Abstract
This paper reviews the finite difference method (FDM) for pricing interest rate derivatives (IRDs) under the Hull–White Extended Vasicek model (HW model) and provides the MATLAB codes for it. Among the financial derivatives on various underlying assets, IRDs have the largest trading volume and the HW model is widely used for pricing them. We introduce general backgrounds of the HW model, its associated partial differential equations (PDEs), and FDM formulation for one- and two-asset problems. The two-asset problem is solved by the basic operator splitting method. For numerical tests, one- and two-asset bond options are considered. The computational results show close values to analytic solutions. We conclude with a brief comment on the research topics for the PDE approach to IRD pricing.
Highlights
The finite difference method (FDM) has been widely used to compute the prices of financial derivatives numerically (Duffy [1])
The partial differential equations (PDEs) approach to interest rate derivatives (IRDs) pricing is naturally associated with short rate as interest rates are defined under a single probability measure and Markov in the models
One of the advantages of the short rate models is that they often provide analytical formulas for the prices of bonds and liquidly traded IRDs (Wong and Zhao [14]). Both the PDE approach and Monte Carlo simulation (MCS) can be directly applicable as r (t) in short rate models is defined under a single probability measure and satisfies Markov property
Summary
The finite difference method (FDM) has been widely used to compute the prices of financial derivatives numerically (Duffy [1]). Among financial derivatives on various underlying assets, interest rate derivatives (IRDs), whose payoffs depend on interest rates or bond prices, have the largest trading volume in the global over-the-counter market (BIS [3]). Despite their popularity, FDM for IRD pricing has received relatively less attention. This paper reviews the HW model and the associated FDM formulation under a simplified setting for pricing IRDs. We provide the MATLAB codes for one- and two-asset problems as Supplementary Materials.
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