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- W185154709 abstract "Keywords: nancial econometrics, quasi-likelihood analysis, stochastic di erential equations, simulation,mathematical nanceIn this talk we will introduce the package sde which contains generic functions for simulation and inferenceon stochastic di erential equations. In particular, stochastic di erential equations corresponding to di usionprocesses driven by the Wiener process are considered.Most of the theoretical results in modern nance rely on the assumption that the underlying dynamics ofasset prices, currencies exchange rates, interest rates, etc are continuous time stochastic processes driven bystochastic di erential equations. Continuous time models are also at the basis of option pricing and optionpricing often requires Monte Carlo methods. In turn, the Monte Carlo method requires a preliminary goodmodel to simulate whose parameters has to be estimated from the data. On the other side, most applicationsin nancial econometrics make use of pure time series modeling because many statistical procedures arealready available in many statistical packages.The discrepancy between theoretical and applied mathematical nance is motivated by the fact thatwhile the model is continuous, the observations always come in discrete time. Inference for continuous timedata from stochastic di erential equation dates back to Jacod and Shiryayev (1987) and today is consideredas a solved problem. On the contrary, the likelihood function for discretized stochastic di erential equationsis available only for a very limited class of models and exact likelihood inference is usually not possible. Also,discretization of the estimators obtained from continuous time analysis is always biased and not useful inpractice.Recently, many authors have considered ways to establish approximate and/or quasi-likelihood inferencefor stochastic di erential equations (for a review see Iacus, 2008). The sde package implements those methodsin the hope to ll the gap between theoretical results and applied nancial econometrics. In particular, thepackage allow to build several kinds of likelihood functions to be used in a standard R context via the mlefunction.The sde package also implements model selection procedures based on AIC statistics for stochasticdi erential equations, identi cation of structural changes in the volatility component of the model andhypotheses testing along with other estimation procedures like estimating functions, the method of themoments, etc. Some tools for nonparametric statistics are also available.Due to the fact that simulation is part of modern nancial analysis, the sde package includes the functionsde:sim which implements several simulation schemes for one dimensional stochastic di erential equations,including those presented in the fundamental reference of Kloden and Planten (1999), e.g. Euler’s and bothMilstein’s schemes, as well as several new simulation methods appeared in the last ten years, e.g. Ozaki andShoji-Ozaki local linearization methods, Berkos et al. Exact Sampling, and Kloden-Platen-Soeresen method.ReferencesIacus. S.M. (2008). Simulation and Inference for Stochastic Di erential Equations with R Example,Springer, New York.Jacod, J., Shiryayev, A.N. (1987) Limit Theorems for Stochastic Processes, Springer-Verlag, New York.Kloden, P., Platen, E. (1999). Numerical Solution of Stochastic Di erential Equations, Applied Mathemat-ics, 23, Third corrected printing, Springer, New York." @default.
- W185154709 created "2016-06-24" @default.
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- W185154709 date "2008-01-01" @default.
- W185154709 modified "2023-09-26" @default.
- W185154709 title "Financial econometrics based on stochastic dierential equations and the sde package" @default.
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