QUADRATIC VARIANCE TERM STRUCTURE MODELS

Abstract

Popular and tractable affine term structure models assume that the short interest rate is affine in factors whose conditional mean and conditional variance are also affine in the factors. This paper shows that bond prices in approximate closed form are still available even when, other things equal, the factors conditional variance is quadratic in the factors. The resulting "quadratic variance" term structure models: can rule out negative yields; can break the deterministic link between the level and the volatility of the short rate; encompass affine models as special cases; admit negative correlation between non-negative factors driving the short rate; are amenable to Extended Kalman Filter estimation; seem promising also for credit risk pricing.