Volatility Level Dependence and Linear-Rational Term Structure Models

We outline a subclass of linear-rational term structure models, based on CEV dynamics. A tractable and arbitrage-free term structure results from the linear-rational aspect of the model, independently of the term-structure volatility dynamics that follow from the CEV specification. This specification is devised to capture a flexible degree of volatility-level dependence, i.e., the degree to which yield-curve volatility depends on yield levels. We estimate the model based on a panel of South African swap rates, and extract the degree of volatility-level dependence inherent in the time series of rates, without interference from the shape of the swap curve. The CEV exponent parameters are found to be essential for matching the low degree of volatility-level dependence that tends to be observed in the high interest-rate environments of emerging markets.