Efficient Second-order Weak Scheme for Stochastic Volatility Models

机译：随机波动率模型的高效二阶弱方案

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Stochastic volatility models can be seen as a particular family of two-dimensional stochastic differential equations (SDE) in which the volatility process follows an autonomous one-dimensional SDE. We take advantage of this structure to propose an efficient discretization scheme with order two of weak convergence. We prove that the order two holds for the asset price and not only for the log-asset as usually found in the literature. Numerical experiments confirm our theoretical result and we show the superiority of our scheme compared to the Euler scheme, with or without Romberg extrapolation.

机译：随机挥发性模型可以被视为特定的二维随机微分方程（SDE），其中波动率处理遵循自主一维SDE。我们利用这种结构来提出一种有效的离散化方案，其中弱收敛的顺序。我们证明，这两项订单适用于资产价格，不仅适用于文献中通常在文献中发现的日志资产。数值实验证实了我们的理论结果，与欧拉方案相比，我们的方案的优势与欧拉方案相比，有或没有Romberg推断。

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《Seminar on Stochastic Analysis, Random Fields, and Applications》|2013年||共16页
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作者
Benjamin Jourdain; Mohamed Sbai;
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中图分类 O211.6-532;
关键词
Discretization schemes; weak convergence; Lamperti transform; stochastic volatility models;

机译：离散化方案;弱收敛;LAMPERTI变换;随机波动模型;

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1. VALUE-AT-RISK COMPUTATIONS IN STOCHASTIC VOLATILITY MODELS USING SECOND-ORDER WEAK APPROXIMATION SCHEMES [J] . EVA LüTKEBOHMERT, LYDIENNE MATCHIE International journal of theoretical and applied finance . 2014,第1期

机译：使用二阶弱逼近方案的随机波动率模型中的风险值计算
2. Weak first- and second-order numerical schemes for stochastic differential equations appearing in Lagrangian two-phase flow modeling [J] . Jean-Pierre Minier, Eric Peirano, Sergio Chibbaro Monte Carlo Methods and Applications . 2003,第2期

机译：拉格朗日两相流建模中出现的随机微分方程的弱一阶和二阶数值格式
3. WEAK CONVERGENCE RATE OF A TIME-DISCRETE SCHEME FOR THE HESTON STOCHASTIC VOLATILITY MODEL [J] . Zheng Chao SIAM Journal on Numerical Analysis . 2017,第3期

机译：饱和随机波动率模型的时间离散方案的弱收敛速度
4. Efficient Second-order Weak Scheme for Stochastic Volatility Models [C] . Benjamin Jourdain, Mohamed Sbai Seminar on Stochastic Analysis, Random Fields, and Applications . 2013

机译：随机波动率模型的高效二阶弱方案
5. Three essays in multivariate stochastic volatility: Multivariate stochastic volatility via Wishart random walks. Efficient frontier bounds under stochastic covariances. High dimensional factor multivariate stochastic volatility via Wishart random walks [D] . Philipov, Alexander. 2003

机译：多变量随机波动的三篇论文：通过Wishart随机散步多变量随机波动性。随机考律下的高效前沿界限。通过Wishart随机行走的高尺寸因子多变量随机波动率
6. Test data sets for calibration of stochastic and fractional stochastic volatility models [O] . Jan Pospíšil, Tomáš Sobotka 2016

机译：用于校准随机和分数随机波动率模型的测试数据集
7. Supplement: efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations [O] . Komori Yoshio, Burrage Kevin 2011

机译：补充：非交换型Stratonovich随机微分方程的有效弱二阶随机Runge-Kutta方法

Efficient Second-order Weak Scheme for Stochastic Volatility Models

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