CAJ | 학술논문

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.
위료극복다원후미분포정형하적비선성VaR수치계산적곤난,용다원Laplace분포래묘술회솔회보분포후미성,인입풍험함수전환기술화관우다유Laplace다중적분근사계산적결과,래해결다원Laplace분포정형하적반영외회기권조합개치변화적구모함수문제;진일보장중요추양기술발전도다원Laplace분포정형하적외회기권조합비선성VaR모형중,사득해정형하불재시희유사건Monte Carlo모의,종이감소Monte Carlo모의계산공작량,경정학지고계출조합적손실개솔.수치결과표명해산법비상용Monte Carlo모의법적계산효솔경유효,차능흔대정도상감소소요고계적손실개솔적방차.
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.