Vasicek随机利率模型下基于条件矩匹配的算术平均亚式期权定价  

Conditional Moment Matching for Pricing Arithmetic Asian Options under Vasicek Interest Rate Model

作　　者：韦晓 WEI Xiao(China Institute for Actuarial Science,Central University of Finance and Economics,Beijing,102206,China)

机构地区：[1]中央财经大学中国精算研究院,北京102206

出　　处：《应用概率统计》2024年第3期378-397,共20页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National 111 Project of China(Grant No.B17050);China Ministry of Education Project of the Humanity and Social Science Research Foundation(Grant No.19YJC790150).

摘　　要：在Vasicek随机利率模型下,本文引入了基于条件矩匹配的近似方法对算术平均型的亚式期权进行定价.该方法的基本原理是运用条件矩匹配找到伽马分布或者对数正态分布去近似在给定到期日标的资产价格的条件下的标的资产的积分的分布函数.为了在带有Vasicek随机利率的二维随机模型下运用分层近似方法,需要运用测度变换技巧去分离在期权价格公式中关于期权在到期日支付函数折现期望中的随机利率和标的资产函数,从而使得可将近似分布用于替换标的资产的积分的分布.基于用蒙特卡洛模拟得到的亚式期权的基准价格,我们通过几个数值例子测试本文提出的分层近似方法的有效性和稳健性.本文发现,分层近似方法与蒙特卡洛方法相比能极大地提高了亚式期权价格的计算速度,同时也保证了定价的准确性,并且用对数正态分布近似比用伽马分布的准确度更高.Under the Vasicek interest rate model,a conditional moment matching approximation for pricing arithmetic Asian options is introduced in this paper.The essential idea of this approximation is to find a proper gamma or lognormal distribution by conditional moment matching to approximate the conditional distribution of the underlying asset's integral given the terminal value of the underlying asset.In order to deal with the two-dimensional stochastic models with Vasicek interest rate,a change of measure techniques is applied to separate the stochastic interest rate and the underlying asset in the expectation about the present value of Asian option's payoff function,thus it allows to apply the strati-fied approximation to the conditional distribution of the integral of the underlying asset.Based on the benchmark price of Asian options by Monte Carlo simulation,we test the efficiency and robustness of the proposed approximation method by some numerical examples.It is found that this approximation method improves greatly in computation speed over standard Monte Carlo simulation while keeping precision of the price,and the approximation by lognormal distribution is more accurate than by gamma distribution in general.

关 键 词：亚式期权 条件矩匹配 分层近似 Vasicek随机利率 

分 类 号：O211.67[理学—概率论与数理统计] O211.9[理学—数学]