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Quantitative Finance, Vol. 9, No. 3, April 2009, 289296 An analytic approximation of the likelihood function
 

Summary: Quantitative Finance, Vol. 9, No. 3, April 2009, 289296
An analytic approximation of the likelihood function
for the Heston model volatility estimation problem
AMIR F. ATIYA*y and STEVE WALLxz
yDepartment of Computer Engineering, Cairo University, Giza, Egypt
zLong View Research Associates, Greenwich, CT, USA
(Received 25 August 2006; in final form 8 January 2008)
Estimating the volatility from the underlying asset price history for the discrete observations
case is a challenging inference problem. Yet it has attracted much research interest due to the
key role of volatility in many areas of finance. In this paper we consider the Heston stochastic
volatility model and propose an accurate analytic approximation for the volatility likelihood
function. The model is based on considering the joint probability density of the asset and the
volatility, and integrating out past volatility variables. The likelihood simplifies to a product
of T terms, where T is the length of the past history considered. An extension to the problem
of fixed parameter estimation is also presented. Simulation results indicate the effectiveness
and accuracy of the proposed method.
Keywords: Volatility; Volatility estimation; Heston model; Stochastic volatility; Particle filter
1. Introduction
Volatility plays a central role in many areas of finance,
such as derivatives pricing, risk management and

  

Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology

 

Collections: Computer Technologies and Information Sciences