标题： 具有随机系数的波动率参数化：隐含波动率曲面的解析灵活性 显示英文标题

标题： Volatility Parametrizations with Random Coefficients: Analytic Flexibility for Implied Volatility Surfaces

摘要： 市场惯例是以某种参数形式表达隐含波动率。最流行的参数化方法基于或受某种基础随机模型的启发，如Heston模型（SVI方法）或SABR模型（SABR参数化）。它们的流行通常是因为封闭形式的表示能够实现高效的校准。然而，这些表示间接地对可观察的市场价格施加了特定模型的波动率结构。当市场的波动率不符合参数化模型的范围时，校准过程会失败或导致极端参数，表明存在不一致性。 本文解决了这一关键限制——我们提出了一种无套利框架，使参数化隐含波动率公式中的参数成为随机变量。该方法增强了现有的参数化，并且能够在保持解析性和计算效率的同时，显著扩大隐含波动率形状的允许范围。我们在短期指数和股票期权的真实数据上展示了这种方法的有效性，在这些数据上标准参数化无法捕捉市场动态。我们的结果显示，所提出的方法在建模临近收益公告的短期到期期权的隐含波动率曲线时特别强大，此时风险中性概率密度函数呈现双峰形式。 显示英文摘要

摘要： It is a market practice to express market-implied volatilities in some parametric form. The most popular parametrizations are based on or inspired by an underlying stochastic model, like the Heston model (SVI method) or the SABR model (SABR parametrization). Their popularity is often driven by a closed-form representation enabling efficient calibration. However, these representations indirectly impose a model-specific volatility structure on observable market quotes. When the market's volatility does not follow the parametric model regime, the calibration procedure will fail or lead to extreme parameters, indicating inconsistency. This article addresses this critical limitation - we propose an arbitrage-free framework for letting the parameters from the parametric implied volatility formula be random. The method enhances the existing parametrizations and enables a significant widening of the spectrum of permissible shapes of implied volatilities while preserving analyticity and, therefore, computation efficiency. We demonstrate the effectiveness of the novel method on real data from short-term index and equity options, where the standard parametrizations fail to capture market dynamics. Our results show that the proposed method is particularly powerful in modeling the implied volatility curves of short expiry options preceding an earnings announcement, when the risk-neutral probability density function exhibits a bimodal form.