Digital power generalized exchange option pricing considering liquidity risk

Kaihang Zhang; Liting Gao; Kaihang Zhang; Liting Gao

doi:10.3934/math.2026073

AIMS Mathematics

2026, Volume 11, Issue 1: 1761-1776. doi: 10.3934/math.2026073

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Digital power generalized exchange option pricing considering liquidity risk

Kaihang Zhang ^,,
Liting Gao

School of Mathematics and Big Data, Mianyang Teachers' College, Mianyang 621000, Sichuan, China

Received: 07 October 2025 Revised: 27 December 2025 Accepted: 13 January 2026 Published: 19 January 2026
MSC : Primary 91G20, 60G44; Secondary 60H05, 65C05

Traditional option pricing models mostly assume that the market is frictionless, ignoring the impact of liquidity on option price. In response, this paper considers a digital power generalized exchange option pricing problem when the underlying asset has liquidity risk. We obtained a closed-form digital power option pricing formula in a incomplete market by measure transformation. Finally, numerical experiments were conducted by comparing the prices computed by the new formula with those from Monte-Carlo simulations, thereby validating the accuracy of the new formula. Building on this, the impact of liquidity on option prices was further investigated.
- digital power exchange options,
- liquidity,
- measure transformation,
- numerical analysis
Citation: Kaihang Zhang, Liting Gao. Digital power generalized exchange option pricing considering liquidity risk[J]. AIMS Mathematics, 2026, 11(1): 1761-1776. doi: 10.3934/math.2026073

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Abstract

Traditional option pricing models mostly assume that the market is frictionless, ignoring the impact of liquidity on option price. In response, this paper considers a digital power generalized exchange option pricing problem when the underlying asset has liquidity risk. We obtained a closed-form digital power option pricing formula in a incomplete market by measure transformation. Finally, numerical experiments were conducted by comparing the prices computed by the new formula with those from Monte-Carlo simulations, thereby validating the accuracy of the new formula. Building on this, the impact of liquidity on option prices was further investigated.

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