48 citations · 119 across the 18 of their papers we have counts for
6 papers · 1 filter
On Uniformly Subelliptic Operators and Stochastic Area
Peter Friz, Nicolas Victoir
We consider uniformly subelliptic operators on certain unimodular Lie groups of polynomial growth. It was shown by Saloff-Coste and Stroock that classical results of De Giorgi, Nas…
The Burkholder-Davis-Gundy Inequality for Enhanced Martingales
Peter Friz, Nicolas Victoir
Multi-dimensional continuous local martingales, enhanced with their stochastic area process, give rise to geometric rough paths with a.s. finite homogenous p-variation, p>2. Here w…
Smile Asymptotics II: Models with Known Moment Generating Function
Shalom Benaim, Peter Friz
In a recent article the authors obtained a formula which relates explicitly the tail of risk neutral returns with the wing behavior of the Black Scholes implied volatility smile. I…
The Bismut-Elworthy-Li formula for jump-diffusions and applications to Monte Carlo pricing in finance
T. R. Cass, P. K. Friz
We extend the Bismut-Elworthy-Li formula to non-degenerate jump diffusions and "payoff" functions depending on the process at multiple future times. In the spirit of Fournie et al…
Regular Variation and Smile Asymptotics
Shalom Benaim, Peter Friz
We consider risk-neutral returns and show how their tail asymptotics translate directly to asymptotics of the implied volatility smile, thereby sharpening Roger Lee's celebrated mo…
Euler Estimates of Rough Differential Equations
Peter Friz, Nicolas Victoir
We consider controlled differential equations and give new estimates for higher order Euler schemes. Our proofs are inspired by recent work of A. M. Davie who considers first and s…