本文選題：MCMC方法 + 利率期限結(jié)構(gòu)模型��； 參考：《暨南大學(xué)》2012年碩士論文

【摘要】：動(dòng)態(tài)資產(chǎn)定價(jià)理論運(yùn)用套匯和平衡理論來(lái)得到資產(chǎn)價(jià)格和經(jīng)濟(jì)基礎(chǔ)之間的關(guān)系，其中包括：狀態(tài)變量，結(jié)構(gòu)參數(shù)和市場(chǎng)價(jià)格風(fēng)險(xiǎn)。連續(xù)時(shí)間模型是這種方法的核心，因?yàn)樗哂幸滋幚硇浴Ｔ诖蠖鄶?shù)情況下，這些模型能夠得到封閉形式的解或者容易計(jì)算各種我們感興趣對(duì)象的方程，例如，各種價(jià)格或最佳的投資組合加權(quán)。 動(dòng)態(tài)資產(chǎn)定價(jià)模型的經(jīng)驗(yàn)分析解決了一些方面的問(wèn)題，從觀察到得價(jià)格上提取了一些關(guān)于潛在狀態(tài)變量，，結(jié)構(gòu)參數(shù)和市場(chǎng)價(jià)格風(fēng)險(xiǎn)的信息。而利用貝葉斯推斷是要得到參數(shù)，狀態(tài)變量X，在觀察價(jià)格Y上的條件分布。這個(gè)后驗(yàn)分布p，，結(jié)合了模型和觀察價(jià)格兩方面的信息，是在參數(shù)和狀態(tài)變量的基礎(chǔ)上進(jìn)行推斷的關(guān)鍵。 這篇文章主要討論了利用Markov Chain Monte Carlo(MCMC)方法在連續(xù)時(shí)間資產(chǎn)定價(jià)模型中得到后驗(yàn)分布。本文討論的連續(xù)時(shí)間定價(jià)模型主要是利率期限結(jié)構(gòu)模型，利用MCMC方法從這些復(fù)雜的高維分布中抽樣，并在空間，X上產(chǎn)生一條馬爾可夫鏈它的目標(biāo)分布是p θ，X Y。這種蒙特卡洛方法利用這些樣本進(jìn)行積分，并最終進(jìn)行參數(shù)估計(jì)，狀態(tài)估計(jì)和模型比較。 在連續(xù)時(shí)間定資產(chǎn)定價(jià)模型中確定p θ，X Y是比較困難的。原因如下：第一，觀察到的價(jià)格是離散的而這個(gè)模型在理論上要求價(jià)格和狀態(tài)變量在時(shí)間上是連續(xù)的。第二，從研究者的角度來(lái)看，狀態(tài)變量是潛伏的。第三，p θ，X Y是很高維的分布，普通的抽樣方法行不通的。第四：特別是對(duì)于利率期限結(jié)構(gòu)模型來(lái)說(shuō)，參數(shù)是非線性的甚至是非解析形式的。在這篇文章中我們將說(shuō)明MCMC方法能解決上述問(wèn)題。 在文章的第二，三部分，我們將給出貝葉斯推斷和MCMC方法的簡(jiǎn)要綜述。在第四部分，我們將著重討論MCMC方法在利率期限結(jié)構(gòu)模型中的的具體應(yīng)用。
[Abstract]:Dynamic asset pricing theory uses arbitrage and equilibrium theory to obtain the relationship between asset price and economic base, including: state variables, structural parameters and market price risk. Continuous time model is the core of this method because it is easy to deal with. In most cases, these models can obtain closed form solutions or can easily calculate the equations of various objects of interest, for example, various prices or optimal portfolio weights. The empirical analysis of dynamic asset pricing model solves some problems, and extracts some information about potential state variables, structural parameters and market price risks from observed prices. By using Bayesian inference, the conditional distribution of the parameter, the state variable X, and the observed price Y is obtained. This posterior distribution, which combines the information of model and observed price, is the key to infer on the basis of parameters and state variables. In this paper, we mainly discuss the posteriori distribution in the continuous time asset pricing model by using the Markov Chain Monte Carlogne MCMC method. The continuous time pricing model discussed in this paper is mainly the term structure model of interest rate. The MCMC method is used to sample these complex high-dimensional distributions, and a Markov chain is generated on space X, the target distribution of which is p 胃 X Y. The Monte Carlo method uses these samples to integrate, and finally carries out parameter estimation, state estimation and model comparison. It is difficult to determine p 胃 X Y in the continuous time fixed asset pricing model. The reasons are as follows: first, the observed price is discrete and the model theoretically requires price and state variables to be continuous in time. Second, from the perspective of researchers, state variables are latent. The third p 胃 X Y is a very high dimensional distribution, and the ordinary sampling method is not feasible. Fourth, especially for the term structure model of interest rate, the parameters are nonlinear and even non-analytical. In this article we will show that the MCMC method can solve these problems. In the second and third parts, we give a brief overview of Bayesian inference and MCMC methods. In the fourth part, we will discuss the application of MCMC method in the term structure model of interest rate.
【學(xué)位授予單位】：暨南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：O212.8;F820

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

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