Hull-White 2-factor Model: 1) Introduction

This post introduces Hull-White 2-factor model and derives integrations of some important stochastic process which are ingredients of short rate process.


We are going to derive the Hull-White 2-factor model.

Given money market account Bt as a numeraire under the Q measure, short rate r(t) is assumed as follows.

Here a(t)b(t) and σ(t)η(t) are mean-reversion and volatility parameters for each process respectively. Wx(t) and Wy(t) are correlated standard Wiener process and φ(t) is the deterministic process which is adapted to an initial term structure.

Like 1-factor model, θ(t) and φ(t) are reflected in the process of derivation implicitly. Hence our focus is on x(t)+y(t)x(t)+y(t).

Using W1(t) and W2(t) as independent Wiener processes, x(t) and y(t) can be rewritten.

For any s(<t), we can get the integrated from of r(t) from dr(t) as follows.

The derivation of the above equation is skipped because that is the similar logic of the corresponding derivation of HW 1-factor model.

Using these results, we will derive a zero coupon bond price of Hull-White 2-factor model in the next post.

For additional insight on this topic visit the SH Fintech Modeling Blog.

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