How Interest Rate Movements Affect Options Prices

Option traders spend a lot of time calculating 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, time to expiration, implied volatility, and interest rates.

Of these metrics, interest rates typically get the least attention. Although interest rates fluctuate along with everything else, they typically move much more slowly and with less regularity than other factors. Also, many option traders trade short-dated options—expiring in one month or less. And generally, the shorter the time to expiration, the less options respond to changes in interest rates.

Still, interest rate shifts directly impact options pricing, early exercise decisions, and assignment risk. This makes rho—which measures an option's sensitivity to changes in the risk-free rate of interest—important to understand.

Positive rho means the option will increase in value when interest rates go up, while negative rho means the option will decrease 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 can influence the outcome of trading strategies.

In general, with all else being equal, long call options increase in value as interest rates rise, while long put options decrease in value. This means long call options have positive rho and long put options have negative rho. The rho value itself represents the theoretical dollar change in an option's price for a one-percentage-point change in interest rates. For example, if an option's rho is –0.30, the option price would decline by $0.30 if interest rates increased from 4% to 5%. (Note that a 100-basis-point rate hike is uncommon, occurring just once since 1994.)

To understand how interest rate changes can impact option prices and option traders' decisions, it's important to think about rates' effects on borrowing costs and returns more generally. Recall that higher interest rates mean potentially better returns from cash equivalents, such as short-term Treasury securities, but also higher borrowing costs for margin loans and other forms of debt.

As a result, if an option trader wants to buy $100,000 worth of stock on margin, the cost to use margin could be three times higher when interest rates are at 6% instead of 2%. With a long call option, a trader can attempt to benefit from a potential increase in the stock price without paying margin interest. Therefore, in higher-interest-rate environments, some traders may choose the increased risk of buying call options to avoid the increased margin cost of direct stock ownership.

At the same time, when rates are higher, covered call sellers could potentially earn more interest on cash proceeds by selling the underlying stock rather than writing a call against it. As a result, covered call sellers may demand a higher premium to justify forgoing the additional interest income.

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. Some institutional 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 owning the put can mean forgoing interest that could have been earned on proceeds from a short stock sale. This is only part of the picture, however, as interest rates can also impact option prices through the costs of carrying and hedging positions for both investors and market makers.

Still, this demonstrates why the net effect of rising interest rates—through associated higher margin costs and increased cash equivalent returns—is higher call premiums and lower put premiums.

In addition to dividends (which often require their own exercise decision tree), interest rates are a major determining factor in early exercise decisions for American-style options. 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 cash received from exercising the option and shorting the stock at the strike price is large enough to make a difference to the trader. Traders will determine that threshold differently based on their own opportunity costs and risk tolerance. In general, though, higher interest rates mean more positions will reach that "large enough" point.

Consider the following example:

•    Shares of ZYX are trading at $100 per share.
•    There's no expected dividend between now and expiration. 
•    A trader is long one 125-strike put expiring in eight days. (This is a standard contract, representing 100 shares of ZYX.)   
•    Interest rates recently increased to 6%. 
•    ZYX 125 calls are trading for $0.01—meaning there's a penny of extrinsic value (a.k.a. time value) in the 125-strike put, per put-call parity.
•    The 125-strike put is trading at $25.01, representing $25 in intrinsic value and $0.01 in extrinsic value. 
•    The stock is readily available for short sale, so there's no so-called "hard-to-borrow" cost.

In this case, the trader's exercise decision may depend on how much it would cost to carry the position to expiration relative to the put's lost extrinsic value—when a trader exercises an option, they lose any remaining extrinsic value. The cost-of-carry formula is essentially the strike price (the price at which a trader has the right to sell the stock) multiplied by the contract multiplier of 100 multiplied by the interest rate multiplied by the time period. And because interest rates are annualized, the trader should divide the number of days until expiration by the number of days in a year—generally rounded to 360 under a standard money-market convention.

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 x 100 x 6% x 8/360 = $16.67

The $16.67 in interest is greater than the call's $1 ($0.01 x 100 shares) extrinsic value. In this example, the long put holder could consider exercising the ZYX 125-strike put, especially if they'd like to take a short position in the stock.

Additionally, if the trader is long 100 shares of ZYX and long the 125 put against it (a protective put), they might opt to exercise their put prior to expiration, effectively closing both positions. This could allow them to earn interest on the cash proceeds rather than waiting until expiration.

Another options strategy where early exercise comes into play is a conversion strategy—a delta-neutral arbitrage strategy consisting of a long stock position paired with a synthetic short stock position (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. This allows the trader to sell the stock at the strike price and collect the cash (earning interest on the proceeds), while buying back the short call. The higher the interest rate, the more likely the interest amount outweighs the long put's remaining extrinsic value, making early exercise worthwhile.

During periods when interest rates are low, it's easy for traders to overlook rho. However, rho can affect an option holder's decision to exercise before expiration at any time. For example, if a trader is short an in-the-money (ITM) put 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 if interest rates (and therefore rho) rise. Or, if a trader is short an ITM call option, they're more likely to get assigned before expiration when rates and rho fall.

While rho can be difficult to understand at first, it can potentially help traders gauge interest rates' influence on options prices and trading strategies. By understanding this greek, traders can potentially make more informed exercise decisions and more accurately assess the risk of early assignment.