Estimación clásica y bayesiana de la volatilidad en el modelo de Black-Scholes; Classical and Bayesian estimation of volatility in the Black-Scholes model - Alvaro Javier Cangrejo Esquivel; José Rafael Tovar Cuevas; Isabel Cristina García; Diego Fernando Manotas Duque (Revista de Métodos Cuantitativos para la Economía y la Empresa, 2022)
– The valuation of options and to a large extent the financial derivatives market require an optimal estimation of the volatility, since this is precisely the variable that is negotiated. We present then a statistical methodology for the estimation of the volatility parameter for an asset using methods of the Bayesian approach to statistics. As prior distributions for volatility parameter, models of the Gamma family and the Standard Levy are assumed. The results obtained using the proposed methodology are contrasted with those obtained when estimating the parameter from the classical approach, where the maximum likelihood method and the Boostrap technique are implemented. It is possible to demonstrate that the estimation procedure from the Bayesian paradigm, allowed to obtain more adjusted and precise volatility parameter estimations, when in the distribution of the returns, extreme values are considered. These characteristics of the estimator allow that predictions of the prices of the options obtained using the BlackScholes model to be closer to what is expected to occur in the financial market.
Keywords: C11; C12; C2; C51; G1; 330; stochastic differential equation; previous distribution; posterior distribution; estimation; volatility; bootstrap; extreme values; hyperparameters; elicitation