Resumen de Parameter calibration of stochastic volatility Heston’s model: Constrained optimization vs. differential evolution
Ambrosio Ortiz Ramírez, Francisco Venegas Martínez, María Teresa V. Martínez Palacios
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.
