This paper proposes a comparative analysis in periods of high volatility of the persistence (measure with Hurst exponent process). In general the persistence is constant or even reduced for the underlying Índice de Precios y Cotizaciones (IPC) before the highest volatility value. Besides using The H-J-B method gets the Black Scholes equation and to propose a solution for the case with stochastic volatility and finally call and put options are valuated for different Hurst coefficients and the volatility.
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