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Equacions diferencials estocàstiques --- Anàlisi numèrica --- Equació de Fokker-Planck --- Stochastic differential equations. --- Differential equations --- Fokker-Planck equation

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This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Mathematical statistics --- statistiek --- Parameter estimation. --- Stochastic differential equations. --- Estimació d'un paràmetre --- Equacions diferencials estocàstiques --- Estimació d'un paràmetre.

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Stochastic differential equations. --- Equacions diferencials estocàstiques --- Stochastic differential equations --- Numerical solutions. --- Anàlisi numèrica --- Equació de Fokker-Planck --- Numerical analysis --- Differential equations --- Fokker-Planck equation

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Estimació d'un paràmetre --- Equacions diferencials estocàstiques --- Anàlisi numèrica --- Equació de Fokker-Planck --- Estimació estadística --- Estimació (Estadística) --- Estimació de paràmetres --- Estimació paramètrica --- Paràmetres d'estimació --- Sistemes estocàstics --- Teoria de l'estimació --- Parameter estimation. --- Stochastic differential equations. --- Differential equations --- Fokker-Planck equation --- Estimation theory --- Stochastic systems

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Mathematical analysis --- Operational research. Game theory --- Probability theory --- Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- analyse (wiskunde) --- waarschijnlijkheidstheorie --- stochastische analyse --- wiskunde --- fysica --- kansrekening --- mechanica --- Stochastic differential equations. --- Stochastic differential equations --- Numerical solutions. --- Numerical analysis --- Differential equations --- Fokker-Planck equation --- Equacions diferencials estocàstiques --- Anàlisi numèrica --- Equació de Fokker-Planck