Scholarlink

<p>We study the problem of European option pricing in markets characterized by regime-switching jump-diffusion dynamics and proportional transaction costs. Classical pricing frameworks become analytically intractable in this setting, motivating asymptotic approximation methods that provide arbitrage-regularized pricing under small transaction costs while remaining computationally tractable. We introduce a neural stochastic differential equation (SDE) framework that employs flexible nonparametric parameterizations implemented via neural networks to parameterize drift, diffusion, and jump coefficients, controlled by a latent finite-state Markov chain. Non-smooth transaction cost adjustments are handled within the standard Itô jump-diffusion framework using a jump-adapted Euler–Maruyama scheme. We establish existence and uniqueness of strong càdlàg solutions, L<sup>2</sup>-stability bounds, and weak convergence of a jump-adapted Euler–Maruyama scheme. Option prices are approximated via a Feynman–Kac representation with a Leland-type compensator adjustment, yielding arbitrage-regularized prices that approximate super-replication bounds to first order in the cost parameter. Numerical experiments validate the theoretical results and demonstrate accurate recovery of regime-dependent volatility surfaces while maintaining robustness under misclassification.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Option pricing under regime-switching jump-diffusion dynamics with transaction costs: a neural SDE approach

  • 期刊论文

  • 发表日期：

    2026年5月21日

查看全文
  • Mohd Raagib Shakeel,
  • Satyam Yadav,
  • Musheer Ahmad

摘要

We study the problem of European option pricing in markets characterized by regime-switching jump-diffusion dynamics and proportional transaction costs. Classical pricing frameworks become analytically intractable in this setting, motivating asymptotic approximation methods that provide arbitrage-regularized pricing under small transaction costs while remaining computationally tractable. We introduce a neural stochastic differential equation (SDE) framework that employs flexible nonparametric parameterizations implemented via neural networks to parameterize drift, diffusion, and jump coefficients, controlled by a latent finite-state Markov chain. Non-smooth transaction cost adjustments are handled within the standard Itô jump-diffusion framework using a jump-adapted Euler–Maruyama scheme. We establish existence and uniqueness of strong càdlàg solutions, L2-stability bounds, and weak convergence of a jump-adapted Euler–Maruyama scheme. Option prices are approximated via a Feynman–Kac representation with a Leland-type compensator adjustment, yielding arbitrage-regularized prices that approximate super-replication bounds to first order in the cost parameter. Numerical experiments validate the theoretical results and demonstrate accurate recovery of regime-dependent volatility surfaces while maintaining robustness under misclassification.