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

Taranto, Aldo ORCID: https://orcid.org/0000-0001-6763-4997 and Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X (2020) Bi-directional grid absorption barrier constrained stochastic processes with applications in finance and investment. Risk Governance & Control: Financial Markets & Institutions, 10 (3). pp. 20-33. ISSN 2077-429X

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Date Deposited: 10 Sep 2020 04:27
Last Modified: 11 Sep 2020 03:24
Uncontrolled Keywords: Grid Trading, Random Walks, Probability of Ruin, Gambler’s Ruin Problem, Semimartingales, Martingales, Stopping Times, Bi-Directional Grids
Fields of Research (2008): 01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling
01 Mathematical Sciences > 0102 Applied Mathematics > 010205 Financial Mathematics
01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010399 Numerical and Computational Mathematics not elsewhere classified
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490510 Stochastic analysis and modelling
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490106 Financial mathematics
49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490399 Numerical and computational mathematics not elsewhere classified
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970114 Expanding Knowledge in Economics
E Expanding Knowledge > 97 Expanding Knowledge > 970108 Expanding Knowledge in the Information and Computing Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi:10.22495/rgcv10i3p2
URI: http://eprints.usq.edu.au/id/eprint/39449

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