TY - JOUR

T1 - A note on the discontinuity problem in Heston's stochastic volatility model

AU - Guo, Jia-Hau

AU - Hung, Mao Wei

PY - 2007/9/1

Y1 - 2007/9/1

N2 - Although quasi-analytic formulas can be derived for European-style financial claims in Heston's stochastic volatility model, the inverse Fourier integration involved makes the calculation somewhat complicated. This challenge has puzzled practitioners for many years because most implementations of Heston's formula are not robust, even for customarily-used Heston parameters, as time to maturity is increased. In this article, a simplified approach is proposed to solve the numerical instability problem inherent to the fundamental solution of the Heston model. Specifically, the solution does not require any additional function or a particular mechanism for most software packages or programming library routines to correctly evaluate Heston's analytics.

AB - Although quasi-analytic formulas can be derived for European-style financial claims in Heston's stochastic volatility model, the inverse Fourier integration involved makes the calculation somewhat complicated. This challenge has puzzled practitioners for many years because most implementations of Heston's formula are not robust, even for customarily-used Heston parameters, as time to maturity is increased. In this article, a simplified approach is proposed to solve the numerical instability problem inherent to the fundamental solution of the Heston model. Specifically, the solution does not require any additional function or a particular mechanism for most software packages or programming library routines to correctly evaluate Heston's analytics.

KW - Discountinuity

KW - Heston

KW - Options

KW - Stochastic volatility model

UR - http://www.scopus.com/inward/record.url?scp=34547532228&partnerID=8YFLogxK

U2 - 10.1080/13504860601170534

DO - 10.1080/13504860601170534

M3 - Article

AN - SCOPUS:34547532228

VL - 14

SP - 339

EP - 345

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

SN - 1350-486X

IS - 4

ER -