Download or read book Maximum Likelihood Estimation of Discretely Sampled Diffusions written by Yacine Ait-Sahalia and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.

Download or read book Maximum Likelihood Estimation of Discretely Sampled Diffusions written by Yacine Ait-Sahalia and published by . This book was released on 2000 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a continuous-time diffusion is observed only at discrete dates, not necessarily close together, the likelihood function of the observations is in most cases not explicitly computable. Researchers have relied on simulations of sample paths in between the observation points, or numerical solutions of partial differential equations, to obtain estimates of the function to be maximized. By contrast, we construct a sequence of fully explicit functions which we show converge under very general conditions, including non-ergodicity, to the true (but unknown) likelihood function of the discretely-sampled diffusion. We document that the rate of convergence of the sequence is extremely fast for a number of examples relevant in finance. We then show that maximizing the sequence instead of the true function results in an estimator which converges to the true maximum-likelihood estimator and shares its asymptotic properties of consistency, asymptotic normality and efficiency. Applications to the valuation of derivative securities are also discussed.

Download or read book Maximum Likelihood Estimation of Discretely Sampled Diffusions written by Yacine Aït-Sahalia and published by . This book was released on 1998 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a continuous-time diffusion is observed only at discrete dates, not necessarily close together, the likelihood function of the observations is in most cases not explicitly computable. Researchers have relied on simulations of sample paths in between the observations points, or numerical solutions of partial differential equations, to obtain estimates of the function to be maximized. By contrast, we construct a sequence of fully explicit functions which we show converge under very general conditions, including non-ergodicity, to the true (but unknown) likelihood function of the discretely-sampled diffusion. We document that the rate of convergence of the sequence is extremely fast for a number of examples relevant in finance. We then show that maximizing the sequence instead of the true function results in an estimator which converges to the true maximum-likelihood estimator and shares its asymptotic properties of consistency, asymptotic normality and efficiency. Applications to the valuation of derivative securities are also discussed.

Download or read book A Refinement to Ait Sahalia s 2002 Maximum Likelihood Estimation of Discretely Sampled Diffusions written by Gurdip Bakshi and published by . This book was released on 2004 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a closed-form density approximation when the underlying state variable is a one-dimensional diffusion. Building on Ait-Sahalia (2002), we show that our refinement is applicable under a wide class of drift and diffusion functions. In addition, it facilitates the maximum likelihood estimation of discretely sampled diffusion models of short interest-rate or stock volatility with unknown conditional densities. Our interest-rate examples demonstrate that the analytical approximation is accurate.

Download or read book Maximum Likelihood Estimation of Time Inhomogeneous Diffusions written by Alexei V. Egorov and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend the maximum likelihood estimation method of Ait-Sahalia (2002) for time-homogeneous diffusions to time-inhomogeneous ones. We derive a closed-form approximation of the likelihood function for discretely sampled time-inhomogeneous diffusions, and prove that this approximation converges to the true likelihood function and yields consistent parameter estimates. Monte Carlo simulations for several financial models reveal that our method largely outperforms other widely used numerical procedures in approximating the likelihood function. Furthermore, parameter estimates produced by our method are very close to the parameter estimates obtained by maximizing the true likelihood function, and superior to estimates obtained from the Euler approximation.

Download or read book Approximate Maximum Likelihood Estimation of Discretely Observed Diffusion Processes written by Rolf Poulsen and published by . This book was released on 1999 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Effects of Random and Discrete Sampling when Estimating Continuous time Diffusions written by Yacine Aït-Sahalia and published by . This book was released on 2001 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-frequency financial data are not only discretely sampled in time but the time separating successive observations is often random. We analyze the consequences of this dual feature of the data when estimating a continuous-time model. In particular, we measure the additional effects of the randomness of the sampling intervals over and beyond those due to the discreteness of the data. We also examine the effect of simply ignoring the sampling randomness. We find that in many situations the randomness of the sampling has a larger impact than the discreteness of the data.

Download or read book Maximum Likelihood Estimation of Non linear Continuous time Term structure Models written by Peter Honoré and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Simulated Likelihood Estimation of Diffusions with an Application to Exchange Rate Dynamics in Incomplete Markets written by Michael W. Brandt and published by . This book was released on 2001 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: We present an econometric method for estimating the parameters of a diffusion model from discretely sampled data. The estimator is transparent, adaptive, and inherits the asymptotic properties of the generally unattainable maximum likelihood estimator. We use this method to estimate a new continuous-time model of the Joint dynamics of interest rates in two countries and the exchange rate between the two currencies. The model allows financial markets to be incomplete and specifies the degree of incompleteness as a stochastic process. Our empirical results offer several new insights into the dynamics of exchange rates

Download or read book Maximum Simulated Likelihood Methods and Applications written by William Greene and published by Emerald Group Publishing. This book was released on 2010-12-03 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of methodological developments and applications of simulation-based methods were presented at a workshop at Louisiana State University in November, 2009. Topics include: extensions of the GHK simulator; maximum-simulated likelihood; composite marginal likelihood; and modelling and forecasting volatility in a bayesian approach.

Download or read book Inference for Diffusion Processes written by Christiane Fuchs and published by Springer Science & Business Media. This book was released on 2013-01-18 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.

Download or read book A Two Stage Realized Volatility Approach to the Estimation for Diffusion Processes from Discrete Observations written by Peter C. B. Phillips and published by . This book was released on 2013 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper motivates and introduces a two-stage method for estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as recently developed in Barndorff-Nielsen and Shephard (2002), to provide a regression model for estimating the parameters in the diffusion function. In the second stage the in-fill likelihood function is derived by means of the Girsanov theorem and then used to estimate the parameters in the drift function. Consistency and asymptotic distribution theory for these estimates are established in various contexts. The finite sample performance of the proposed method is compared with that of the approximate maximum likelihood method of Aiuml;t-Sahalia (2002).

Download or read book Parametric Inference for Discretely Sampled Stochastic Differential Equations written by Michael Sorensen and published by . This book was released on 2008 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: A review is given of parametric estimation methods for discretely sampled multivariate diffusion processes. The main focus is on estimating functions and asymptotic results. Maximum likelihood estimation is briefly considered, but the emphasis is on computationally less demanding martingale estimating functions. Particular attention is given to explicit estimating functions. Results on both fixed frequency and high frequency asymptotics are given. When choosing among the many estimators available, guidance is provided by simple criteria for high frequency efficiency and rate optimality that are presented in the framework of approximate martingale estimating functions.

Download or read book Consistency and Asymptotic Normality of an Approximate Maximum Likelihood Estimator for Discretely Observed Diffusion Processes written by Asger Roer Pedersen and published by . This book was released on 1993 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptively Weighted Maximum Likelihood Estimation of Discrete Distributions written by Michael Amiguet and published by . This book was released on 2011 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parameter Estimation in Stochastic Differential Equations written by Jaya P. N. Bishwal and published by Springer. This book was released on 2007-09-26 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Download or read book Statistical Inference in Financial and Insurance Mathematics with R written by Alexandre Brouste and published by Elsevier. This book was released on 2017-11-22 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finance and insurance companies are facing a wide range of parametric statistical problems. Statistical experiments generated by a sample of independent and identically distributed random variables are frequent and well understood, especially those consisting of probability measures of an exponential type. However, the aforementioned applications also offer non-classical experiments implying observation samples of independent but not identically distributed random variables or even dependent random variables. Three examples of such experiments are treated in this book. First, the Generalized Linear Models are studied. They extend the standard regression model to non-Gaussian distributions. Statistical experiments with Markov chains are considered next. Finally, various statistical experiments generated by fractional Gaussian noise are also described. In this book, asymptotic properties of several sequences of estimators are detailed. The notion of asymptotical efficiency is discussed for the different statistical experiments considered in order to give the proper sense of estimation risk. Eighty examples and computations with R software are given throughout the text. Examines a range of statistical inference methods in the context of finance and insurance applications Presents the LAN (local asymptotic normality) property of likelihoods Combines the proofs of LAN property for different statistical experiments that appears in financial and insurance mathematics Provides the proper description of such statistical experiments and invites readers to seek optimal estimators (performed in R) for such statistical experiments