Modelación de derivados europeos con distribuciones no gaussianas
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El modelo Black-Scholes (1973) para valoración de opciones europeas es ampliamente usado en el mercado debido a su fácil implementación. Sin embargo, hay evidencia empírica que contradice los supuestos básicos del modelo Black-Scholes tales como que el retorno del activo tiene una distribución de probabilidad lognormal. Varios investigadores han trabajado en nuevas fórmulas de valoración de derivados suponiendo diferentes distribuciones ya sea para el precio del activo subyacente o para el retorno del mismo. El objetivo de este trabajo es analizar fórmulas para valoración de derivados europeos que son más generales y permiten mayor flexibilidad sobre las distribuciones del activo subyacente. Los trabajos Corrado and Su (1996) ajustan la distribución del activo incluyendo la asimetría y exceso de curtosis; mientras Savickas (2002) supone que la distribución es Weibull. Frente a estos supuestos, se proponen fórmulas modificadas de valoración al introducir parámetros de localización y escala a las distribuciones del activo. Se presentan resultados numéricos comparando estos modelos y la volatilidad implícita de los precios de las opciones.
Abstract. The Black- Scholes (1973) valuation model for European options is widely used in the market due to its easy implementation. However, there is empirical evidence that contradicts the basic assumptions of the Black- Scholes model such as the return of the asset has a lognormal probability distribution. Several researchers have worked on new valuation formulas assuming different distributions for either the price of the underlying asset or for the return. The aim of this work is to analyze valuation formulas for European derivatives that are more general and allow greater flexibility on the distributions of the underlying asset. In Corrado and Su (1996) it is adjusted the asset distribution by adding the effect of skewness and leptokurtosis, while Savickas (2002) states that the distribution is Weibull. Given these assumptions, it was modified valuation formulas proposing to introduce location and scale parameters to the distributions of the asset. Numerical results are presented comparing these models and the implied volatility of option prices.
Abstract. The Black- Scholes (1973) valuation model for European options is widely used in the market due to its easy implementation. However, there is empirical evidence that contradicts the basic assumptions of the Black- Scholes model such as the return of the asset has a lognormal probability distribution. Several researchers have worked on new valuation formulas assuming different distributions for either the price of the underlying asset or for the return. The aim of this work is to analyze valuation formulas for European derivatives that are more general and allow greater flexibility on the distributions of the underlying asset. In Corrado and Su (1996) it is adjusted the asset distribution by adding the effect of skewness and leptokurtosis, while Savickas (2002) states that the distribution is Weibull. Given these assumptions, it was modified valuation formulas proposing to introduce location and scale parameters to the distributions of the asset. Numerical results are presented comparing these models and the implied volatility of option prices.