Calibration of The Heston Model

Abstract

The Heston Model is a stochastic volatility model heavily used in finance due to its applicability, simplicity and closed-form European call option. Calibrating the Heston Model involves estimating its parameters to match observed market prices. Traditionally, the Heston Model has been calibrated using a combination of least squares, options inference and gradient methods. These traditional calibration techniques provide relatively simple and efficient ways to estimate the parameters of the Heston Model. However, they have limitations in capturing more complex market dynamics. In this thesis, we have worked on a new calibration technique based on an explicit price solution of the Heston Model and stochastic calculus techniques. We use a novel method based on co-variation techniques to estimate the diffusion parameters and a particle filter to estimate the drift parameters. The explicit price solution and the filter used in the calibration process are found to be key for an explicit solution to the Markowitz problem for one Heston stock and one bond.