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Robust Calibration of the Stochastic Volatility Model

  • Seungho Yang Department of Industrial and Management Engineering Pohang University of Science and Technology (POSTECH) San 31 Hyoja Pohang 790-784 South Korea
  • Hyejin Park Department of Industrial and Management Engineering Pohang University of Science and Technology (POSTECH) San 31 Hyoja Pohang 790-784 South Korea
  • Jaewook Lee Department of Industrial and Management Engineering Pohang University of Science and Technology (POSTECH) San 31 Hyoja Pohang 790-784 South Korea
We investigate a parametric method for calibrating European option pricing using a Heston stochastic volatility model.We propose a numerical implementation scheme for calibrating a parameter set of the Heston stochastic volatility model through the particle swarm optimization method to conquer the ill-posed inverse problem of the non-linear least squares and show that it can resolve the instability of the inverse problems. To verify the performance of the proposed method, we conduct simulations on some model-generated option prices and compare the performance with the Levenberg Marquardt method which is one of the popular nonlinear optimization method. We also use S& P 500 index option prices to check performances. The simulation results show that the proposed method has a better performance.

  • Seungho Yang
  • Hyejin Park
  • Jaewook Lee
We investigate a parametric method for calibrating European option pricing using a Heston stochastic volatility model.We propose a numerical implementation scheme for calibrating a parameter set of the Heston stochastic volatility model through the particle swarm optimization method to conquer the ill-posed inverse problem of the non-linear least squares and show that it can resolve the instability of the inverse problems. To verify the performance of the proposed method, we conduct simulations on some model-generated option prices and compare the performance with the Levenberg Marquardt method which is one of the popular nonlinear optimization method. We also use S& P 500 index option prices to check performances. The simulation results show that the proposed method has a better performance.
Option markets,Stochastic volatility models,Model calibration and selection,Particle Swarm optimization.