论文标题
零件公式对某些随机波动率模型的概率表示，无界漂移
Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift
论文作者
论文摘要
在本文中，我们在某些具有无界漂移的随机波动率模型的给定时间成熟的情况下建立了一个概率表示以及通过部分公式为边缘定律的部分集成。我们的公式依靠Markov Semigroups的扰动技术，基于一个简单的Markov链在随机的时间网格上演变而来，我们为其开发了量身定制的Malliavin colculus。除其他应用外，一种公正的蒙特卡洛路径模拟方法源于我们的公式，因此可以使用最佳的复杂性期权价格价格来计算数值，以及它们相对于金融初始价值或希腊人的敏感性，即Delta和vega，不属于Delta和Vega，以供大量的不太平滑的欧洲收益类别。提出了数值结果来说明该方法的效率。
In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a given time maturity of some stochastic volatility model with unbounded drift. Relying on a perturbation technique for Markov semigroups, our formulae are based on a simple Markov chain evolving on a random time grid for which we develop a tailor-made Malliavin calculus. Among other applications, an unbiased Monte Carlo path simulation method stems from our formulas so that it can be used in order to numerically compute with optimal complexity option prices as well as their sensitivities with respect to the initial values or Greeks in finance, namely the Delta and Vega, for a large class of non-smooth European payoff. Numerical results are proposed to illustrate the efficiency of the method.
