Real-World Model In The Hull{White Model

Abstract

This chapter studies construction of a Hull{White-type real-world model, using the results of Section 6 to do so. First, we brie y summarize some approaches to volatility estimation in the short rate model. Next, we present two methods for calibrating the Hull{White model. One is to analyze the short rate dynamics. The other is to analyze the forward rate dynamics, working within the HJM framework. Additionally, we remark on some practical aspects of volatility estimation with respect to the mean reversion rate. Accordingly, we present a method for constructing a Hull{White model under the real-world measure. The chief benet of this is that the real-world Hull{White model is simple to compute; Section 8.6 summarizes the numerical procedures necessary to construct the real-world model. Further, some numerical examples will be presented in Chapter 10.

Keywords: Historical volatility, HullWhite model, HullWhite volatility, Humped volatility, Implied volatility, Market price of risk, Mean reversion, Monte Carlo simulation, Negative mean reversion, NelsonSiegel model, Norm- invariant condition, Numerical procedure, One-factor model, Principal compo- nent analysis, Real-world model, Risk-neutral model, Rolled trend score, short rate model, Volatility estimation.