LOEX Option: A Combination of Exchange andLookback Options

Authors

  • Ananta Maity * Department of Mathematics, Raja Narendralal Khan Women’s College (Autonomous), Gope Palace, Midnapore 721102, West Bengal, India.
  • Ajay Babu Department of B.Ed., Tamralipta Mahavidyalaya, Tamluk, Purba Medinipur 721636, West Bengal, India.
  • Sukumar Mondal Department of Mathematics, Raja Narendralal Khan Women’s College (Autonomous), Gope Palace, Midnapore 721102, West Bengal, India.

https://doi.org/10.48314/tsc.v1i3.71

Abstract

This paper studies a path-dependent derivative obtained by combining exchange and lookback features, called the LOEX option. The terminal payoff is the positive part of the running maximum of the first asset minus the running minimum of the second asset. A two-asset Black–Scholes framework is formulated with the running extrema included as state variables. The interior pricing partial differential equation is stated, and a meshfree radial-basis-function discretization is described for fixed extrema. Numerical illustrations compare the reduced-state LOEX surface with a standard exchange-option surface. Several mathematical inconsistencies
in the supplied formulation are corrected, including the exchange-payoff orientation, the normal distribution function, the Ito differential, the extrema in the conditional expectation, and the radial-basis centers. Because the supplied numerical files do not include MATLAB code, convergence tests, or a full discretization of the extrema variables, the reported plots should be regarded as exploratory rather than as a validated market-pricing implementation.

Keywords:

Exchange option, Lookback option, Path dependence, Black–Scholes model, Meshfree method

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Published

2025-09-23

Issue

Vol. 1 No. 3 (2025): Transactions on Soft Computing

Section

Articles

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Maity, A., Babu, A., & Mondal, S. (2025). LOEX Option: A Combination of Exchange andLookback Options. Transactions on Soft Computing , 1(3), 229-237. https://doi.org/10.48314/tsc.v1i3.71

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