1 Other names applied to this model include the martingale measure, risk-neutral probability, or hedging model.
2 OAS is included in MBS models because of sub-optimal exercise of the prepayment option. Financial economists typically model prepayment behavior with a flexible functional form, but the function never fits the behavior exactly; rather, there is always noise surrounding the estimates. Even though the deviations may be independent and symmetric the impact of the deviations is asymmetric to the investor. For example, surprise prepayment when interest rates are low leads to greater cost due toworsened reinvestment opportunities than when interest rates are high. Moreover, OAS arises because of the asymmetric costs of modeling error.
3 These models are too simplistic for pricing corporate bonds in practice. This model is, however, sufficient to illustrate the key concepts that are relevant to this discussion. Extensions that accommodate the complexities of these bonds include Duffee (1999), Duffie and Lando (2000), Duffie and Singleton (1999), Jarrow and Turnbull (1995), Kim, Ramaswamy, and Sundaresan (1993).
The underlying assets include plant and equipment, franchise value, customer relationships, etc. These parts of the asset value are difficult to observe and price. Nonetheless, the model has still been used successfully in pricing credit derivatives. The inability to observe the value of assets is less of a concern for insurance liabilities where the vast majority of assets are financial and easily observed.
Consider a simple non-financial company with equity holders and a single bond issuance. Note that the bondholders are entitled to the value of the assets up to the face amount of the debt and that the equity holders are entitled to the value of the assets in excess of that amount. This means that we can view equity as a call option on the assets with a strike price equal to the face value of the debt. For a zero coupon bond, in a world of constant interest rates, the value of equity is given by the Black-Scholes call option formula. Extensions for coupon bonds have also been derived. The value of the bond is given by subtracting the equity call option from the underlying assets. Thus, the bondholders are described as owning the assets and selling a call option to equity holders.