Modeling interest rate processes has been a major topic in financial research for decades. In more recent decades, interest rate models have perhaps become even more important due to the growing market for interest rate derivatives. Vasicek (1977) and Cox, Ingersoll and Ross (1985) are two of the older classic models while Hull and White (1990), Black and Karsinki (1991), Heath, Jarrow and Morton (1990) and Pearson and Sun (1994) developed more recent models.
The proper theoretical specification of interest rate volatility as related to the level of interest rates has been a major part of interest rate modeling but a case can be made that price volatility (variance) is an equally important concept. Of course, the variance of price changes is one obvious measure of portfolio risk. As just one example, bond mutual fund managers, whose performance is typically measured in holding period return performance over monthly, quarterly, or annual periods, should seek good measures of conditional variance of price changes (VP).
As another example, consider bank regulators and managers computing value at risk (VAR) measures for bond portfolios where VAR is computed by utilizing confidence intervals and variance of bond values. VAR is computed in dollar value where a sizeable error in variance (standard deviation) of price changes obviously leads to a proportionate sizeable error in VAR. In this case, interest rate volatility is important only in that it affects price variance and thus VAR.
Because interest rate volatility is commonly dependent on the level of interest rates in the above models, so is VP. Consider a bond portfolio manager who models expected return and risk where risk is measured by (conditional) variance of returns. Assume the manager is expecting an increase in interest rates. In a basic expected return and risk formulation, this means a negative expected holding period return (unless coupon income is greater than the expected price loss). Such a loss is obviously unappealing but it is even less appealing if VP is positively related to interest rates such that the risk of the portfolio is expected to increase in the face of negative expected returns. On the other hand, if VP is negatively related to interest rates, then an expected increase in interest rates at least reduces the conditional variance of the portfolio and the negative expected return is not quite as distasteful.