英文标题:
《Convergence of an Euler scheme for a hybrid stochastic-local volatility
model with stochastic rates in foreign exchange markets》
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作者:
Andrei Cozma and Matthieu Mariapragassam and Christoph Reisinger
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最新提交年份:
2016
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英文摘要:
We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility component and the stochastic domestic and foreign short interest rates with the log-Euler scheme for the exchange rate. We establish the exponential integrability of full truncation Euler approximations for the Cox-Ingersoll-Ross process and find a lower bound on the explosion time of these exponential moments. Under a full correlation structure and a realistic set of assumptions on the so-called leverage function, we prove the strong convergence of the exchange rate approximations and deduce the convergence of Monte Carlo estimators for a number of vanilla and path-dependent options. Then, we perform a series of numerical experiments for an autocallable barrier dual currency note.
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中文摘要:
我们在外汇市场背景下研究了Heston-Cox-Ingersoll-Ross++随机局部波动率模型,并提出了一种蒙特卡罗模拟方案,该方案将随机波动率分量的全截断欧拉方案和随机国内外短期利率与汇率的对数欧拉方案相结合。我们建立了Cox-Ingersoll-Ross过程的全截断Euler逼近的指数可积性,并找到了这些指数矩的爆发时间的下界。在完全相关结构和一组关于杠杆函数的现实假设下,我们证明了汇率近似值的强收敛性,并推导了一些普通期权和路径依赖期权的蒙特卡罗估计值的收敛性。然后,我们对一种自动消除障碍的双货币纸币进行了一系列的数值实验。
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分类信息:
一级分类:Quantitative Finance 数量金融学
二级分类:Computational Finance 计算金融学
分类描述:Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法,包括蒙特卡罗,偏微分方程,格子和其他数值方法,并应用于金融建模
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