Bi-directional grid absorption barrier constrained stochastic processes with applications in finance & investment

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Abstract

Whilst the gambler’s ruin problem (GRP) is based on martingales and the established probability theory proves that the GRP is a doomed strategy, this research details how the semimartingale framework is required for the grid trading problem (GTP) of financial markets, especially foreign exchange (FX) markets. As banks and financial institutions have the requirement to hedge their FX exposure, the GTP can help provide a framework for greater automation of the hedging process and help forecast which hedge scenarios to avoid. Two theorems are adapted from GRP to GTP and prove that grid trading, whilst still subject to the risk of ruin, has the ability to generate significantly more profitable returns in the short term. This is also supported by extensive simulation and distributional analysis. We introduce two absorption barriers, one at zero balance (ruin) and one at a specified profit target. This extends the traditional GRP and the GTP further by deriving both the probability of ruin and the expected number of steps (of reaching a barrier) to better demonstrate that GTP takes longer to reach ruin than GRP. These statistical results have applications into finance such as multivariate dynamic hedging (Noorian, Flower, & Leong, 2016), portfolio risk optimization, and algorithmic loss recovery.

Keywords: Grid Trading, Random Walks, Probability of Ruin, Gambler’s Ruin Problem, Semimartingales, Martingales, Stopping Times, Bi-Directional Grids

Authors’ individual contribution: Conceptualization – A.T.; Methodology – A.T.; Software – A.T.; Validation – A.T. and S.K.; Formal Analysis – A.T.; Investigation – A.T.; Writing – Original Draft – A.T.; Writing – Review & Editing – A.T. and S.K.; Visualization – A.T.; Supervision – S.K.

Declaration of conflicting interests: The Authors declare that there is no conflict of interest.

Acknowledgements: The co-author, Aldo Taranto, was supported by an Australian Government Research Training Program (RTP) Scholarship. We would like to thank A/Prof. Ravinesh C. Deo and A/Prof. Ron Addie of the University of Southern Queensland for their invaluable advice on refining this paper.

JEL Classification: C63, C61, G1

Received: 22.06.2020
Accepted: 25.08.2020
Published online: 28.08.2020

How to cite this paper: Taranto, A., & Khan, S. (2020). Bi-directional grid absorption barrier constrained stochastic processes with applications in finance & investment. Risk Governance and Control: Financial Markets & Institutions, 10(3), 20-33. https://doi.org/10.22495/rgcv10i3p2