Papers, ranked by score

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

Joint calibration to SPX and VIX options with signature-based models

We consider a stochastic volatility model where the dynamics of the volatility are described by a linear function of the (time extended) signature of a primary process which is supposed to be a polynomial diffusion. We obtain closed form expressions for the VIX squared, exploiting the fact that the

Holy Grail Math 8.5 Rigor 6.5 ·  January 30, 2023

Signature SDEs from an affine and polynomial perspective

Signature stochastic differential equations (SDEs) constitute a large class of stochastic processes, here driven by Brownian motions, whose characteristics are linear maps of their own signature, i.e. of iterated integrals of the process with itself, and allow therefore for a generic path dependence

Lab Rats Math 9.5 Rigor 4 ·  February 2, 2023

Local signature-based expansions

We study the local (in time) expansion of a continuous-time process and its conditional moments, including the process’ characteristic function. The expansions are conducted by using the properties of the (time-extended) Ito signature, a tractable basis composed of iterated integrals of the driving

Lab Rats Math 8.5 Rigor 2 ·  April 8, 2025

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