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Two Factor Option Pricing with Uncertain Volatility

机译:具有不确定波动性的两因素期权定价

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摘要

The practical difficulty of estimating volatility values for underlying assets has lead to the uncertain volatility model for option pricing in finance. The pricing equations in this model are often cast in the form of nonlinear partial differential equations. It is well known that for one factor problems, these equations can be numerically solved by selecting volatility values according to the sign of gamma. However, with two (or more) factors, a small, constrained optimization problem must be solved for each node at every timestep. In this paper, we discuss some technical details of solving these optimization problems in the context of the overall numerical solution process. Examples are provided for max of two asset problems, as well as two asset butterfly options.
机译:估计基础资产波动率值的实际困难导致了金融期权定价的不确定性波动率模型。该模型中的定价方程通常以非线性偏微分方程的形式来表示。众所周知,对于一个因素问题,可以通过根据伽马的符号选择波动率值来对这些方程进行数值求解。但是,有两个(或多个)因素,必须在每个时间步长为每个节点解决一个小的约束优化问题。在本文中,我们讨论了在整体数值求解过程中解决这些优化问题的一些技术细节。提供了最多两个资产问题以及两个资产蝶型选择的示例。

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