Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation
提出一种基于测度值微分的新模拟方法，用于估计金融合约价格对分布参数的导数（希腊值），适用于离散时间Lévy过程下的多种期权（如回溯期权、亚式期权）定价。
Monte Carlo simulation methods have become more and more important in the financial sector in the past years. In this paper, we introduce a new simulation method for the estimation of the derivatives of prices of financial contracts with respect to (w.r.t.) certain distributional parameters called the ‘Greeks’. In particular, we assume that the underlying financial process is a Lévy-type process in discrete time. Our method is based on the Measure-Valued Differentiation (MVD) approach, which allows representation of derivatives as differences of two processes, called the phantoms. We discuss the applicability of MVD for different types of option pay-offs in combination with different types of models of the underlying and provide a framework for the applicability of MVD for path-dependent pay-off functions, as Lookback Options or Asian Options.