Statistical arbitrage in jump-diffusion models with compound Poisson processes

Erdinc Akyildirim; Frank J. Fabozzi; Ahmet Goncu; Ahmet Sensoy

doi:10.1007/s10479-021-03965-w

Statistical arbitrage in jump-diffusion models with compound Poisson processes

Erdinc Akyildirim, Frank J. Fabozzi, Ahmet Goncu, Ahmet Sensoy^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical arbitrage is demonstrated via ‘buy-and-hold until barrier’ and ‘short until barrier’ strategies with both single and double barrier. In order to exploit statistical arbitrage opportunities, the investor needs to have a good approximation of the physical probability measure and the drift of the stochastic process for a given asset.

Original language	English
Pages (from-to)	1357-1371
Number of pages	15
Journal	Annals of Operations Research
Volume	313
Issue number	2
DOIs	https://doi.org/10.1007/s10479-021-03965-w
Publication status	Published - Jun 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

Keywords

Compound Poisson process
Jump-diffusion model
Monte Carlo simulation
Statistical arbitrage

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10.1007/s10479-021-03965-w

Cite this

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title = "Statistical arbitrage in jump-diffusion models with compound Poisson processes",

abstract = "We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical arbitrage is demonstrated via {\textquoteleft}buy-and-hold until barrier{\textquoteright} and {\textquoteleft}short until barrier{\textquoteright} strategies with both single and double barrier. In order to exploit statistical arbitrage opportunities, the investor needs to have a good approximation of the physical probability measure and the drift of the stochastic process for a given asset.",

keywords = "Compound Poisson process, Jump-diffusion model, Monte Carlo simulation, Statistical arbitrage",

author = "Erdinc Akyildirim and Fabozzi, {Frank J.} and Ahmet Goncu and Ahmet Sensoy",

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doi = "10.1007/s10479-021-03965-w",

language = "English",

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T1 - Statistical arbitrage in jump-diffusion models with compound Poisson processes

AU - Akyildirim, Erdinc

AU - Fabozzi, Frank J.

AU - Goncu, Ahmet

AU - Sensoy, Ahmet

PY - 2022/6

Y1 - 2022/6

N2 - We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical arbitrage is demonstrated via ‘buy-and-hold until barrier’ and ‘short until barrier’ strategies with both single and double barrier. In order to exploit statistical arbitrage opportunities, the investor needs to have a good approximation of the physical probability measure and the drift of the stochastic process for a given asset.

AB - We prove the existence of statistical arbitrage opportunities for jump-diffusion models of stock prices when the jump-size distribution is assumed to have finite moments. We show that to obtain statistical arbitrage, the risky asset holding must go to zero in time. Existence of statistical arbitrage is demonstrated via ‘buy-and-hold until barrier’ and ‘short until barrier’ strategies with both single and double barrier. In order to exploit statistical arbitrage opportunities, the investor needs to have a good approximation of the physical probability measure and the drift of the stochastic process for a given asset.

KW - Compound Poisson process

KW - Jump-diffusion model

KW - Monte Carlo simulation

KW - Statistical arbitrage

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DO - 10.1007/s10479-021-03965-w

M3 - Article

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SN - 0254-5330

VL - 313

SP - 1357

EP - 1371

JO - Annals of Operations Research

JF - Annals of Operations Research

IS - 2

ER -

Statistical arbitrage in jump-diffusion models with compound Poisson processes

Abstract

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Keywords

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