CHAPTER 4Hull–White Short‐Rate Model
The first problem we shall seek to apply our pricing kernel methodology to is the well-known short‐rate model of Hull and White [1990]. This has the felicitous property that it possesses an exact pricing kernel. We deduce below a formula for this pricing kernel, then demonstrate how it can be used to derive some important derivatives pricing formulae, basing our derivations on the work of Turfus [2019].
Rather than the short rate 
itself, we shall find it convenient to work with an auxiliary process 
satisfying the following canonical Ornstein–Uhlenbeck process
where 
are piecewise continuous functions, the former 
‐ and the latter 
‐integrable, and 
is a Brownian motion under the risk‐neutral measure for . Under the Hull–White model, this auxiliary ...
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