考虑分红情形下QLBS模型的期权定价与对冲

Option Pricing and Hedging of the QLBS Model under Dividend Scenarios

摘要: 本文针对标的资产分红的实际市场特征，对基于强化学习的QLBS期权定价与对冲模型进行扩展。 推导了连续分红情形下QLBS模型的离散时间理论框架，重构了含分红的自融资复制组合、奖励 函数与最优对冲解析解，并通过蒙特卡洛模拟与B样条基函数逼近完成数值实现。数值实验结果表 明，QLBS^(q)模型在不同分红率下均可稳定逼近含分红BSM模型的定价结果，有效提升了模型对 实际市场的适配性。

Abstract: This paper addresses the limitations of the the actual market characteristics of under- lying asset dividends, extending the option pricing and hedging model (QLBS) based on reinforcement learning. Derived the discrete-time theoretical framework of the QLBS model under continuous dividend scenarios , and the self-financing replication portfolio with dividends, the reward function. And the optimal hedging analytical so- lution are reconstructed. Numerical implementation is achieved through Monte Carlo simulation and B-splines basis function approximation. Numerical experimental re- sults show that the QLBS^(q) model can stably approximate the pricing results of the dividend-paying BSM model under different dividend rates, effectively improving the model’s adaptability to the real market.