基于赫斯顿模型的欧式期权定价的封闭式解决方案，其中包含信用和流动性风险

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-12 DOI:10.1016/j.cnsns.2025.108595

Xin-Jiang He , Shou-De Huang , Sha Lin

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引用次数: 0

摘要

信用风险是一种危险的金融风险，因此需要考虑脆弱期权。所涉及的标的资产和期权卖方资产均遵循不同参数的赫斯顿随机波动率，其价格通过依赖于随机市场流动性的随机因子贴现。在建立了一个风险中性测度后，我们推导出了一个通用公式，由于我们能够推导出一个封闭形式的联合特征函数，所以它可以解析计算。通过数值实验证明流动性和波动率风险对期权价格有显著影响。

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A closed-form solution for pricing European-style options under the Heston model with credit and liquidity risks

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.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

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.