带违约风险跳—扩散市场下的期权定价及性质

发布时间：2018-01-14 22:15

本文关键词：带违约风险跳—扩散市场下的期权定价及性质　出处：《中国科学技术大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文首先总结带违约风险简单跳-扩散市场(跳跃强度为给定的函数情况)下的期权定价问题及价格公式,由期权价格遵循给定的抛物积分微分方程的事实,研究其价格的凸性和单调性。并给出保凸的条件。再利用保凸的性质来获得期权价值分别关于模型中不同参数的单调性质,例如波动率,跳跃大小以及跳跃强度。然后研究更一般的跳-扩散市场下(跳跃强度为正的随机过程),"跳至违约模型"中的期权定价问题并给出其价格为唯一经典解的条件。特别的,找到一个确切的条件使在违约边界的期权价格与回收规则中的支付相符。最后本文总结了这种模型中的期权价格的空间凸性以及保凸与参数单调性的关系。
[Abstract]:In this paper, we first summarize the pricing problem and pricing formula of options in a simple jump-diffusion market with default risk (the jump intensity is a given function), and the fact that the option price follows a given parabolic integro-differential equation. In this paper, we study the price convexity and monotonicity, and give the condition of preserving convexity. Then we use the convexity property to obtain the monotone properties of the value of the option on different parameters in the model, such as volatility. Jump size and jump intensity. Then study the more general jump-diffusion market (jump intensity is a positive stochastic process). The option pricing problem in "jumping to default Model" and giving the condition that its price is the unique classical solution. An exact condition is found to match the option price at the default boundary with the payment in the return rule. Finally, this paper summarizes the spatial convexity of the option price in this model and the relationship between the guaranteed convexity and parametric monotonicity.
【学位授予单位】：中国科学技术大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.6;F830.9

【相似文献】