The effect of interest rates on options prices—rho—is sometimes considered the forgotten greek. But interest rates matter, especially when deciding when to exercise options positions.
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- Relative to other options risks such as delta and theta, changes in interest rates (rho) tend to be less dynamic, so they may get less attention
In general, an increase in interest rates will drive up call premiums and cause put premiums to decrease
Interest rates affect exercise decisions for American-style options
If you’ve ever traded options—or you’ve at least explored options education—you know that options are flexible, with lots of available strategies depending on your objectives and risk tolerance. Options can be used to generate income, to hedge and help protect existing positions, and to speculate in a capital-efficient way.
But options are risky. Once you’re familiar with how options prices are derived, you’ll know that there are a few essential components, and each component has its own risk metric (known collectively as “the greeks”). Option traders monitor these greeks because any changes will affect their positions’ theoretical value.
Greeks are risk measures that can help you choose which options to buy and sell and measure the overall risk of a portfolio. Here are some of the factors (and greeks) that affect options prices:
- The price of the underlying stock (delta is the position’s sensitivity to changes in the underlying stock price)
- The rate of change of delta (gamma is the sensitivity of delta to changes in the underlying price)
- The time left until expiration (theta is sensitivity to time)
- The implied volatility of the security (vega is sensitivity to changes in implied volatility)
- The prevailing “risk-free” interest rate (rho is sensitivity to changes in interest rates)
As the price of the underlying asset moves, so does delta; so much, in fact, that the rate of change of delta has its own greek risk—gamma. Also, it’s worth noting that dividends affect options prices, but some options pricing models lump dividends in with the interest calculation. Dividend yield is input in option pricing models because it affects the forward price of the underlying security. Delta, gamma theta, and vega are the greeks that most option buyers are most concerned with.
Rho: The Forgotten Greek
Of these risks, rho typically gets the least attention. Although interest rates fluctuate along with everything else, they move much more slowly and with less regularity than the others. And in a low interest rate environment, combined with the fact that most options traded are short term—expiring in one month or less—interest rates often have less overall impact than other risks, at least on a day-to-day basis.
But that doesn’t mean interest rates should be ignored. It’s still important to understand how interest rates affect options prices, if only because they can affect the decision to exercise an option before its expiration date. This also means that, if you’re short an in-the-money (ITM) option, you might get assigned before expiration.
Remember, most listed options in the United States are American-style options, which may be exercised anytime before the expiration date.
The Interest Rate Effect
In general, and with all else equal, an increase in interest rates will drive up call premiums and cause put premiums to decrease. Perhaps the easiest way to understand why is to compare owning a stock versus holding an options position, while remembering that a higher interest rate is a benefit to a saver and a detriment to a borrower. When you buy a stock, you must pay for it, which reduces your available cash. Someone who sells a stock—whether to liquidate a long position or to establish a short sale position—takes in cash.
Each standard equity options contract represents 100 shares of the underlying stock. Because it’s much cheaper to buy a call options contract than it is to buy 100 shares of stock, call buyers are willing to pay more for call options when rates are relatively high because they can invest the difference. A call seller, on the other hand, would want additional incentive to sell a call option (versus selling the stock outright) if interest rates are high in order to compensate for forgoing the cash from the stock sale.
In other words, the higher call options premium when interest rates are high is the “opportunity cost” of forgone interest.
It’s the similar—but reverse—argument in the case of put options. A long put can be considered as a substitute for short 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 there would be more forgone interest by owning a put versus selling the stock.
Time to Exercise?
Aside from dividends (which sometimes require their own exercise decision tree), interest rates are the determining factor in early exercise decisions for American-style options.
For example, a put option becomes an early exercise candidate anytime the interest that could be earned on the proceeds from the sale of the stock at the strike price is large enough. Determining exactly when this happens is difficult, because each position has different opportunity costs, but it does mean that early exercise for a stock put option can be optimal at any time, provided the interest earned is great enough.
To illustrate, suppose the following conditions:
- Shares of XYZ are trading at $100 per share.
- The quarterly dividend is zero, i.e., there’s no expected dividend between now and expiration.
- You’re long the 125-strike put expiring in eight days.
- Interest rates recently increased to 2%.
- The XYZ 125 calls are trading for $0.01—which put-call parity tells us means there’s a penny of extrinsic value (aka, 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 depends on how much it would cost to carry the position to expiration, relative to the lost extrinsic value of the put (remember, when you exercise an option, you lose any remaining time value). The cost-of-carry formula is essentially the strike price (the price at which you have an option to sell the stock), times the interest rate, times the time period. And because interest rates are annualized, you need to divide the number of days until expiration by the number of days in a year—generally rounded to 360.
Cost of carry = strike price x interest rate x days to expiration/calendar days
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 is a good candidate for early exercise.
Let’s plug in the values:
$125 x 2% x 8/360 = $0.05
In this example, the long put holder would consider exercising the XYZ 125-strike put, especially if they’d like to take a short position in the stock. So, for example, if you’re long 100 shares of XYZ and long the 125 put against it, and you planned to exercise anyway, it would be better to do it now rather than wait eight days.
Another options strategy where early exercise comes into play is if a client has a conversion strategy—a delta-neutral strategy consisting of long stock offset with a short stock equivalent (a short call + long put) of the same strike and expiration date. If rates are increasing, it may become cheaper to exit the position through exercise of the long put and purchase of the short call than to carry the position.
A final note regarding “hard to borrow” (HTB) positions. The same equation can be used for HTB stocks, but you’d need to use a different rate in the calculation. Because HTB shares require the broker’s stock loan department to locate and maintain these positions, a fee is assessed to the borrower based on the dollar value of the short position times the current rate being charged on the short stock. And remember, the HTB rate can vary from day to day depending on market conditions.
To the uninitiated trader, options can seem complex. But these intricacies are part of what makes options flexible and useful for a number of different strategies. Understanding the relationship of calls and puts to changing market dynamics—including interest rates—can help you make better trading decisions, such as determining when to exercise a long options position or anticipating assignment of a short position.