论文标题
赫斯顿模型的系列扩展和直接反转
Series expansions and direct inversion for the Heston model
论文作者
论文摘要
赫斯顿随机波动率模型中有条件的时间综合方差过程的有效抽样是基于其确切分布模拟股票价格的关键。我们通过更改度量和平方贝塞尔桥的分解来构建该积分的新序列扩展，以对特定独立随机变量的双重无限加权总和进行构建。当通过串联截断近似时，此表示形式呈指数衰减的截断误差。我们提出了可行的策略，以很大程度上将新系列的实施减少到独立于任何模型参数的简单随机变量的模拟。我们进一步开发了直接的反转算法，以基于Chebyshev多项式近似为其反向分布函数生成此类随机变量的样品。这些近似值可在任何市场条件下使用。因此，我们为赫斯顿模型建立了强，有效且几乎精确的采样方案。
Efficient sampling for the conditional time integrated variance process in the Heston stochastic volatility model is key to the simulation of the stock price based on its exact distribution. We construct a new series expansion for this integral in terms of double infinite weighted sums of particular independent random variables through a change of measure and the decomposition of squared Bessel bridges. When approximated by series truncations, this representation has exponentially decaying truncation errors. We propose feasible strategies to largely reduce the implementation of the new series to simulations of simple random variables that are independent of any model parameters. We further develop direct inversion algorithms to generate samples for such random variables based on Chebyshev polynomial approximations for their inverse distribution functions. These approximations can be used under any market conditions. Thus, we establish a strong, efficient and almost exact sampling scheme for the Heston model.
