Geometric Brownian Motion with Tempered Stable Waiting Times

被引：24

作者：

Gajda, Janusz ^{[1
]}

Wylomanska, Agnieszka ^{[1
]}

机构：

[1] Wroclaw Univ Technol, Inst Math & Comp Sci, Hugo Steinhaus Ctr, PL-50370 Wroclaw, Poland

来源：

JOURNAL OF STATISTICAL PHYSICS | 2012年 / 148卷 / 02期

关键词：

Geometric Brownian motion; Tempered inverse subordinator; Calibration; FINANCIAL DATA; RANDOM-WALKS; DYNAMICS;

D O I：

10.1007/s10955-012-0537-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

One of the earliest system that was used to asset prices description is Black-Scholes model. It is based on geometric Brownian motion and was used as a tool for pricing various financial instruments. However, when it comes to data description, geometric Brownian motion is not capable to capture many properties of present financial markets. One can name here for instance periods of constant values. Therefore we propose an alternative approach based on subordinated tempered stable geometric Brownian motion which is a combination of the popular geometric Brownian motion and inverse tempered stable subordinator. In this paper we introduce the mentioned process and present its main properties. We propose also the estimation procedure and calibrate the analyzed system to real data.

引用

页码：296 / 305

页数：10

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