A GEOMETRIC BROWNIAN MOTION MODEL WITH COMPOUND POISSON PROCESS AND FRACTIONAL STOCHASTIC VOLATILITY

被引：0
|
作者：
Intarasit, A. [1 ]
Sattayatham, P. [1 ]
机构：
[1] Suranaree Univ Technol, Dept Math, Nakhon Ratchasima, Thailand
来源：
ADVANCES AND APPLICATIONS IN STATISTICS | 2010年 / 16卷 / 01期
关键词：
geometric Brownian motion; compound Poisson process; fractional stochastic volatility; approximate models;
D O I：
暂无
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：
In this paper, we introduce an approximate approach to a geometric Brownian motion (gBm) model with compound Poisson processes and fractional stochastic volatility. Based on a fundamental result on the L-2 -approximation of this fractional noise by semimartingales, we prove a convergence theorem concerning an approximate solution. A simulation example shows a significant reduction of error in a gBm with jump and fractional stochastic volatility as compared to the stochastic volatility.
引用
收藏
页码：25 / 47
页数：23
相关论文
共 50 条
  • [1] Stochastic volatility and fractional Brownian motion
    Gloter, A
    Hoffmann, M
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2004, 113 (01) : 143 - 172
  • [2] Stochastic interest model driven by compound Poisson process and Brownian motion with applications in life contingencies
    Li, Shilong
    Zhao, Xia
    Yin, Chuancun
    Huang, Zhiyue
    QUANTITATIVE FINANCE AND ECONOMICS, 2018, 2 (01): : 246 - 260
  • [3] Stochastic differential equations driven by fractional Brownian motion and Poisson point process
    Bai, Lihua
    Ma, Jin
    BERNOULLI, 2015, 21 (01) : 303 - 334
  • [4] Stochastic volatility modeling via mixed fractional Brownian motion
    Belhadj, Amel
    Kandouci, Abdeldjebbar
    Bouchentouf, Amina Angelika
    RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2025, 33 (01) : 67 - 74
  • [5] A stochastic clearing model with a Brownian and a compound Poisson component
    Kella, O
    Perry, D
    Stadje, W
    PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 2003, 17 (01) : 1 - 22
  • [6] Stochastic Differential Equations Driven by Multi-fractional Brownian Motion and Poisson Point Process
    Liu Hailing
    Xu Liping
    Li Zhi
    JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS, 2019, 32 (04): : 352 - 368
  • [7] Mathematical Modeling of Pricing European Put Options in Geometric Brownian Motion: Stochastic Volatility Model
    Ouafoudi, Maryeme
    Fei, Gao
    PROCEEDINGS OF THE 14TH INTERNATIONAL CONFERENCE ON INNOVATION AND MANAGEMENT, VOLS I & II, 2017, : 331 - 337
  • [8] Existence for stochastic sweeping process with fractional Brownian motion
    Blouhi, Tayeb
    Ferhat, Mohamed
    Benmansour, Safia
    STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2022, 67 (04): : 749 - 771
  • [9] Stability of Switched Stochastic Dynamical Systems driven by Brownian Motion and Markov Modulated Compound Poisson Process
    Cetinkaya, Ahmet
    Hayakawa, Tomohisa
    2011 AMERICAN CONTROL CONFERENCE, 2011,
  • [10] Stochastic Volatility and Multifractional Brownian Motion
    Ayache, Antoine
    Peng, Qidi
    STOCHASTIC DIFFERENTIAL EQUATIONS AND PROCESSES, 2012, 7 : 210 - 236
12345