双跳跃仿射扩散模型的美式看跌期权定价  

Valuation on American Put Option in an Affine Diffusion Model with Double Jumps

作　　者：邓国和 DENG Guohe(College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004)

机构地区：[1]广西师范大学数学与统计学院,桂林541004

出　　处：《系统科学与数学》2017年第7期1646-1663,共18页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11461008)资助课题

摘　　要：美式期权是一类具有提前实施权利的奇异型合约.2000年Duffie等人提出了一类双跳跃仿射扩散模型,假定标的资产及其波动率过程具有相关的共同跳跃,且波动率过程的跳跃大小服从指数分布.文章扩展了该模型,允许波动率过程的跳跃大小服从伽玛分布,并在具有跳跃风险的随机利率环境下研究美式看跌期权的定价.应用Bermudan期权和Richardson插值加速方法给出了美式看跌期权价格计算的解析近似公式.用数值计算实例,以最小二乘蒙特卡罗模拟法检验文章结果的准确性和有效性.最后,分析了常利率与随机利率情形下波动率过程中的相关系数对期权价格的影响.结果表明,相关系数对美式期权价格的作用是反向的.文章结果可以应用于利率与信用衍生品的定价研究.This paper presents an extension of the affine jump-diffusion model with common jumps in variance process being the exponential distribution to the Gamma distribution, and values the American put option under the stochastic interest rate framework with jump risks. The analytical approximate formula for the American put option is provided by integrating the Bermudan options and Richardson extrapolation technique, in which the prices of the Bermudan options are derived by using Fourier transform method. By applying the least-square Monte Curio simulations as the benchmarks, we prove that this proposed model is accurate and efficient from the results of numerical experiments. Finally, the influence of the correlation between the underlying asset and its variance process is analyzed under the cases of both constant and stochastic interest rate. Numerical results show that the impacts of the correlation have negative effects on the American put option. This paper＇s results can be applied to value the interest rate derivatives and credit derivatives.

关 键 词：美式期权 仿射跳扩散模型 Bermudan期权 MONTE Carlo模拟法. 

分 类 号：F224[经济管理—国民经济] F830.91