Lech Grzelak

Universiteit Utrecht

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 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 traditional parametrizations fail to capture market dynamics. Our results show that the proposed method accurately reflects market behavior, offering a robust extension of existing models