Heston模型的级数展开和直接反演
Series expansions and direct inversion for the Heston model
摘要：
对Heston随机波动率模型中条件时间积分方差过程的有效采样是模拟股票价格精确分布的关键。我们构造了一个新的级数展开，这个积分的双无限加权和特别独立的随机变量，通过改变措施和分解的平方贝塞尔桥。当用级数截断近似时，这种表示具有指数衰减的截断误差。我们提出了可行的策略，在很大程度上减少了新系列的实施，简单的随机变量，是独立于任何模型参数的模拟。我们进一步开发直接反演算法，以生成样本的基础上切比雪夫多项式近似的逆分布函数的随机变量。这些近似值可以在任何市场条件下使用。因此，我们建立了一个强大的，有效的和几乎精确的抽样方案的赫斯顿模型。
英文摘要：
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.
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