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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.
American option is a kind of singular contract with advance implementation right.Duffie et al proposed a kind of double-jump affine diffusion model in 2000, assuming that the underlying asset and its volatility process have the related common jump and the jump of the volatility process The size obeys the exponential distribution.The paper expands the model to allow the jump size of the volatility process to obey the gamma distribution and study the pricing of the American put options under the random interest rate environment with jumping risk.The application of Bermudan option and Richardson interpolation acceleration method The analytical approximate formula of American put option price is calculated.A numerical example is given to verify the accuracy and validity of the article results by the least square Monte Carlo simulation method.Finally, the relationship between the constant interest rate and the stochastic interest rate volatility The correlation coefficient on the option price.The results show that the correlation coefficient plays a reverse role on the price of the American option.The results can be applied to the pricing of interest rate and credit derivatives.