Pricing in Interest Rate Moves

In the same way that volatility can get priced in to an option’s value, so can the interest rate. When interest rates are expected to rise or fall, those expectations can be reflected in the prices of options. Say current interest rates are at 8 percent, but the Fed has announced that the economy is growing at too fast of a pace and that it may raise interest rates at the next Federal Open Market Committee meeting. Analysts expect more rate hikes to follow.

The options with expiration dates falling after the date of the expected rate hikes will have higher interest rates priced in. In this situation,the higher interest rates in the longer-dated options will be evident when entering parameters into the model.Take options on Already Been Chewed Bubblegum Corp. (ABC). A trader, Kyle, enters parameters into the model for ABC options and notices that the prices don’t line up.

To get the theoretical values of the ATM calls for all the expiration months to sit in the middle of the actual market values, Kyle may have to tinker with the interest rate inputs.Assume the following markets for the ATM 70-strike calls in ABC options:Entering the known inputs for strike price, stock price, time to expiration,volatility, and dividend and using an 8 percent interest rate yields the following theoretical values for ABC options:

The theoretical values, in bold type, are those that don’t line up in the middle of the call and put markets. These values are wrong. The call theoretical values are too low, and the put theoretical values are too high. They are the product of an interest rate that is too low being applied to the model.To generate values that are indicative of market prices, Kyle must change the interest input to the pricing model to reflect the market’s expectations of future interest rate changes.Using new values for the interest rate yields the following new values:

After recalculating, the theoretical values line up in the middle of the call and put markets. Using higher interest rates for the longer expirations raises the call values and lowers the put values for these months. These interest rates were inferred from, or backed out of, the option-market prices by use of the option-pricing model. In practice, it may take some trial and error to find the correct interest values to use.In times of interest rate uncertainty, rho can be an important factor in determining which strategy to select.

When rates are generally expected to continue to rise or fall over time, they are normally priced in to the options,as shown in the previous example. When there is no consensus among analysts and traders, the rates that are priced in may change as economic data are made available. This can cause a revision of option values. In long-term options that have higher rhos, this is a bona fide risk. Short-term options are a safer play in this environment.

But as all traders know, risk also implies opportunity.Trading Rho:While it’s possible to trade rho, most traders forgo this niche for more dynamic strategies with greater profitability. The effects of rho are often overshadowed by the more profound effects of the other greeks. The opportunity to profit from rho is outweighed by other risks. For most traders,rho is hardly ever even looked at.

Because LEAPS have higher rho values than corresponding short-term options, it makes sense that these instruments would be appropriate for interest-rate plays. But even with LEAPS, rho exposure usually pales in comparison with that of delta, theta, and vega.It is not uncommon for the rho of a long-term option to be 5 to 8
percent of the option’s value. For example, Exhibit 7.2 shows a two-year LEAPS on a $70 stock with the following pricing-model inputs and outputs:The rho is 10.793, or about 5.8 percent of the call value.

That means a 25-basis-point rise in rates contributes to only a 20-cent profit on the call.That’s only about 1.5 percent of the call’s value. On one hand, 1.5 percent is not a very big profit on a trade. On the other hand, if there are more rate rises at following Fed meetings, the trader can expect further gains on rho.Even if the trader is compelled to wait until the next Fed meeting to make another $0.20—or less, as rho will get smaller as time passes—from a second 25-basis-point rate increase, other influences will diminish rho’s significance.

If over the six-week period between Fed meetings, the underlying declines by just $0.60, the $0.40 that the trader hoped to make on rho is wiped out by delta loss. With the share price $0.60 lower, the 0.760 delta costs the trade about $0.46. Furthermore, the passing of six weeks (42 days) will lead to a loss of about $0.55 from time decay because of the 20.013 theta. There is also the risk from the fat vegas associated with LEAPS. A 1.5 percent drop in implied volatility completely negates any hopes of rho profits.