Option-adjusted spread

Option-adjusted spread The OAS is used for bonds with embedded options. This spread is calculated as the difference between the Z-spread and option value expressed in basis points. 

Kopprasch, R., 1994. Option-adjusted spread analysis going down the wrong path Financial Analysts Journal, 121-135. 

As introduced in Chapter 8, the most suitable measure of return for bonds with embedded options is known as option-adjusted spread or OAS. In this chapter, we show the analysis of bonds with embedded options, with particular focus on pricing methodology. 

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. 

Consider also that the optirai element can be included in the interest rate. In Section 11.1.3, we explained the concept of option-adjusted spread. Given the bond s price, we can calculate the spread including the option element. This is performed with a binomial tree used for pricing an option-free bond. 

In other words, if the callable bond price is 103.82, we set this price in the binomial tree shown in Figure 11.9 and through an iterative procedure, we find an option-adjusted spread that matches the price sought. In our case, the option-adjusted spread is around 630 bps over the risk-free yield curve (Figure 11.12). 

FIGURE 11.12 The binomial price tree with the option-adjusted spread. 

Windas, T., 1993. An introduction to option-adjusted spread analysis, first ed. Bloomberg Press. 

The spread measures discussed thus far fail to recognize any embedded options that may be present in a bond. A spread measure that takes into account embedded options is the option-adjusted spread or OAS. A discussion of how this spread measure is computed is beyond the scope of this chapter. Basically, it is a byproduct of a model that is used for val-... 

The problem is, what spread is assumed to change There are three measures that are commonly used for fixed-rate bonds nominal spread, zero-volatility spread, and option-adjusted spread. Each of these spread measures were defined earlier in this book. 

Finally, the option-adjusted spread (OAS) is the constant spread that, when added to all the rates on the interest rate tree, will make the theoretical value equal to the market price. Spread duration based on OAS can be interpreted as the approximate percentage change in price of a nongovernment for a 100 basis point change in the OAS, holding the government rate constant. 

If a bond s actual redemption date differs from the assumed one, its return computed this way is meaningless. The market, therefore, prefers to use other methods to calculate the return of callable bonds. The most common method is option-adjusted spread, or OAS, analysis. Although the discussion in this chapter centers on callable bonds, the principles enunciated apply to all bonds with embedded options. 

Windas, T. 1996. An Introduction to Option-Adjusted Spread Analysis. Princeton Bloomberg Press. 

A better measure of the relative value of a bond with an embedded option is the constant spread that, when added to all the short rates in the binomial tree, makes the bond s theoretical (model-derived) price equal to its observed market price. The constant spread that satisfies this requirement is the option-adjusted spread. It is option adjusted because it refiects the option feature attached to the bond. 

The modified duration and convexity methods we have described are only suitable for use in the analysis of conventional fixed-income instruments with known fixed cash flows and maturity dates. They are not satisfactory for use with bonds that contain embedded options such as callable bonds or instruments with unknown final redemption dates such as mortgage-backed bonds. For these and other bonds that exhibit uncertainties in their cash flow pattern and redemption date, so-called option-adjusted measures are used. The most common of these is option-adjusted spread (OAS) and option-adjusted duration (OAD). The techniques were developed to allow for the uncertain cash flow structure of non-vanilla fixed-income instruments, and model the effect of the option element of such bonds. 

A complete description of option-adjusted spread is outside of the scope of this book here we present an overview of the basic concepts. An excellent in-depth account of this technique is given by Windas (1993). 

Option-adjusted spread analysis uses simulated interest rate paths as part of its calculation of bond yield and convexity. Therefore an OAS model is a stochastic model. The OAS refers to the yield spread between a callable or mortgage-backed bond and a government benchmark bond. The government bond chosen ideally will have similar coupon and duration values. 

Applying this approach to the model in Figure 12.1, under the 0 percent volatility, the spread implied by the price of 97.00 is, unsurprisingly, 67.6 basis points. In the 25 percent volatility environment, however, this spread results in a price of 97.296, which is higher than the observed price. This suggests the spread is too low. By iteration, we find that the spread that generates a price of 97.00 is 89.76 basis points, which is the bonds option-adjusted spread. This is shown below. 

Chen, S. 1996. Understanding Option-Adjusted Spreads The Implied Prepayment Wy ot es s. Journal of Portfolio Management, Summer, 104—113. 

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