基于多维跳跃扩散过程的外国股权期权定价

发布时间：2018-01-02 23:00

本文关键词：基于多维跳跃扩散过程的外国股权期权定价　出处：《河北师范大学》2012年硕士论文　论文类型：学位论文

【摘要】：外国股权期权,是这样一种期权,它的最终收益(以本国货币单位度量)不仅依赖于一特定外国股票价格的波动,而且还依赖于汇率的变化.投资人投资外国股票时,除了关心外国股票价格的风险,也很关切汇率变动的风险,如何把握汇率风险,如何利用外国股权期权来规避风险已成为期权定价领域中的热点问题.因而研究外国股权期权的定价问题具有实际意义.本文主要讨论了外国股权期权的定价问题. 第二章首先在本国风险中性概率测度Q下建立了模型:假设本国无风险利率rd(t)和外国无风险利率rf(t)均为随机且服从多维Vasicek扩展模型;外国股票价格S(t)和汇率C(t)均遵循多维几何Browian运动.然后利用鞅方法得到了S(t)和C(t)的漂移项应具有的形式.接着利用伊藤引理及一些分析技巧，，通过计算得到了rd(t), rf(t),S(t)和C(t)的表达式,为计算期权的价格打下了基础. 第三章,利用伊藤积分的高斯分布性质及等距性质,通过计算得到了敲定价格为外国货币的看涨期权价格,敲定价格为本国货币的看涨期权价格, Quanto看涨期权价格,与股权连接的外汇看涨期权四种期权的定价公式.进一步,我们给出了看涨看跌的平价关系式,得到了这些外国股权看跌期权的定价公式. 在第四章中,考虑到资产价格、汇率可能会受到某些重大事件的影响引起跳跃的情况.利用测度变换、鞅方法以及伊藤积分的性质等知识得到了上述四种外国股权看涨期权的定价公式.另外我们通过看涨看跌的平价关系式,得到了这些外国股权看跌期权的定价公式.
[Abstract]:Foreign stock option , which is an option , is not only dependent on the fluctuation of the price of a particular foreign stock but also depends on the change of exchange rate . When investors invest in foreign stocks , they are also concerned about the risk of exchange rate , how to seize the risk of exchange rate , how to use foreign equity option to avoid risk has become a hot issue in the field of option pricing . In the second chapter , a model is established under the national risk neutral probability measure Q : it is assumed that both the national non - risk interest rate rd ( t ) and the foreign non - risk interest rate rf ( t ) are random and subject to the multi - dimensional Vasicek extension model ; the foreign stock price S ( t ) and the exchange rate C ( t ) all follow the multi - dimensional geometric Browian exercise . In chapter 3 , using the Gaussian distribution character and the equidistance property of Ivine integral , we calculate the price of the call options for the foreign currency by calculating the price of the call options for the foreign currency , and the price is the pricing formula of the four options of the inflation option price of the national currency , the price of Quanto and the foreign exchange of the stock option . In chapter 4 , considering the price of assets , the exchange rate may be affected by some important events . The pricing formula of these four foreign stock options is obtained by using the knowledge of measure transformation , Martingales method and the nature of Itoh ' s integral .

【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】：F224;F831.51

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