In this paper we consider an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model, and propose a new model calibration based on a nonlinear optimization problem. The model considered was introduced previously by the authors in [8] to describe the dynamics of an asset price and of its two stochastic variances. The risk neutral measure associated with the model and the risk premium parameters are introduced and the corresponding formulae to price call and put European vanilla options are derived. These formulae are given as one dimensional integrals of explicitly known integrands. We use these formulae to calibrate the multiscale model using European option prices as data, that is, to determine the values of the model parameters, of the correlation coefficients of the Wiener processes appearing in the model and of the initial stochastic variances implied by the “observed” option prices. The results obtained by solving the calibration problem are used to forecast future option prices. The calibration problem is translated into a suitable constrained nonlinear least squares problem. The proposed formulation of the calibration problem is applied to S&P 500 index data on the prices of European vanilla options in November 2005. This analysis points out some interesting facts.

Calibration of a multiscale stochastic volatility model using as data European option prices

MARIANI, FRANCESCA;
2008

Abstract

In this paper we consider an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model, and propose a new model calibration based on a nonlinear optimization problem. The model considered was introduced previously by the authors in [8] to describe the dynamics of an asset price and of its two stochastic variances. The risk neutral measure associated with the model and the risk premium parameters are introduced and the corresponding formulae to price call and put European vanilla options are derived. These formulae are given as one dimensional integrals of explicitly known integrands. We use these formulae to calibrate the multiscale model using European option prices as data, that is, to determine the values of the model parameters, of the correlation coefficients of the Wiener processes appearing in the model and of the initial stochastic variances implied by the “observed” option prices. The results obtained by solving the calibration problem are used to forecast future option prices. The calibration problem is translated into a suitable constrained nonlinear least squares problem. The proposed formulation of the calibration problem is applied to S&P 500 index data on the prices of European vanilla options in November 2005. This analysis points out some interesting facts.
multiscale stochastic volatility models; calibration model; option pricing
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/388328
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