This chapter studies construction of a Hull-White-type real-world
model, using the results of Section 6 to do so.
First, we briefly 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 benefit 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, Hull-White model, Hull-White volatility,
Humped volatility, Implied volatility, Market price of risk, Mean reversion,
Monte Carlo simulation, Negative mean reversion, Nelson-Siegel model, Norminvariant condition, Numerical procedure, One-factor model, Principal component
analysis, Real-world model, Risk-neutral model, Rolled trend score, short
rate model, Volatility estimation.
