Variance Gamma过程下考虑利率期限结构的可转债定价分析

发布时间：2018-01-04 01:04

本文关键词：Variance Gamma过程下考虑利率期限结构的可转债定价分析　出处：《西南财经大学》2013年硕士论文　论文类型：学位论文

【摘要】：可转换债券作为一种金融衍生产品,既具备股性又具备债性,是一种“攻守兼备”的投资产品。在可转债的定价模型上,通常都假设标的资产价格服从几何布朗运动。然而越来越多的研究者发现,在实际市场交易中,金融资产的价格具有不连续性和非正态性,其收益具有“尖峰厚尾”的现象。故越来越多的研究人员使用带跳的随机过程来描述市场真实收益的变动。这方面主要有两类模型：跳跃-扩散模型和无限活动纯跳跃模型。特别的,在无限活动纯跳跃模型中,方差伽玛(VG)模型通过引入更多的参数e和v来表示偏度和峰度,更好的刻画了金融资产的波动。方差伽玛过程是有限变差过程,这个过程的增量具有尖峰和厚尾的分布。在期权定价中,经典的Black-Scho1es期权定价模型存在波动率微笑的问题,而假设标的资产对数价格服从方差伽玛分布的期权定价模型可以解决这个问题。本文在可转债的定价中,假设资产对数价格服从方差伽玛过程,采用国债利率期限结构曲线中相同期限的利率为无风险利率,分析赎回条款、回售条款等对可转债价值的影响,分析可转债的最优执行策略,采用最小二乘蒙特卡罗模拟法进行定价分析,得到了可转债的最优停时,用不同的贴现因子贴现,计算可得可转债的理论价格。对石化转债的实证分析表明,采用方差伽玛模型得到的理论价格与实际价格趋势一致,符合较好。与BS模型下的定价结果对比也显示,方差伽玛模型的误差更小。
[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.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.91;F224

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