Not-so-complex Logarithms in the Heston Model

Christian Kahl and Peter Jäckel propose a new approach to solve an inherent numerical instability which enables the use of Heston's analytics for practically all levels of parameters and even maturities of many decades

In Heston’s stochastic volatility framework [Heston 1993], semi-analytical formulæ for plain vanilla option prices can be derived. Unfortunately, these formulæ require the evaluation of logarithms with complex arguments during the involved inverse Fourier integration step. This gives rise to an inherent numerical instability as a consequence of which most implementations of Heston’s formulæ are not robust for moderate to long dated maturities or strong mean reversion. In this article, we propose a new approach to solve this problem which enables the use of Heston’s analytics for practically all levels of parameters and even maturities of many decades.

Logged-in members can download the article by clicking the link below. To log in or register visit here.

Related Posts

Order Statistics for Value at Risk Estimation and ... We apply order statistics to the setting of VaR estimation. Here techniques like historical and Monte Carlo simulation rely on using the k-th heaviest...
Monte Carlo Methods in Quantitative Finance Generi... We describe how we have designed and implemented a software architecture in C++ to model one-factor and multifactor option pricing problems. We pa...
American π: Piece of Cake? An American option can be exercised by its holder at any time he wishes, not just at the expiration date. Textbooks tell you that pricing it in the co...
Forecasting the Yield Curve with S-Plus Methods capable of forecasting the entire yield curve based on a time series extension of the Nelson-Siegel model Nelson and Siegel (1987) were su...
Amaranthus Extermino On September 19, 2006 the hedge fund Amaranth Advisors of Greenwich, Connecticut announced that it had lost $6 billion, about two thirds of the $9...
Option Pricing and the Dirichlet Problem Laplace’s equation is ubiquitous in physics: it arises in the study of many areas such as electromagnetism, gravity and fluid dynamics since it ca...
Poker as a Lottery Doyle Brunson , two-time winner of the World Series of Poker main event, has likened a poker tournament to a lottery in which more skilled players...
Building Your Wings on the Way Down Ray Bradbury famously defined “living at risk” as jumping off a cliff and building your wings on the way down. Too many financial risk managers wh...
110208_heston