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標題: 使用馬可夫鏈蒙地卡羅法估計連續時間隨機過程模型參數
Estimating the Continuous-Time Model Parameters Using the Markov Chain Monte Carlo Method
作者: 楊濟丞
Yang, Chi-Chen
關鍵字: Markov Chain Monte Carlo method;馬可夫鏈蒙地卡羅法;Continuous-Time model;連續時間模型
出版社: 財務金融系所
引用: Andersen, Torben, Hyung-Jin Chung, and Bent Sorensen, 1999, Efficient method of moments estimation of a stochastic volatility model, Journal of Econometrics 91, 61-87. Andersen, Torben, Luca Benzoni, and Jesper Lund, 1998, Estimating jump-diffusion for equity returns, Working Paper, J.L. Kellogg Graduate School of Management, Northwestern University. Asgharian, Hossein, and Christoffer Bengtsson, 2006, Jump spillover in international equity markets, Journal of Financial Econometrics 4, 167-203. Bakshi, Gurdip, Charles Cao, and Zhiwu Chen, 1997, Empirical performance of alternative option pricing models, Journal of Finance 52, 2003-2049. Bates, David, 1996, Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options, Review of Finance Studies 9, 69-107. Black, Fischer, and Myron Scholes, 1973, The pricing of options and corporate liabilities, Journal of Political Economy 81, 637-654. Bollerslev, Tim, 1986, Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics 31, 307-327. Brooks, Stephen, 1998, Markov chain Monte Carlo method and its application, The Statistician 47, 69-100. Duffie, Darrell, Jun Pan, and Kenneth Singleton, 2000, Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343-1376. Eraler, Bjørn, 2001, MCMC analysis of diffusion models with application to finance, Journal of Business and Economic Statistics 19, 177-191. Eraker, Bjørn, 2004, Do stock prices and volatility jump? Reconciling evidence from spot and option prices, Journal of Finance 59, 1367-1404. Eraker, Bjørn, Michael Johannes, and Nicholas Polson, 2003, The impact of jumps in volatility and returns, Journal of Finance 53, 1269-1300 Engle, Robert, 1982, Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. Inflation, Econometrica 50, 987-1008. Gelman, Andrew, and Donald Rubin, 1992, Inference from iterative simulation using multiple sequences, Statistical Science 17,457-511. Gelman, Andrew, Gareth Roberts, and Walter Gilks, 1996, Efficient Metropolis jumping rules, Bayesian Statistics 5, 599-607. Geweke, John, 1992, Bayesian treatment of the independent student-t linear model, Journal of Applied Econometrics 8, 19-40. Geyer, Charles, 1992, Practical Markov chain Monte Carlo, Statistical Science 17, 473-483. Geyer, Charles, and Thompson Elizabeth, 1995, Annealing Markov chain Monte Carlo with applications to ancestral inference, Journal of American Statistical Association 90, 909-920. Heston, Steven, 1993, A closed-form solution for option with stochastic volatility with applications to bond and currency options, Review of Finance Studies 6, 327-343. Honore, Peter, 1998, Pitfalls in estimating jump-diffusion models, Working Paper, University of Aarhus. Hull, John, and Alan White, 1987, The pricing of options on assets with stochastic volatilities, Journal of Finance 42, 281-300. Jacquier, Eric, Nicholas Polson, and Peter Rossi, 1994, Bayesian analysis of stochastic volatility models, Journal of Economics and Business Statistic 12, 371-389. Jiang, George, 1998, Jump-diffusion models of exchange rate dynamics: Estimation via indirect inference, Working Paper, Tilberg University. Johannes, Michael, Rohit Kumar, and Nicholas Polson, 1999, State dependent jump models: How do U.S. equity indices jump? Working Paper, University of Chicago. Johannes, Michael, and Nicholas Polson, 2002, MCMC methods for continuous-time financial econometrics, in Yacine Aït-Sahalia and Lars Hansen, eds.: Handbook of Financial Econometrics (Elsevier, New York). Jones, Galin, and James Hobert, 2001, Honest exploration of intractable probability distributions via Markov chain Monte Carlo, Statistical Science 16, 312-334. Neal, Radford, 1993, Probabilistic inference using Markov chain Monte Carlo methods, Computer and Information Science 62. Robert, Christian, and George Casella, 1999, Monte Carlo statistical methods (Springer-Verlag). Scott, Louis, 1987, Option pricing when the variance changes randomly: Theory, estimation and an application, Journal of Financial and Quantitative Analysis 22, 419-438.
自從Black and Scholes (1973)推導出Black-Scholes模型之後,連續時間模型成為了財務研究當中相當重要的一個分支。但是隨著金融市場的改變和衍生性金融商品的創新,原本的Black-Scholes模型遠遠無法滿足現在的金融環境。因此後續的連續時間模型研究如雨後春筍般冒出,而這些連續時間模型的設計和實際金融市場仍然存在的落差,其中一個問題即是連續時間模型假設市場的交易是連續的,但是受限於金融市場中資料的型態為一個間斷的資料形式,因此在估計連續時間模型的參數時必須要先離散化連續時間模型。而隨著連續時間模型的設計越來越複雜,傳統的參數估計方法在實務應用上面存在缺陷,此外參數估計值直接的影響到模型的效果。因此一個有效率且準確的參數估計方法在連續時間模型研究中勢必受到重視,有鑑於此本論文研究發現於眾多的參數估計方法中,馬可夫鏈蒙地卡羅法對於連續時間模型的參數估計上面相較於其他估計方法有優勢,尤其是較複雜的連續時間模型設計。但是國內的論文對於馬可夫鏈蒙地卡羅法的研究相對國外來的少,因此本論文想要提供詳細的連續時間模型估計方法的步驟和程式,提供後續研究者更方便、更有效率來了解此估計方法,甚至進一步研究。因此本論文主要是使用馬可夫鏈蒙地卡羅法來估計連續時間模型的參數─即隨機波動報酬和波動度相關跳躍(correlated jumps in prices and volatility with stochastic volatility,簡稱SVCJ)模型。使用2001年1月2日至2010年12月30日的標準普爾五百指數日報酬資料來做參數的估計,並且使用Matlab語言來撰寫程式來進行實證研究分析。最後透過Geweke收斂性檢驗指標來檢驗參數估計值收斂與否和均方根誤差來檢驗參數估計值的準確性。

Since Black and Scholes (1973) derived the Black-Scholes model, continuous-time models have become very import financial processes in financial research. Nevertheless, the assumptions behind the original Black-Scholes model cannot match the current financial markets and derivatives. Therefore, follow-up research such as estimating continuous-time models using discrete-time data was studied. Estimating the parameters of continuous-time models using actual data must be carefully proceeded. An efficient and accurate method of parameter estimation for a series of complicated continuous-time models based on actual data is studied in this thesis. The Markov chain Monte Carlo method is chosen to be addressed in this thesis because it has advantages when compared to other estimation methods, especially in a complex model. In light of few domestic master theses focusing on this topic, this dissertation would like to provide a detailed discussion for this estimation procedure and relevant coding programs to more understand the Markov chain Monte Carlo method. Specifically, this thesis uses the Markov chain Monte Carlo method to estimate the parameters of a continuous model, which has correlated jumps in prices and volatility and stochastic volatility (SVCJ) model. Using the daily S&P 500 index from January 2, 2001 to December 31, 2010, we use Matlab coding language to illustrate our implementation. Finally, we test the convergence of parameter estimates by the Geweke convergence diagnostic, and check the accuracy of estimates by root mean square error.
其他識別: U0005-0602201204374400
Appears in Collections:財務金融學系所

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