Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Rough Bergomi turns grey

We propose a tractable extension of the rough Bergomi model, replacing the fractional Brownian motion with a generalised grey Brownian motion, which we show to be reminiscent of models with stochastic volatility of volatility. This extension breaks away from the log-Normal assumption of rough Bergom

Holy Grail Math 9 Rigor 6 ·  September 23, 2026

Rough differential equations for volatility

We introduce a canonical way of performing the joint lift of a Brownian motion $W$ and a low-regularity adapted stochastic rough path $\mathbf{X}$, extending [Diehl, Oberhauser and Riedel (2015). A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and

Holy Grail Math 9.5 Rigor 5 ·  December 30, 2024

Risk premium and rough volatility

One the one hand, rough volatility has been shown to provide a consistent framework to capture the properties of stock price dynamics both under the historical measure and for pricing purposes. On the other hand, market price of volatility risk is a well-studied object in Financial Economics, and em

Holy Grail Math 8 Rigor 5.5 ·  March 18, 2024

Propagation of a carbon price in a credit portfolio through macroeconomic factors

We study how the climate transition through a low-carbon economy, implemented by carbon pricing, propagates in a credit portfolio and precisely describe how carbon price dynamics affects credit risk measures such as probability of default, expected and unexpected losses. We adapt a stochastic multis

Lab Rats Math 7 Rigor 4.5 ·  July 24, 2023

Rough volatility, path-dependent PDEs and weak rates of convergence

In the setting of stochastic Volterra equations, and in particular rough volatility models, we show that conditional expectations are the unique classical solutions to path-dependent PDEs. The latter arise from the functional Itô formula developed by [Viens, F., & Zhang, J. (2019). A martingale appr

Lab Rats Math 9.5 Rigor 2 ·  April 6, 2023

Transportation-cost inequalities for non-linear Gaussian functionals

We study concentration properties for laws of non-linear Gaussian functionals on metric spaces. Our focus lies on measures with non-Gaussian tail behaviour which are beyond the reach of Talagrand’s classical Transportation-Cost Inequalities (TCIs). Motivated by solutions of Rough Differential Equati

Lab Rats Math 9.5 Rigor 1.5 ·  October 9, 2023

Quantum Computing for Financial Mathematics

Quantum computing has recently appeared in the headlines of many scientific and popular publications. In the context of quantitative finance, we provide here an overview of its potential.

Philosophers Math 4 Rigor 3 ·  November 11, 2023

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