Valuing Mortgage‐Backed and Asset‐Backed Securities

Abstract

The valuing (or pricing) of a bond without an embedded option (that is, an option-free bond) is straightforward. The value is equal to the present value of the expected cash flows. Ignoring defaults, for an option-free bond the cash flows are known and consist of the periodic interest payments and principal at the maturity date. The interest or discount rates for computing the present value of the cash flows begin with the spot rates for a benchmark security and to those rates an appropriate spread is added. Moving from valuing option-free bonds to corporate bonds and agency debentures with embedded options is not simple. The interest rate–sensitive options that can be embedded into these bonds are call options, put options, accelerated sinking provisions, and, for floating-rate securities, caps on the interest rate. The reason valuation is complicated is that the embedded options must be taken into account and the theoretical option-free value of the bond must be adjusted accordingly. The technique typically used for valuing corporate bonds and agency debentures with embedded options is the lattice method. Mortgage-backed securities also have embedded options: The right of the borrowers in a loan pool to prepay their mortgage loan. However, because future cash flows for a loan pool are sensitive to not only the current interest rate but the history of rates since the loans were originated, the lattice method which is solved using backward induction cannot be employed. Instead, the most common methodology used for valuing mortgage-backed securities and mortgage-related asset-backed securities is the Monte Carlo simulation model. Other types of asset-backed securities are straightforward to value. In addition to the complications in valuing mortgage-backed securities and mortgage-related asset-backed securities, there is the difficulty in estimating their price sensitivity to changes in interest rates (that is, duration and convexity). The Monte Carlo simulation model can be used to compute the effective duration of these securities. This duration measures takes into consideration how a change in interest rates can impact a security's cash flow. Keywords: asset-backed securities (ABS); mortgage-backed securities (MBS); Monte Carlo simulation model; cash-flow yield; reinvestment risk; interest rate risk; modeling risk; nominal spread; zero-volatility spread (Z-spread); option-adjusted spread (OAS); theoretical value; option cost; effective duration; option-adjusted duration; effective convexity; positive convexity; negative convexity