脆弱期权论文：基于Lévy过程的期权信用风险定价.docVIP

脆弱期权论文：基于Lévy过程的期权信用风险定价 【中文摘要】随着金融市场的发展,在研究金融产品定价的过程中,很多新的方法不断的被引入。例如,鞅方法。鞅方法在期权定价中是一种非常有用的数学工具,它的引入解决了很多偏微分方程不易解决的问题,使期权定价变得更方便简洁。而Esscher变换是一种非常有效的鞅方法,它为寻找等价鞅测度提供了有效的解决方法。Esscher变换最早是由Gerber和Shiu引入的,他们利用Esscher变换讨论了普通期权的定价问题。本文中我们将一维的Esscher变换推广到多维Esscher变换,并利用多维Esscher变换对脆弱期权定价。本文研究的对象是一类特殊的期权–脆弱期权,它是一种存在违约风险的期权;我们讨论了脆弱期权的性质并研究了在不同Levy过程推动下它的定价问题。文中还着重研究了脆弱期权的一种特殊形式,备兑期权。由于脆弱期权涉及两项资产,因此我们利用二维的Esscher变换来研究脆弱期权定价问题,最终导出了脆弱期权的定价公式。本文中讨论的股价过程是由不同Levy过程推动的,包括维纳过程,逆高斯过程等。对于由维纳过程推动的脆弱期权,文中导出了它最终的定价公式。对于由其它Levy过程推动的脆弱期权,本文用蒙特卡洛数值模拟方法比较了它们的股价变化。 【英文摘要】With the development of financial market, a lot of new methods are implement-ed to price these derivatives. E.g. martingale method. Martingale is a very usefulmathematical tool in option pricing. It solves a lot of problems which is difficult forpartial differential equations to solve and it makes the option pricing easier. Esschertransform is a very effective martingale method to find the equivalent martingale mea-sure. Esscher transform was first introduced by Gerber and Shiu. They use Esschertransform to price the ordinary option. We extend one-dimensional Esscher transformto multi-dimensional Esscher transform, and use multi-dimensional Esscher transformto price the vulnerable option.In this paper, the research object is a special class of options - vulnerable option,the option with default risk. We discuss its nature and the pricing problem driven bydifferent Levy process. Esscher transform is used in this paper to price the vulnerableoption. We find the equivalent martingale measure to price the option. We also discussthe options driven by different Levy process. The article also focused on a special formof vulnerable option, covered options. As the vulnerable option involves two assets,we use two-dimensional Esscher transform to price the vulnerable option. 【关键词】脆弱期权 Esscher变换 Le′vy过程 【英文关键词】vulnerable option Esscher transform Le′vy process 【目录】基于Lévy过程的期权信用风险定价 摘要 3-4 ABSTRACT 4 表格索引 7-8 插图索引 8-9 第一章 Le′