**Dividends and Interest Rates**

Jim Graham

While the math behind options pricing models may seem complex, the underlying concepts are not. The variables used in these models are price (of the underlying asset), volatility, time, dividends, and interest rates. The first three of these deservedly get most of the attention because they have the largest effect on option prices. But it is still important to understand the effect dividends and interest rates have on options prices.

The original Black-Scholes pricing model was designed to evaluate European-style options where early exercise is not permitted. American-style options give you the right of early exercise, which theoretically makes an American-style option more valuable than a similar European-style option.

Black and Scholes never addressed the problem how much the right of early exercise might be worth but the majority of exchange-traded options carry with them the right of early exercise. But since their pioneering work, many modified Black-Scholes models have since been developed to allow the accurate evaluation of American-style options.

**Interest Rates**

Let's first look at the effect of interest rates on option prices. An increase in interest rates will tend to drive up call premiums and decrease put premiums. To understand why this is, think about the effect of interest rates in the context of comparing an option position to simply owning the stock. Since it is much cheaper to buy a call option than 100 shares of the stock, the call buyer is willing to pay more for the option when rates are relatively high, since he can invest the difference in capital requirements between the two positions.

Interest rates have been low in recent years relative to historic rates in the United States When short-term rates were around 1.5% to 2.0%, interest rates had a minimal effect on option prices. Now that the Federal Reserve has followed a policy monetary tightening by steadily increasing the discount rate over the past couple years, short term rates are now closer to 5%.

*page 2*

Let’s look at an example by comparing the fair value of an option at the current 5% rate relative to what its value would be if short-term interest rates were still at 1.5% using the September at-the-money options with 46 days left to expiration in the Spyder exchange traded fund (Symbol: SPY), which tracks the S&P 500 index.

Let’s start with the September at-the-money call option, which has a current fair value $2.73. Remember that an increase in interest rates will drive up call premiums, while a decrease in rates will drive down call premiums. Changing the current interest rate used in the option pricing model from 5% to 1.5%, OptionVue 6 shows the call option would only be worth $2.45 at the lower rate. That means the option would be worth 28 cents less, a decrease in value of more than 10%, at the lower interest rate.

The September at-the-money (ATM) put shows a current fair value of $2.35. Remember, changes in interest rates have the opposite effect on put options as call options, so a decrease in interest rates should drive up put premiums. After changing the current interest rate used in the option pricing model from 5% to 1.5%, OptionVue 6 shows the put option would be worth $2.62 at the lower rate, an increase in value of 27 cents.

One of the derivative parameters, known collectively as the “Greeks”, allows you to see how sensitive the value of an option is to a change in interest rates: Rho. Rho tells you how much the value of an option will change due to a 1% increase in interest rates and is always positive for calls and negative for puts. In the above examples, the at-the-money call has a Rho of 7.96 and the put has a Rho of -7.93. That means a 1% increase in interest rates would cause the call option to increase in value by 7.96 cents and the put ot decrease in value by 7.93 cents.

Interest rates are an important factor in determining whether to exercise a put option early. A stock 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 since each individual 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 becomes sufficiently great.

*page 3*

**The Effect of Dividends**

Cash dividends affect option prices through their effect on the underlying stock price. Because the stock price is expected to drop by the amount of the dividend on the ex-dividend date, high cash dividends imply lower call premiums and higher put premiums.

While the stock price itself usually undergoes a single adjustment by the amount of the dividend, option prices factor in the anticipation of dividends in the weeks and months before they are announced. Because an index contains many stocks, the total projected dividends of all component stocks, adjusted for their weight in the index, is used to determine the fair value of an index option.

Both buyers and sellers of options need to consider the impact of dividends on the option price. Whoever owns the stock as of the ex-dividend date receives the cash dividend, so owners of call options may exercise in-the-money options early to capture the cash dividend. Therefore dividends are critical in determining whether it makes sense to exercise a stock call option early. Early exercise usually makes sense for a call option only if the stock is expected to pay a dividend prior to the expiration date.

There are a couple minor exceptions. If some important news was announced after the close of option trading, but before the OCC deadline for notification of exercise, the owner of a call option may exercise it to capture the likely rise in the stock price at the next day's open. Also, if the owner of the call option needs to buy so much stock that it will move the stock price significantly; he may find it cheaper to simply exercise his calls. An example of this would be when a new stock is added to an index, and the manager of a fund tied to that index needs to rebalance his holdings by buying the stock.

Let’s look at the effect dividends have on option prices by looking at a stock that pays a large dividend, and then comparing the current option values to what they would be if the stock did not pay a dividend. For this example I will use Altria (Symbol: MO), which is expected to pay an 80 cent dividend on September 13 (with underlying stock price currently at $80), and the ATM options with an expiration date of September 16, which is 46 days from today.

The ATM September 80 call currently shows a fair value of $2.45, while the September 80 put shows a fair value of $2.49. Removing the expected dividends should increase the value of the call and decrease the value of the put, and that is in fact what happens. Without the dividend payment (and subsequent 80 cent drop in the underlying price on September 13) the call option would currently be worth $2.56, an increase in value of 11 cents. The ATM September would be worth only $2.26, a decrease in value of 23 cents.

*page 4*

**Conclusion**

While interest rates and dividends are not the primary factors affecting an option’s price, all option traders have to be aware of their effect on option prices. In fact, the primary drawback I have seen to most of the web-based option trading tools available is that they tend to use a simple Black Scholes model and do not properly adjust for these factors.

The impact of not adjusting for early exercise can be large, causing software that does not take it into account to show that an option is over- or under-valued by as much as 15%. When competing in the options market against sophisticated investors and professional market makers, it only makes sense to use the most accurate modeling tools available.