{"title":"A closed-form solution for pricing European-style options under the Heston model with credit and liquidity risks","authors":"Xin-Jiang He , Shou-De Huang , Sha Lin","doi":"10.1016/j.cnsns.2025.108595","DOIUrl":null,"url":null,"abstract":"<div><div>Credit risks are one type of hazardous financial risks, which results in the necessity of considering vulnerable options. Two involved assets, corresponding to underlying and option seller’s ones, both follow Heston stochastic volatility with different parameters, and their prices are discounted via a stochastic factor relying on stochastic market-wide liquidity. We then develop a general formula after the establishment of a risk-neutral measure, and it can be computed analytically since we are able to derive a closed-form joint characteristic function. Liquidity and volatility risks are shown through numerical experiments to significantly impact vulnerable option prices.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108595"},"PeriodicalIF":3.4000,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570425000061","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
Credit risks are one type of hazardous financial risks, which results in the necessity of considering vulnerable options. Two involved assets, corresponding to underlying and option seller’s ones, both follow Heston stochastic volatility with different parameters, and their prices are discounted via a stochastic factor relying on stochastic market-wide liquidity. We then develop a general formula after the establishment of a risk-neutral measure, and it can be computed analytically since we are able to derive a closed-form joint characteristic function. Liquidity and volatility risks are shown through numerical experiments to significantly impact vulnerable option prices.
期刊介绍：
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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