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.

Introduction

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.

Disclosure: Interactive Brokers

Information posted on IBKR Traders’ Insight that is provided by third-parties and not by Interactive Brokers does NOT constitute a recommendation by Interactive Brokers that you should contract for the services of that third party. Third-party participants who contribute to IBKR Traders’ Insight are independent of Interactive Brokers and Interactive Brokers does not make any representations or warranties concerning the services offered, their past or future performance, or the accuracy of the information provided by the third party. Past performance is no guarantee of future results.

This material is from SH Fintech Modeling and is being posted with permission from SH Fintech Modeling. The views expressed in this material are solely those of the author and/or SH Fintech Modeling and IBKR is not endorsing or recommending any investment or trading discussed in the material. This material is not and should not be construed as an offer to sell or the solicitation of an offer to buy any security. To the extent that this material discusses general market activity, industry or sector trends or other broad based economic or political conditions, it should not be construed as research or investment advice. To the extent that it includes references to specific securities, commodities, currencies, or other instruments, those references do not constitute a recommendation to buy, sell or hold such security. This material does not and is not intended to take into account the particular financial conditions, investment objectives or requirements of individual customers. Before acting on this material, you should consider whether it is suitable for your particular circumstances and, as necessary, seek professional advice.

In accordance with EU regulation: The statements in this document shall not be considered as an objective or independent explanation of the matters. Please note that this document (a) has not been prepared in accordance with legal requirements designed to promote the independence of investment research, and (b) is not subject to any prohibition on dealing ahead of the dissemination or publication of investment research.

Any trading symbols displayed are for illustrative purposes only and are not intended to portray recommendations.