Language

Multilingual content from IBKR

Close Navigation
Learn more about IBKR accounts
Hull-White 2-factor Model: 1) Introduction

Hull-White 2-factor Model: 1) Introduction

Posted October 26, 2022 at 11:44 am
Sang-Heon Lee
SHLee AI Financial Model

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 Campus that is provided by third-parties does NOT constitute a recommendation that you should contract for the services of that third party. Third-party participants who contribute to IBKR Campus 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 SHLee AI Financial Model and is being posted with its permission. The views expressed in this material are solely those of the author and/or SHLee AI Financial Model and Interactive Brokers 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 buy or sell any security. It should not be construed as research or investment advice or a recommendation to buy, sell or hold any security or commodity. 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.

IBKR Campus Newsletters

This website uses cookies to collect usage information in order to offer a better browsing experience. By browsing this site or by clicking on the "ACCEPT COOKIES" button you accept our Cookie Policy.