Not so long ago, it was pretty common to use volatility assumptions like a flat 15% or 18% short volatility with 3% mean reversion. Bloomberg's OAS1 page for mortgage securities still defaults to 15% flat volatility. Unfortunately, more recent volatilities are in the area of 30 to 60%, depending on their term. This is a very significant increase that can have a large impact on risk and return analysis.

Let's look at the impact on a simple pass through, FNMA 30 year 5% for example. At a recent price of 100-20, using the default volatility on Bloomberg's OAS 1 screen and the Andrew Davidson & Co. Inc. prepayment model, the OAS is calculated as 79 basis points to the LIBOR curve. (The Bloomberg screen also still defaults to the US Treasury curve.) If we change the volatility assumption to a more realistic 30%, the OAS drops to 37 basis points.

Conversely, going from OAS to price, say we assume an OAS of 37 bp. If we use the default volatility of 15%, we would get a price of 102-27, vs 100-20, a difference of over 2 points. Here, we see that if we were to price a portfolio of MBSs using market OASs and out of date volatilities, we would be overvaluing the portfolio by a significant amount. In a similar manner, the risk profile of a bond or portfolio could be notably misstated if an unrealistic volatility assumption were used.

From a derivatives and hedge perspective, many options that were put on a while ago are currently way out of the money. They have little to no intrinsic value, their current value is derived almost totally from the volatility. Thus, using an appropriate volatility assumption is critical for these types of instruments.

Interest Rate Models

Underlying OAS models is an interest rate model. This model generates the numerous paths of interest rates used to value the security under each scenario. Until recently, most models used were based on the perspective that rates are lognormally distributed and volatility was measured on a relative basis. However, a recent study has shown that rates demonstrate a more normal distribution as absolute rates have declined. (See Andrew Davidson & Co., Inc. Quantitative Perspectives, dated September, 2002, entitled "Interest Rate Modeling: A Conscientious Choice") Therefore, use of a normal model, such as the Hull-White model, or a Gaussian- squared model, would be more appropriate than use of a lognormal model, such as the Black-Karasinski model.

The Quantitative Perspectives publication gives some examples of how bond profiles are >>>