一个简单的前向密度过程的时间一致性模型
A simple time-consistent model for the forward density process
摘要：
本文提出了一个简单的模型，为未来价值的资产的远期密度的演变。该模型允许一个简单的初始校准期权价格，并具有动态的期权价格数据的实证研究结果是一致的。该模型的目的是既简单又现实，并避免频繁的重新校准的需要。将$n$期权和远期合约的模型价格表示为$(n+1)$维布朗运动的时变函数，并研究了如何由价格过程的轨迹确定布朗运动轨迹.提出了一种基于粒子滤波的方法，用于从离散时间的期权价格观测值中确定驱动布朗运动的位置。通过对标准普尔500指数看涨期权的模拟研究和实证研究表明，该模型能很好地拟合期权价格数据。
英文摘要：
In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with empirical findings from option price data. The model is constructed with the aim of being both simple and realistic, and avoid the need for frequent re-calibration. The model prices of $n$ options and a forward contract are expressed as time-varying functions of an $(n+1)$-dimensional Brownian motion and it is investigated how the Brownian trajectory can be determined from the trajectories of the price processes. An approach based on particle filtering is presented for determining the location of the driving Brownian motion from option prices observed in discrete time. A simulation study and an empirical study of call options on the S&P 500 index illustrates that the model provides a good fit to option price data.
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