几类具有违约风险的期权定价模型
发布时间：2018-11-14 17:27
【摘要】：脆弱期权(vulnerable option)是指含有信用风险的期权.它是由Johnson和Stulz(1978)首次提出的.信用风险,即违约风险,是指交易一方因为另一方违约或不能全部履行合约而遭受损失的可能性.信用风险是主要的金融风险之一. 在金融衍生产品的构成中,有近百分之九十左右的衍生产品是属于场外交易(OTC)的.OTC金融衍生品与在交易所内集中清算和结算的产品是不同的,它没有诸如第三方清算机构.因此,对场外交易市场上含有信用风险期权的定价问题的研究是很有实际意义的.本文采用偏微分方程的方法对Kein模型几类具有违约风险的期权进行了研究. 1、将kein模型中的常数波动率改进为随机波动率,采用PDE方法对脆弱期权进行建模,推导出定价方程,然后利用有限差分方法给出数值解法,并对数值结果和参数进行了分析. 2、考虑含有交易对手违约风险的双币种期权的定价,在固定汇率和浮动汇率情况下,采用PDE方法对双币种脆弱期权进行建模,推导出定价方程.然后利用蒙特卡罗(Monte Carlo)方法给出数值解法,并对数值结果和参数进行了分析. 3、考虑含有交易对手违约风险的彩虹障碍期权的定价,采用PDE方法对脆弱彩虹障碍期权进行建模,推导出具有违约风险的八种彩虹障碍期权满足的偏微分方程,然后利用有限差分方法给出数值解法.
[Abstract]:Weak option (vulnerable option) is an option with credit risk. It was first proposed by Johnson and Stulz (1978). Credit risk, that is, default risk, refers to the possibility that one party of the transaction will suffer losses because the other party defaults or fails to perform the contract in its entirety. Credit risk is one of the main financial risks. In the composition of financial derivatives, nearly 90% of them belong to over-the-counter (OTC). OTC financial derivatives are different from centralized clearing and clearing products in exchanges. It does not have, for example, a third party clearing house. Therefore, it is of practical significance to study the pricing of options with credit risk in OTC market. In this paper, the partial differential equation is used to study several kinds of options with default risk in Kein model. 1. The constant volatility in the kein model is improved to random volatility, the PDE method is used to model the fragile options, the pricing equation is derived, and the numerical solution is given by using the finite difference method, and the numerical results and parameters are analyzed. 2. Considering the pricing of dual-currency options with counterparty default risk, under the condition of fixed exchange rate and floating exchange rate, the PDE method is used to model the dual-currency vulnerable options, and the pricing equation is derived. Then the numerical solution is given by Monte Carlo (Monte Carlo) method, and the numerical results and parameters are analyzed. 3. Considering the pricing of rainbow barrier options with counterparty default risk, using PDE method to model fragile rainbow barrier options, the partial differential equations of eight rainbow barrier options with default risk are derived. Then the numerical method is given by the finite difference method.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
本文编号：2331825
[Abstract]:Weak option (vulnerable option) is an option with credit risk. It was first proposed by Johnson and Stulz (1978). Credit risk, that is, default risk, refers to the possibility that one party of the transaction will suffer losses because the other party defaults or fails to perform the contract in its entirety. Credit risk is one of the main financial risks. In the composition of financial derivatives, nearly 90% of them belong to over-the-counter (OTC). OTC financial derivatives are different from centralized clearing and clearing products in exchanges. It does not have, for example, a third party clearing house. Therefore, it is of practical significance to study the pricing of options with credit risk in OTC market. In this paper, the partial differential equation is used to study several kinds of options with default risk in Kein model. 1. The constant volatility in the kein model is improved to random volatility, the PDE method is used to model the fragile options, the pricing equation is derived, and the numerical solution is given by using the finite difference method, and the numerical results and parameters are analyzed. 2. Considering the pricing of dual-currency options with counterparty default risk, under the condition of fixed exchange rate and floating exchange rate, the PDE method is used to model the dual-currency vulnerable options, and the pricing equation is derived. Then the numerical solution is given by Monte Carlo (Monte Carlo) method, and the numerical results and parameters are analyzed. 3. Considering the pricing of rainbow barrier options with counterparty default risk, using PDE method to model fragile rainbow barrier options, the partial differential equations of eight rainbow barrier options with default risk are derived. Then the numerical method is given by the finite difference method.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
【参考文献】
相关期刊论文 前10条
1 胡俞越;;全球金融危机下中国期货市场的创新之路[J];北京工商大学学报(社会科学版);2009年02期
2 付长青,张世斌;具有违约风险的美式买权的定价问题[J];复旦学报(自然科学版);2002年05期
3 黄国安;邓国和;;国内外利率为随机的双币种重置型期权定价[J];大学数学;2011年02期
4 周香英;潘坚;;随机利率下两类奇异期权定价的偏微分方程方法[J];赣南师范学院学报;2010年06期
5 李亚琼;黄立宏;;两种汇率制度的双币种期权定价模型及其解[J];经济数学;2009年04期
6 周媛;李亚琼;;使用双币种期权的风险管理[J];经济数学;2010年04期
7 刘文娟;孙宁华;;百年期权定价[J];科技情报开发与经济;2006年04期
8 周密;;跳跃扩散型双币种期权的定价[J];科学技术与工程;2010年34期
9 刘蕊蕊;徐云;;考虑信用风险的亚式期权定价[J];数学理论与应用;2010年03期
10 郭培栋,张寄洲;随机利率下双币种期权的定价[J];上海师范大学学报(自然科学版);2006年06期
相关硕士学位论文 前3条
1 陈俊霞;欧式期权定价的两个问题探讨[D];华中科技大学;2006年
2 王博;含信用风险的障碍期权的定价[D];华中科技大学;2007年
3 柳士峰;具有交易费用的双币种期权定价[D];湖南大学;2010年
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