Papers, ranked by score

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

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

Efficient simulation of a new class of Volterra-type SDEs

We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go back, i.e., the transformation is reversible. We discuss existe

Lab Rats Math 8.5 Rigor 3 ·  June 5, 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

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