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| Title: | Empirical Performance and Asset Pricing in Markov Jump Diffusion Models
馬可夫跳躍擴散模型的實證與資產定價 |
| Authors: | 林士貴
Lin, Shih-Kuei |
| Contributors: | 傅承德
翁久幸
Fuh, Cheng-Der
Weng, Chiu-Hsing
林士貴
Lin, Shih-Kuei |
| Keywords: | 均衡分析
歐式選擇權
拉氏倒轉變換
長記憶
馬可夫跳躍擴散模型
馬可夫控制瓦松過程
數值倒轉方法
換跳躍擴散過程
變波動聚集
波動度微笑
Equilibrium analysis
European call option
Laplace inverse transform
Leptokurtic
Long memory
Markov jump diffusion model
Markov modulated Poisson process
Numerical inversion method
Switch jump diffusion model
Volatility clustering
Volatility smile |
| Date: | 2003 |
| Issue Date: | 2009-09-18 19:08:37 (UTC+8) |
| Abstract: | 為了改進Black-Scholes模式的實證現象，許多其他的模型被建議有leptokurtic特性以及波動度聚集的現象。然而對於其他的模型分析的處理依然是一個問題。在本論文中，我們建議使用馬可夫跳躍擴散過程，不僅能整合leptokurtic與波動度微笑特性，而且能產生波動度聚集的與長記憶的現象。然後，我們應用Lucas的一般均衡架構計算選擇權價格，提供均衡下當跳躍的大小服從一些特別的分配時則選擇權價格的解析解。特別地，考慮當跳躍的大小服從兩個情況，破產與lognormal分配。當馬可夫跳躍擴散模型的馬可夫鏈有兩個狀態時，稱為轉換跳躍擴散模型，當跳躍的大小服從lognormal分配我們得到選擇權公式。使用轉換跳躍擴散模型選擇權公式，我們給定一些參數下研究公式的數值極限分析以及敏感度分析。
To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address the leptokurtic feature of the asset return distribution, and the effects of volatility clustering phenomenon. However,
analytical tractability remains a problem for most of the alternative models. In this dissertation, we propose a Markov jump diffusion model, that can not only incorporate both the leptokurtic feature and volatility smile, but also present the economic features of volatility clustering and long memory.
Next, we apply Lucas`s general equilibrium framework to evaluate option price, and to provide analytical solutions of the equilibrium price for European call options when the jump size follows some specific distributions. In particular, two cases are considered, the defaultable one and the lognormal distribution. When the underlying Markov chain of the Markov jump diffusion model has two states, the so-called switch jump diffusion model, we write an explicit analytic formula under the jump size has a lognormal distribution. Numerical approximations of the option prices as well as sensitivity analysis are also given. |
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| Description: | 博士
國立政治大學
統計研究所
88354503
92 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0088354503 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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