확산과정의 추정 기법에 관한 문헌 연구
A Survey Study on the Estimation Techniques for Diffusion Processes
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참고문헌
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초록
이 논문에서는 확산과정 추정 방법론을 전반적으로 서베이한다. 이산적 자료로부터 연속시간 모형인 확산과정을 추정할 때 중요하게 대두되는 “이산화 편의”의 문제를 줄이기 위한 추정 기법들, 특히 다양한 시뮬레이션 기반 추정 기법들을 중점적으로 논의한다. 시뮬레이션에 기반한 주요 방법론으로는 시뮬레이션 최우법, 중요추출함수를 이용한 시뮬레이션 최우법, 베이지안 MCMC 기법 등이 있다. 기존 문헌에 따르면 시뮬레이션 최우법에 등장하는 중요추출함수와 베이지안 MCMC 기법에 등장하는 후보생성분포가 다소 혼동스럽게 사용되고 있는데 이 논문에서는 두 개념간의 본질적 차이를 명확하게 설명한다. 이에 덧붙여 이 논문은 확산과정 추정기법들을 각 특성에 따라 분류한다. 이러한 분류는 거의 모든 확산과정 추정기법들을 포괄한다. 이로부터 기존 확산과정 추정기법들간의 연관성 및 차이점을 체계적으로 이해하고, 향후 확산과정 추정기법 연구의 방향을 예측해 볼 수 있다.
Abstract
This study comprehensively investigates the state-of-the-art estimation theory of diffusion processes. In the econometrics literature, there are now a number of important works on diffusion process estimation. In particular, statistical methods for minimizing the discretization bias in diffusion estimation continues to be an active area of research, which is another main issues addressed in this study. A comprehensive discussion of diffusion process estimation theory is presented as well as a review and comparison the most recent estimation techniques. The rapid progress of the modern computer has accelerated simulation-based estimation techniques, which is discussed thoroughly in this study. The simulation maximum likelihood estimation (SMLE), including its variant that uses importance sampling, as well as the Bayesian Markov chain Monte-Carlo (MCMC) technique have become important tools in simulation-based estimation. Many existing literatures tend to confuse the function of importance samplers in SMLE that use importance sampling with the proposal distribution of the Bayesian MCMC, both of which are mistakenly thought to be similar concepts. In this paper, the difference between the two is explicitly explained. In addition, a systematic classification of diffusion process estimation techniques is proposed. From which, the relationship and difference between the established diffusion process estimations are categorized, and suggestions on future research on diffusion process estimation is inferred.
참고문헌 (36)
- "Testing Continuous-Time Models of the Spot Interest Rate", 9, pp.385~426 (1996)
- "Transition Densities for Interest Rate and Other Nonlinear Diffusions", 54, pp.1361~1395 (1999)
- "Maximum likelihood estimation of discretely sampled diffusions", eco(metrica), pp.223~262 (2002)
- "Closed-Form Likelihood Expansions for Multivariate Diffusions" (2003)
- "A Parametric Nonlinear Model of Term Structure Dynamics", 12, pp.721~762 (1999)
- "Unit roots and the estimation of interest rate dynamics", 3, pp.215~238 (1996)
- "The Pricing of Options and Corporate Liabilities", 81, pp.637~654 (1973)
- "Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets", 63, pp.161~210 (2002)
- "Analyzing Convertible Bonds", 15, pp.907~929 (1980)
- "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate Journal of Finance", pp.1209~1227 (1992)
- "Is the Short Rate Drift Actually Nonlinear?", 55, pp.355~388 (2000)
- "Understanding the Metropolis Algorithm", 49, pp.327~335 (1995)
- "Comment on Garland B Ronald Gallant’s ‘Numerical technique for maximum likelihood estimation of continuous-time diffusion process’" (2001)
- "Options markets" (2001), Edward Elgar Pub
- "A Theory of the Term Structure of Interest Rates", eco(metrica), pp.385~407 (1985)
- "Numerical techniques for maximum likelihood estimation of continuous time diffusion processes", 20, pp.297~316 (2002)
- "A note on the existence of closed form conditional transition density for the Milstein scheme", nuffield college (1998)
- "Likelihood Inference for Discretely Observed Nonlinear Diffusions", eco(metrica), pp.959~993 (2001)
- "Simulation estimation of continuous-time models with applications to finance University of Oxford" (2001)
- "MCMC Analysis of Diffusion Models with Application to Finance", 19, pp.177~191 (2001)
- "Which Moments to Match", 12, pp.657~681 (1996)
- "and the Bayesian restoration of images IEEE transaction on Pattern Analysis and Machine Inteligence", pp.721~741 (1984)
- "Markov Chain Monte Carlo in Practice" (1996), Chapman and Hall
- "Bayesian Analysis of Stochastic Volatility Models Journal of Business and Economic Statistics", pp.69~87 (1994)
- "A Nonparametric Approach to the Estimation of Diffusion Process with an Application to a Short-Term Interest Interest Rate Model", eco(metric theory), pp.615~645 (1997)
- "State-Space Models with Regime Switching" (1999), MIT Press
- "Likelihood Inference and Comparison with ARCH Models Review of Economic Studies", tility, pp.361~393 (1998)
- "Numerical Solution of Stochastic Differential Equations" (1992), Springer-Verlag
- "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration", 57, pp.995~1026 (1989)
- "Simulation and the Asymptotics of Optimization Estimators", 57, pp.1027~1057 (1989)
- "A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations", 22, pp.55~71 (1995)
- "Monte Carlo Statistical Methods" (1999)
- "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk", 52, pp.1973~2002 (1997)
- Tanner,M.A, "The calculation of posterior distribution by data augmentation", 82, pp.528~550 (1987)
- "An Equilibrium Characterization of the Term Structure", 5, pp.177~188 (1977)
- "An Introduction to Bayesian Inference in Econometrics" (1991)