论文标题
关于几何布朗运动的时间融合的分布
On the distribution of the time-integral of the geometric Brownian motion
论文作者
论文摘要
我们研究了几何布朗运动时间综合分布的小时扩展中出现的几个功能的数值评估，以及其与基础布朗运动的终极值的关节分布。对这些分布的精确评估与以对数 - 正态分布的波动率和黑色 - 甲梁模型中的亚洲选项定价的随机波动率模型的模拟有关。我们得出这些分布的串联扩展，可用于数值评估。使用复杂分析中的工具，我们确定了这些扩展中系数的收敛半径和大阶渐进性。我们构建了GBM时间综合分布及其终端值的联合分布的有效数值近似，并说明了其在黑色 - choles模型中的亚洲选项定价的应用。
We study the numerical evaluation of several functions appearing in the small time expansion of the distribution of the time-integral of the geometric Brownian motion as well as its joint distribution with the terminal value of the underlying Brownian motion. A precise evaluation of these distributions is relevant for the simulation of stochastic volatility models with log-normally distributed volatility, and Asian option pricing in the Black-Scholes model. We derive series expansions for these distributions, which can be used for numerical evaluations. Using tools from complex analysis, we determine the convergence radius and large order asymptotics of the coefficients in these expansions. We construct an efficient numerical approximation of the joint distribution of the time-integral of the gBM and its terminal value, and illustrate its application to Asian option pricing in the Black-Scholes model.
