From an analysis of the time series of volatility using recent high frequency data, Gatheral, Jaisson and Rosenbaum previously showed that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. The resulting Rough...

This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a “broken exponential martingale” expansion that generalizes and unifies the exponentiation result of Alòs, Gatheral, and Radoičić ́ (SSRN'17; [AGR20])...

Ground-breaking recent work by Carr and Lee extends well-known results for variance swaps to arbitrary functions of realized variance, provided a zero-correlation assumption is made. We give a detailed mathematical analysis of some of their computations and work out the cases of volatility swaps...

There are several (mathematical) reasons why Dupire's formula fails in the non-diffusion setting. And yet, in practice, ad-hoc preconditioning of the option data works reasonably well. In this note we attempt to explain why. In particular, we propose a regularization procedure of the option data...

Stochastic Volatility Models (SVMs) are ubiquitous in quantitative finance. But is there a Markovian SVM capable of producing extreme (T^(-1/2)) short-dated implied volatility skew?We here propose a modification of a given SVM "backbone", Heston for instance, to achieve just this - without...