Variable Rate MBS

This article presents a model for computing the fair value of a variable rate BMS (VRMBS). The scope of this study is restricted to a VRMBS that has no option-like features such as caps, floors, or cancellation options. Also, since the MBS coupon is floating, it is reasonable to assume that prepayment speeds are relatively insensitive to interest rate movements.

The model characterizes the VRMBS cashflows using forward rates computed using fixed spreads off an interest rate curve. Prepayments due to turnover, default, and conversions are modeled using constant speeds. The VRMBS cashflows are discounted using a valuation yield curve, whose definition is left unspecified.

The model computes the maximum possible loss for a given confidence level for a single swap. It also uses for a given volatility and confidence level, an appropriate downward shift in the swap curve over time. It then computes the future cashflows, including the reinvestment income, of the swap. The projected fair values of the swap are computed by discounting the cashflows using the downward shifted yield curve.

Unlike the regular pricing model that uses six tranches corresponding to the maturity dates of the mortgages, the model uses only one tranche of mortgages for simplicity. It also ignores the 14 day delay in the MBS cashflows relative to the mortgage cashflows. These simplifications do not materially affect the results of the Calculator.

The model estimates the credit exposure to a swap counterparty. In particular, it estimates the maximum loss should a swap counterparty default, as well as the expected loss based on the probability of default. This calculator will be used when setting the guarantee fee.

Credit Risk and Collateralization

• collateral credit risk
• collateral empirical study