Option Value and Zero Volatility Spreads

Teri Geske
Senior Vice President, Product Development

Options are said to have both intrinsic and time value, where the intrinsic value is the amount the option holder would realize if the option were exercised today. In many cases, the intrinsic value is zero. A simple example of this is a currently callable corporate bond priced below its call price. The intrinsic value of the call is zero, but there is some value to the option as long as one assumes interest rates can deviate from current levels into the future. We can also say that the longer the time to the expiration date, the more time value there is in the option (given a particular term structure of volatility) because there is more opportunity for the option to end up in the money prior to the expiration date.

In this example, although the bond's price of $101.938 is below its call price of $102.760, the call option has a time value of $5.39. When we extend the bond's maturity date (and thus the expiration date of the option) by five years, the option value increases to $9.557.

Prepayment Options

The prepayment option in a mortgage may be thought of as a combination of a call option and a put option, since homeowners have the right to accelerate prepayments, or call their mortgages away from investors when rates fall, and can reduce (or even stop) prepayments when rates rise, thereby forcing the investor to hold an asset whose value has declined. (Unfortunately, since homeowners do not necessarily exercise these options in an economically optimal way they are difficult to value; this issue is addressed in the Prepayment Uncertainty measure we discussed in last month's newsletter).

Both the call and put options embedded in a mortgage-backed security have time value as long as we assume some degree of volatility going forward. That time value will change in response to movements in interest rates (and to changes in volatility estimates, which is described by another risk measure, Vega). As rates fall, the time value of the call option increases, limiting the price increase that a falling rate environment would otherwise produce. As rates increase, the time value of the call option decreases, which cushions the price decline caused by the increase in yield levels. However, just as the value of the call declines when rates rise, the time value of the homeowner's put option increases, somewhat offsetting the benefit derived from the decline in the value of the call. Depending upon the type of collateral, the impact of the change in either the call value or put value will dominate. Both options are reflected in the OAS, which is compared to the ZVO to measure the total time value of the prepayment option. If we were to set volatility to zero, the ZVO and the OAS would be the same.

CMOs are similarly affected, with the added complexity of the deal structure. VADM tranches and PACs with short average lives are not particularly sensitive to changes in the time value of the prepayment option because their cashflows are stable. We would therefore expect there to be little difference between the Zero Volatility Spread and the OAS for these instruments, since interest rate volatility in the future will have little impact on the pattern of cashflows received by the investor.

Interest Rate Caps

The price of a CMO floater with a lifetime cap may be greatly affected by changes in the time value of the option the cap represents. As rates rise, even if the coupon has not yet reached the lifetime cap rate the time value of the cap which the investor has shorted increases, because there is a higher probability that over the remaining life of the bond the coupon formula will exceed the cap rate. This can cause the effective duration of a CMO floater to lengthen considerably in a rising rate environment.

The time value of a cap is also impacted by the slope of the yield curve. For CMO floaters with long average lives, and for Adjustable Rate Mortgages, a positively sloped yield curve implies that a short term index, such as 1 month LIBOR or the 1 Year CMT, will rise into the future. If the curve steepens, the likelihood that a coupon based on one of these rates will ultimately encounter its lifetime cap increases, thereby increasing the time value of the embedded option. Even though an ARM's coupon may be at or near its fully indexed value and below its lifetime cap, the ARM's effective duration can be substantially greater than the time to the next reset date, indicating that there is much time value left in the embedded lifetime cap. The difference between the ARM's Zero Volatility Spread and its OAS measures that value.