本文關鍵詞：Variance Gamma過程下考慮利率期限結(jié)構的可轉(zhuǎn)債定價分析　出處：《西南財經(jīng)大學》2013年碩士論文　論文類型：學位論文

  更多相關文章： 可轉(zhuǎn)債定價 最小二乘蒙特卡羅模擬法 方差伽瑪過程 利率期限結(jié)構

【摘要】：可轉(zhuǎn)換債券作為一種金融衍生產(chǎn)品,既具備股性又具備債性,是一種“攻守兼?zhèn)洹钡耐顿Y產(chǎn)品。在可轉(zhuǎn)債的定價模型上,通常都假設標的資產(chǎn)價格服從幾何布朗運動。然而越來越多的研究者發(fā)現(xiàn),在實際市場交易中,金融資產(chǎn)的價格具有不連續(xù)性和非正態(tài)性,其收益具有“尖峰厚尾”的現(xiàn)象。故越來越多的研究人員使用帶跳的隨機過程來描述市場真實收益的變動。這方面主要有兩類模型：跳躍-擴散模型和無限活動純跳躍模型。特別的,在無限活動純跳躍模型中,方差伽瑪(VG)模型通過引入更多的參數(shù)e和v來表示偏度和峰度,更好的刻畫了金融資產(chǎn)的波動。方差伽瑪過程是有限變差過程,這個過程的增量具有尖峰和厚尾的分布。在期權定價中,經(jīng)典的Black-Scho1es期權定價模型存在波動率微笑的問題,而假設標的資產(chǎn)對數(shù)價格服從方差伽瑪分布的期權定價模型可以解決這個問題。 本文在可轉(zhuǎn)債的定價中,假設資產(chǎn)對數(shù)價格服從方差伽瑪過程,采用國債利率期限結(jié)構曲線中相同期限的利率為無風險利率,分析贖回條款、回售條款等對可轉(zhuǎn)債價值的影響,分析可轉(zhuǎn)債的最優(yōu)執(zhí)行策略,采用最小二乘蒙特卡羅模擬法進行定價分析,得到了可轉(zhuǎn)債的最優(yōu)停時,用不同的貼現(xiàn)因子貼現(xiàn),計算可得可轉(zhuǎn)債的理論價格。對石化轉(zhuǎn)債的實證分析表明,采用方差伽瑪模型得到的理論價格與實際價格趨勢一致,符合較好。與BS模型下的定價結(jié)果對比也顯示,方差伽瑪模型的誤差更小。
[Abstract]:As a kind of financial derivative product, convertible bond is a kind of investment product with both stock and debt, and it is a kind of investment product with "attack and defense", which is based on the pricing model of convertible bond. It is usually assumed that the underlying asset price is driven by geometric Brownian motion. However, more and more researchers find that the price of financial assets is discontinuous and non-normal in actual market transactions. Its returns have the phenomenon of "peak and thick tail". Therefore, more and more researchers use random processes with jumps to describe changes in real market returns. There are two main types of models in this respect:. Leap-Diffusion Model and Infinite activity Pure Jump Model. In the infinite activity pure jump model, the variance gamma ray VG (VG) model is used to represent skewness and kurtosis by introducing more parameters e and v. The variance gamma process is a finite variation process, the increment of this process has peak and thick tail distribution. In option pricing. The classical Black-Scho1es option pricing model has the problem of volatility smile, which can be solved by assuming that the underlying asset logarithmic price is based on the gamma-variance distribution option pricing model. In the pricing of convertible bonds, assuming that the asset logarithmic price follows the variance gamma process, the paper uses the interest rate of the same term in the term structure curve of the national debt interest rate to be the risk-free interest rate, and analyzes the redemption clause. The effect of return clauses on the value of convertible bonds is analyzed, and the optimal execution strategy of convertible bonds is analyzed. The optimal stop time of convertible bonds is obtained by using the least square Monte Carlo simulation method. The theoretical price of convertible bonds is calculated by using different discount factors. The empirical analysis of petrochemical convertible bonds shows that the theoretical price obtained by using variance gamma model is consistent with the actual price trend. Compared with the pricing results of BS model, the variance Gamma model has a smaller error.
【學位授予單位】：西南財經(jīng)大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F830.91;F224

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