Statistical Arbitrage in Jump-Diffusion Models with Compound Poisson Processes

15 Pages Posted: 31 Jul 2019

See all articles by Erdinc Akyildirim

Erdinc Akyildirim

ETH Zürich - Department of Mathematics

Frank J. Fabozzi

EDHEC Business School

Ahmet Goncu

Xi'an Jiaotong University (XJTU)

Ahmet Sensoy

Borsa Istanbul

Date Written: July 27, 2019

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' strategy, where the investor sells the risky asset when it hits a deterministic boundary. 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: Statistical arbitrage, Jump-diffusion model, Compound Poisson process, Monte Carlo simulation

JEL Classification: C60, G11, G12

Suggested Citation

Akyildirim, Erdinc and Fabozzi, Frank J. and Goncu, Ahmet and Sensoy, Ahmet, Statistical Arbitrage in Jump-Diffusion Models with Compound Poisson Processes (July 27, 2019). Available at SSRN: https://ssrn.com/abstract=3427838 or http://dx.doi.org/10.2139/ssrn.3427838

Erdinc Akyildirim (Contact Author)

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
Switzerland

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

Ahmet Goncu

Xi'an Jiaotong University (XJTU) ( email )

26 Xianning W Rd.
Suzhou, Jiangsu 215123
China

Ahmet Sensoy

Borsa Istanbul ( email )

Reşitpaşa mh.
Tuncay Artun cd.
Istanbul, 34467
Turkey

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