多元跳躍模型在金融資產之應用

The application of multivariate jump model in financial assets

洪進興(Chin-Hsing Hung)

指導教授 ： 鍾麗英

國立臺北大學/商學院/統計學系/碩士(2013年)

摘要

根據過去文獻指出,多數的金融資產是用 Black-Scholes (BS) 模型來建造的。然而,用 BS 模型來建造模型卻無法描述出跳躍、偏態和峰態等統計特徵。本研究使用多元 Lèvy 過程的這個方法,因為它可以描述金融資產間的相關結構和解決上述所提到的統計特徵。本研究採用 multivariate Normal Inverse Gaussian (mNIG) 過程來捕捉多元金融資產價格的動態過程,並應用到多元資產的評價和多元資產的違約模型。本研究發現此多元動態過程非常適合應用在摩根士丹利資本國際 (MSCI) 指數的三個區域 : 五大工業國、拉丁美洲和東南亞地區。此外,它也非常適合用來配適台指選擇權,並且也對其敏感度進行了分析。

關鍵字

多元資產價格模型 ； 關聯結構 ； L&egrave ； vy 過程 ； Inverse Gaussian 過程 ； multivariate Normal Inverse Gaussian (mNIG) 過程

並列摘要

In the past, the Black-Scholes (BS) model is used to model financial asset. However, this Brownian world can not take into acount jumps, skewness, and kurtosis. Multivariate Lèvy process is used in this study since it can incorporate dependence structure and the aforementioned characteristics for financial assets. This study uses the multivariate Normal Inverse Gaussian (mNIG) process to describe the dynamic process of diversified financial asset prices, and generalize it for derivatives with multiple correlated underlyers. We found that it fits well for Morgan Stanley Capital International (MSCI) indices for three regions: G5, Latin America, and east Asia. It also has a good fit for vanilla options on Taiwan index. Furthermore, the sensitivity analyses were investigated in this study.

並列關鍵字

Multivariate asset price modele ； Copulas ； L&egrave ； vy processes ； Inverse Gaussian Process ； multivariate Normal Inverse Gaussian (mNIG) Process

參考文獻

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