衍生GARCH模型下的信用利差欧式期权的定价

发布时间：2017-12-31 14:40

本文关键词：衍生GARCH模型下的信用利差欧式期权的定价　出处：《西南财经大学》2013年硕士论文　论文类型：学位论文

更多相关文章： 信用利差 期权 GARCH模型 均值回复

【摘要】：本文使用Longstaff和Schwartz (1995)所研究的信用利差的均值回复特性以及Heston和Nandi (1999)所采用的GARCH模型得出信用利差欧式期权的闭解形式。同时信用利差的对数采用GARCH模型,而不是采用传统的对数正态分布下的几何布朗运动模型。本文所使用的模型能够更好的捕捉到所观测的信用利差的变化特性,这个模型提供了一个便于计算随机波动率(可以由观察到的离散时间段下历史资产价格来估计)下欧式期权的定价公式,专家分析了在标普500指数下的期权利用单因素形式的GARCH模型对于Black-Scholes (1973)模型是一个实质性的突破。另外本文重点考虑Heston and Nandi's (1999)中的风险中性概率条件下,信用利差对数和条件方差成反比的情况下,得到信用利差欧式期权的闭解形式。
[Abstract]:In this paper, the use of Longstaff and Schwartz (1995) Nandi and Heston and the characteristics of mean reversion of credit spreads (1999) closed form solution of GARCH model with that credit spreads for European options. While credit spreads using the GARCH model, instead of using the traditional logarithmic normal distribution is the geometric Brown motion model. The model can better capture the variation characteristics of the observed credit spreads, the model provides a convenient calculation of stochastic volatility (discrete time can be observed by the history of asset prices to estimate the pricing formula of European option), the expert analysis in the S & P 500 index under option by using GARCH single factor model form for Black-Scholes (1973) model is a substantive breakthrough.
Besides, this paper focuses on the risk neutral probability of Heston and Nandi's (1999), and obtains the closed form of European options with credit spreads under the condition that the credit spreads and the conditional variance are inversely proportional to each other.

【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】：F224;F830.9

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