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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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Sistemes estocàstics --- Termodinàmica --- Termologia --- Dinàmica --- Física --- Mecànica --- Bombes de calor --- Dinàmica de gasos --- Entalpia --- Entropia --- Mecànica estadística --- Processos irreversibles --- Radiació del cos negre --- Segon principi de la termodinàmica --- Termodinàmica atmosfèrica --- Termodinàmica del desequilibri --- Termoelasticitat --- Termoquímica --- Transferència de massa --- Anàlisi tèrmica --- Calor --- Fred --- Màquines tèrmiques --- Motors tèrmics --- Teoria quàntica --- Processos estocàstics --- Estimació d'un paràmetre --- Stochastic systems. --- Time delay systems. --- Thermodynamics --- Mathematics. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Time delay control --- Time delay control systems --- Time delay controllers --- Time-delayed systems --- Feedback control systems --- Process control --- Systems, Stochastic --- Stochastic processes --- System analysis