发表机构
Chalmers University of Technology and University of Gothenburg; Lund University; University of Amsterdam（查尔姆斯理工大学和哥德堡大学; 隆德大学; 阿姆斯特丹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Volterra-Heston模型下提出离散监测亚式期权的半闭式定价公式与提升模型对冲方法，利用仿射变换和控制变量提高定价效率，并通过数值实验验证因子收敛与对冲效果。
AI 中文摘要
我们在Volterra-Heston随机波动率模型下，为离散监测的几何和算术亚式期权开发了半闭式定价公式和提升模型对冲方法。利用仿射Volterra结构，我们推导了终端对数价格与离散监测几何平均值联合分布的可处理变换。该变换为几何亚式期权提供了半闭式定价公式，进而为算术亚式期权的蒙特卡洛估值提供了有效的控制变量。在所述实矩和仿射变换假设下，我们还推导了Fourier可表示收益的Galtchouk-Kunita-Watanabe分解，并基于Riccati-Volterra方程和前向方差曲线获得了方差最优对冲。利用N因子马尔可夫近似，我们实现了亚式期权对冲的有限维数值方法。数值实验展示了正则非马尔可夫核的因子收敛性以及再平衡频率对对冲误差的影响。在Heston基准测试中，几何亚式控制变量显著降低了算术亚式价格估计的方差，并相对于直接回归提高了基于回归的对冲的有限样本稳定性。
英文摘要
We develop semi-closed pricing formulas and lifted-model hedging methods for discretely monitored geometric and arithmetic Asian options in the Volterra-Heston stochastic volatility model. Exploiting the affine Volterra structure, we derive a tractable transform for the joint law of the terminal log-price and the discretely monitored geometric average. This transform yields semi-closed pricing formulas for geometric Asian options, which in turn provide effective control variates for Monte Carlo valuation of arithmetic Asian options. Under the stated real-moment and affine-transform hypotheses, we also derive the Galtchouk-Kunita-Watanabe decomposition for Fourier-representable payoffs and obtain a variance-optimal hedge in terms of the Riccati-Volterra equation and the forward-variance curve. Using N-factor Markovian approximations, we obtain a finite-dimensional numerical implementation for hedging Asian options. Our numerical experiments document factor convergence for a regular non-Markovian kernel and the effect of rebalancing frequency on hedging error. In the Heston benchmark, geometric Asian controls substantially reduce the variance of arithmetic-Asian price estimates and improve the finite-sample stability of regression-based hedging relative to direct regression.
