest-earning cash if they sold the underlying stock instead of writing the option. Of course, long calls should not generally be considered substitutes for stock ownership because call options do not pay dividends, do not convey voting and other shareholder rights, and expose buyers the potential to quickly lose 100% of their invested principal.

In the case of put options, it's a similar argument—but reversed. A long put can be considered a temporary alternative to shorting a stock. Investors with a short stock position receive cash (which can be invested in interest-bearing instruments), so buying a put becomes less attractive as interest rates rise, because in many cases, there would be more forgone interest by owning a put versus selling the stock.

Cost of carry = Strike price × Interest rate × Days to expiration/calendar days

## Time to exercise?

Aside from dividends (which often require their own exercise decision tree), interest rates are a major determining factor in early exercise decisions for American-style options. Remember, most listed options in the United States are American style, meaning they may be exercised any time before expiration.

For example, a put option may become an early exercise candidate whenever the interest that could be earned on the proceeds from selling the stock at the strike price is large enough to make a difference to the trader. Traders will determine that price differently based on their own opportunity costs. In general, though, higher interest rates mean more positions will reach that "large enough" point.

Consider the following example:

- Shares of XYZ are trading at $100 per share.
- The quarterly dividend is zero, meaning there's no expected dividend between now and expiration.
- A trader is long one 125-strike put expiring in eight days.
- Interest rates recently increased to 6%.
- The XYZ 125 calls are trading for $0.01—which put-call parity tells us there's a penny of extrinsic value (a.k.a. time value) in the 125-strike put.
- The stock is readily available for short sale, so there's no so-called "hard-to-borrow" cost. (Not sure what that means? Refer to this primer on short selling.)

The exercise decision may depend on how much it would cost to carry the position to expiration relative to the put's lost extrinsic value—remember, when a trader exercises an option, they lose any remaining time value. The cost-of-carry formula is essentially the strike price (the price at which a trader has the right to sell the stock) times the interest rate times the time period. And because interest rates are annualized, the trader needs to divide the number of days until expiration by the number of days in a year—generally rounded down to 360.

If the amount of extrinsic value left in the option, as evidenced by the price of the corresponding call option, is less than the expected interest between now and expiration, the 125-strike put might be a good candidate for early exercise.

Let's plug in the values:

**$125 × 100 × 6% × 8/360 = $16.67**

That $16.67 (assumes standard contract overlying 100 shares of XYX) in interest is greater than the call's $1.00 ($0.01 × 100 shares) value. In this example, the long-put holder could consider exercising the XYZ 125-strike put, especially if they'd like to take a short position in the stock. So, for example, if the trader is long 100 shares of XYZ and long the 125 put against it, and they planned to exercise anyway, it might be better to do it now and earn the extra interest rather than wait eight days.

Another options strategy where early exercise comes into play is if a trader has a conversion strategy—a delta-neutral strategy consisting of a long stock paired with a short stock equivalent (short call + long put) of the same strike and expiration date. If rates are increasing, it may become cheaper to exit the position by exercising the long put and purchasing the short call than to carry the position.

## Rho matters even when rates are low

During periods when the market's interest rate is low, it's easy for traders to overlook rho. They shouldn't, though. Even when rates are low, rho can affect an option holder's decision to exercise before the expiration date. If the trader is short an in-the-money (ITM) option, meaning the option has a favorable strike price compared to the current market price of the underlying asset, they're more likely to get assigned before expiration when rho comes into play.

## Bottom line

Options are complex, and that's partly because of their flexibility. They have different uses depending on various market factors on any given day, including how interest rates influence options pricing, or rho, which can help traders make better exercise or assignment decisions.