多因子Vasicek模型下贴现债券上的复合期权定价

发布时间：2018-04-20 05:32

本文选题：Vasicek利率模型 + Girsanov定理　；参考：《河北师范大学》2012年硕士论文

【摘要】：金融工程是一门比较系统的学科,它包括金融产品的设计,金融产品的定价,金融产品的交易策略以及金融风险的管理等各个方面.其中如何给金融产品定价是人们最为关注的重要问题之一.金融学家以及数学家们为寻求金融产品的合理定价进行了大量的研究. 本文以先前研究成果为基础,对贴现债券上的复合期权的定价进行了研究.考虑到贴现债券的价格波动与利率的波动密切相关,为了与现实生活更加接近,本文首先对原有的Vasicek随机利率模型进行改进,将模型的系数改进为与时间t有关,并将单因子Vasicek随机利率模型扩展为多因子Vasicek随机利率模型.接着应用Ito引理求出贴现债券满足的随机微分方程.最后,我们应用Girsanov定理及鞅定价理论推导出在模型的系数与时间t有关的多因子Vasicek随即利率模型下,贴现债券上的期权定价公式以及在此模型下复合期权定价公式.
[Abstract]:Financial engineering is a systematic subject, which includes the design of financial products, the pricing of financial products, the trading strategies of financial products and the management of financial risks. How to price financial products is one of the most important issues. Financiers and mathematicians have done a lot of research to find reasonable pricing of financial products. Based on the previous research results, this paper studies the pricing of composite options on discounted bonds. Considering that the price fluctuation of discount bond is closely related to the fluctuation of interest rate, in order to be closer to the real life, this paper first improves the original Vasicek stochastic interest rate model, and improves the coefficient of the model to time t. The single-factor Vasicek stochastic interest rate model is extended to the multi-factor Vasicek stochastic interest rate model. Then the stochastic differential equations of discounted bonds are obtained by using Ito Lemma. Finally, we use Girsanov theorem and martingale pricing theory to deduce the option pricing formula on discounted bonds and compound option pricing formula under the multi-factor Vasicek random interest rate model in which the coefficient of the model is related to time t.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.91;F224

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