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

TL;DR

This paper introduces a flexible, arbitrage-free framework for implied volatility parametrizations with random coefficients, allowing better modeling of market data, especially in complex scenarios like short-term options before earnings.

Contribution

It proposes a novel method to make implied volatility parameters random, broadening the shape spectrum while maintaining analyticity and efficiency, addressing limitations of traditional models.

Findings

Enhanced fit to real market data

Effective modeling of bimodal risk-neutral densities

Improved calibration for short-term options

Abstract

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.