Premium
Incorporating boundary conditions in a stochastic volatility model for the numerical approximation of bond prices
Author(s) -
GómezValle Lourdes,
LópezMarcos Miguel Ángel,
MartínezRodríguez Julia
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5815
Subject(s) - zero coupon bond , mathematics , bond valuation , jump diffusion , stochastic volatility , short rate model , interest rate , boundary value problem , boundary (topology) , volatility (finance) , short rate , vasicek model , partial differential equation , stochastic differential equation , econometrics , jump , mathematical analysis , economics , yield curve , physics , quantum mechanics , monetary economics
In this paper, we consider a two‐factor interest rate model with stochastic volatility, and we assume that the instantaneous interest rate follows a jump‐diffusion process. In this kind of problems, a two‐dimensional partial integro‐differential equation is derived for the values of zero‐coupon bonds. To apply standard numerical methods to this equation, it is customary to consider a bounded domain and incorporate suitable boundary conditions. However, for these two‐dimensional interest rate models, there are not well‐known boundary conditions, in general. Here, in order to approximate bond prices, we propose new boundary conditions, which maintain the discount function property of the zero‐coupon bond price. Then, we illustrate the numerical approximation of the corresponding boundary value problem by means of an alternative direction implicit method, which has been already applied for pricing options. We test these boundary conditions with several interest rate pricing models.