基于多元Laplace分布的外汇期权组合非线性VaR模型  

Nonlinear VaR model of FX options portfolio based on multivariate Laplace distributions

作　　者：陈荣达[1,2] 王春发[2] 

机构地区：[1]浙江大学管理学院,杭州310058 [2]浙江财经学院金融学院,杭州310018

出　　处：《系统工程理论与实践》2010年第2期315-323,共9页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(70771099);中国博士后科学基金(20070421167)

摘　　要：为了克服多元厚尾分布情形下的非线性VaR数值计算的困难,用多元Laplace分布来描述汇率回报分布厚尾性,引入风险函数转换技术和关于多维Laplace多重积分近似计算的结果,来解决多元Laplace分布情形下的反映外汇期权组合价值变化的矩母函数问题;进一步将重要抽样技术发展到多元Laplace分布情形下的外汇期权组合非线性VaR模型中,使得该情形下不再是稀有事件Monte Carlo模拟,从而减少Monte Carlo模拟计算工作量,更精确地估计出组合的损失概率.数值结果表明该算法比常用Monte Carlo模拟法的计算效率更有效,且能很大程度上减少所要估计的损失概率的方差.To overcome the difficulty in non-linear VaR calculation under heavy-tailed exchange rate returns, the paper depicts heavy-tailed exchange rate returns using multivariate Laplace distribution, and settles the moment generating function that reflects the change in FX option portfolio value using the hazard function transformation technique and the result of approximate calculation about multidimension Laplace type integral. Moreover, the paper proposes that importance samping technique is developed upto non-linear VaR model of FX option portfolio when exchange rate returns have multivariate Laplace distribution. This makes the state not be rare event simulation. Accordingly, this decreases calculating effort in Monte Carlo simulation. Moreover, the loss probability of portfolio is estimated precisely. The simulation result shows the algorithm has more much effectiveness of computational efficiency than the standard Monte Carlo simulation, and can lead to large variance reductions when estimating the loss probability of portfolio.

关 键 词：外汇期权 多元Laplace分布 MONTE CARLO模拟 风险函数转换技术 重要抽样技术 

分 类 号：F830[经济管理—金融学]