Embedded options risks

The risk-free rate affects both elements, option-free bond and embedded option. Conversely, the credit spread is applied to the risk-free rate in order to find the price of the option-free bond. If the credit spread is also included into the option pricing model, the option value rises. For instance, consider the scenario in which the risk-free rate is 1.04% and the option value is 0.46. If the risk-free rate is 7.04%, then the option value increases to 0.66. Figure 9.16 shows the effect of a different interest rate level. 

The option-adjusted spread (OAS) is the most important measure of risk for bonds with embedded options. It is the average spread required over the yield curve in order to take into account the embedded option element. This is, therefore, the difference between the yield of a bond with embedded option and a government benchmark bond. The spread incorporates the future views of interest rates and it can be determined with an iterative procedure in which the market price obtained by the pricing model is equal to expected cash flow payments (coupons and principal). Also a Monte Carlo simulation may be implemented in order to generate an interest rate path. Note that the option-adjusted spread is influenced by the parameters implemented into the valuation model as the yield curve, but above all by the volatility level assumed. This is referred to volatility dependent. The higher the volatility, the lower the option-adjusted spread for a callable bond and the higher for a putable bond. 

The binomial tree model evaluates the return of a bond with embedded option by adding a spread to the risk-free yield curve. Generally, the price obtained by the model is compared to the one exchanged in the market. If the theoretical price is different, the model can be calibrated with three key elements. The first ones are the volatility and drift factor. They allow to calibrate the model interest rate path in order to obtain the equality with the market yield curve. The third one is the spread applied over the yield curve. Generally, when volatility and drift are correctly calibrated, the last element to select in order to obtain the market parity is the spread. Conventionally, banks define it in the following way ... 

As noted, a bond may contain an embedded option which permits the issuer to call or retire all or part of the issue before the maturity date. The bondholder, in effect, is the writer of the call option. From the bondholder s perspective, there are three disadvantages of the embedded call option. First, relative to bond that is option-free, the call option introduces uncertainty into the cash flow pattern. Second, since the issuer is more likely to call the bond when interest rates have fallen, if the bond is called, then the bondholder must reinvest the proceeds received at the lower interest rates. Third, a callable bond s upside potential is reduced because the bond price will not rise above the price at which the issuer can call the bond. Collectively, these three disadvantages are referred to as call risk. MBS and ABS that are securitized by loans where the borrower has the option to prepay are exposed to similar risks. This is called prepayment risk, which is discussed in Chapter 11. 

Thus far our coverage of valuation has been on fixed-rate coupon bonds. In this section we look at how to value credit-risky floaters. We begin our valuation discussion with the simplest possible case—a default risk-free floater with no embedded options. Suppose the floater pays cash flows quarterly and the coupon formula is 3-month LIBOR flat (i.e., the quoted margin is zero). The coupon reset and payment dates are assumed to coincide. Under these idealized circumstances, the floater s price will always equal par on the coupon reset dates. This result holds because the floater s new coupon rate is always reset to reflect the current market rate (e.g., 3-month LIBOR). Accordingly, on each coupon reset date, any change in interest rates (via the reference rate) is also reflected in the size of the floater s coupon payment. 

The discussion is easily expanded to include risky floaters (e.g., corporate floaters) without a call feature or other embedded options. A floater pays a spread above the reference rate (i.e., the quoted margin) to compensate the investor for the risks (e.g., default, liquidity, etc.) associated with this security. The quoted margin is established on the floater s issue date and is fixed to maturity. If the market s evaluation of the risk of holding the floater does not change, the risky floater will be repriced to par on each coupon reset date just as with the default-free floater. This result holds as long as the issuer s risk can be characterized by a constant markup over the risk-free rate. 

This discussion covers the main factors affecting bond returns in the European fixed income market, namely, the random fluctuations of interest rates and bond yield spreads, the risk of an obligor defaulting on its debt, or issuer-specific risk, and currency risk. There are also other, more subtle sources of risk. Some bonds such as mortgage-backed and asset-backed securities are exposed to prepayment risk, but such instruments still represent a small fraction of the total outstanding European debt. Bonds with embedded options are exposed to volatility risk. However, it is not apparent that this risk is significant outside derivatives markets. 

All bond instruments are characterized by the promise to pay a stream of future cash flows. The term structure of interest rates and associated discount function is crucial to the valuation of any debt security and underpins any valuation framework. Armed with the term structure, we can value any bond, assuming it is liquid and default-free, by breaking it down into a set of cash flows and valuing each cash flow with the appropriate discount factor. Further characteristics of any bond, such as an element of default risk or embedded option, are valued incrementally over its discounted cash flow valuation. 

Consider the following example. We assume to have two hypothetical bonds, a treasury bond and a callable bond. Both bonds have the same maturity of 5 years and pay semiannual coupons, respectively, of 2.4% and 5.5%. We perform a valuation in which we assume a credit spread of 300 basis points and an OAS spread of 400 basis points above the yield curve. Table 11.1 illustrates the prices of a treasury bond, conventional bond and callable bond. In particular, considering only the credit spread we find the price of a conventional bond or option-free bond. Its price is 106.81. To pricing a callable bond, we add the OAS spread over the risk-free yield curve. The price of this last bond is 99.02. We can now see that the OAS spread underlines the embedded call option of the callable bond. It is equal to 106.81-99.02, or 7.79. In Section 11.2.3, we will explain the pricing of a callable bond with the OAS methodology adopting a binomial tree. 

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