ASYMPTOTICS FOR THE DISCRETE-TIME AVERAGE OF THE GEOMETRIC BROWNIAN MOTION AND ASIAN OPTIONS

被引：8

作者：

Pirjol, Dan ^{[1
]}

Zhu, Lingjiong ^{[2
]}

机构：

[1] JP Morgan, New York, NY 10172 USA

[2] Florida State Univ, Dept Math, 1017 Acad Way, Tallahassee, FL 32306 USA

来源：

ADVANCES IN APPLIED PROBABILITY | 2017年 / 49卷 / 02期

基金：

美国国家科学基金会;

关键词：

Asian option; central limit theorem; Berry-Esseen bound; large deviations; IMPLIED VOLATILITY; PRICE; MATURITY; MODEL; FORMULAS;

D O I：

10.1017/apr.2017.9

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps. We derive almost sure limit, fluctuations, large deviations, and also the asymptotics of the moment generating function of the average. Based on these results, we derive the asymptotics for the price of Asian options with discrete-time averaging in the Black-Scholes model, with both fixed and floating strike.

引用

页码：446 / 480

页数：35

共 52 条

[1] A PDE approach to Asian options: Analytical and numerical evidence [J].