Parameter calibration of stochastic volatility Heston’s model: Constrained optimization vs. differential evolution

• Ambrosio Ortiz-Ramírez ^[1] ; Francisco Venegas-Martínez ^[1] ; María Teresa Verónica Martínez-Palacios ^[1]
  1. [1] Instituto Politécnico Nacional

     Instituto Politécnico Nacional

     México

     
• Localización: Contaduría y administración, ISSN 0186-1042, ISSN-e 2448-8410, Vol. 67, Nº. 1, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • This paper calibrates through loss functions the parameters of Heston’s stochastic volatility model by using two different methods: minimizing a nonlinear objective function (a loss function) with constraints on the values of the parameter and using a differential evolution algorithm. Both methods are applied to implied volatilities on the Mexican Stock Exchange Index with four maturities and twenty-eight strike prices. The selection criterion for the parameters is minimizing the value of the mean square error of the implied volatility. The first method has a better performance with less error and time. However, empirical results show that for both methods the adjustment of implied volatilities is better for options with longterm maturities than for short-term maturities.

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