FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs

Choudhary, Vedant; Jaimungal, Sebastian; Bergeron, Maxime

doi:10.2139/ssrn.4377204

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…where \mu (x) and \sigma (x) are parameterized by artificial neural networks. We estimate \mu and \sigma using maximum likelihood estimation based on an Euler discretization of the SDE (4.1); for details on this procedure and other refinements, see, e.g., [9].…”

Section: Numerical Examplementioning

confidence: 99%

Minimal Kullback–Leibler Divergence for Constrained Lévy–Itô Processes

Jaimungal,

Pesenti,

Sánchez-Betancourt

2024

SIAM J. Control Optim.

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Given an n-dimensional stochastic process \bfitX driven by \BbbP -Brownian motions and Poisson random measures, we search for a probability measure \BbbQ , with minimal relative entropy to \BbbP , such that the \BbbQ -expectations of some terminal and running costs are constrained. We prove existence and uniqueness of the optimal probability measure, derive the explicit form of the measure change, and characterize the optimal drift and compensator adjustments under the optimal measure. We provide an analytical solution for Value-at-Risk (quantile) constraints, discuss how to perturb a Brownian motion to have arbitrary variance, and show that pinned measures arise as a limiting case of optimal measures. The results are illustrated in a risk management setting---including an algorithm to simulate under the optimal measure---and explore an example where an agent seeks to answer the question what dynamics are induced by a perturbation of the Value-at-Risk and the average time spent below a barrier on the reference process?

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Section: Numerical Examplementioning

confidence: 99%

Minimal Kullback–Leibler Divergence for Constrained Lévy–Itô Processes

Jaimungal,

Pesenti,

Sánchez-Betancourt

2024

SIAM J. Control Optim.

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“…Indeed, in order to capture the potentially complex dynamics of variables across time, it is not sufficient to learn the time marginals or even the joint distribution without exploiting the sequential structure. An increasing attention has been paid to these methods in the literature and state-of-the-art generative methods for time series are: Time series GAN [27] which combines an unsupervised adversarial loss on real/synthetic data and supervised loss for generating sequential data, Quant GAN [25] with an adversarial generator using temporal convolutional networks, Causal optimal transport COT-GAN [26] with adversarial generator using the adapted Wasserstein distance for processes, Conditional loss Euler generator [20] starting from a diffusion representation time series and minimizing the conditional distance between transition probabilities of real/synthetic samples, Signature embedding of time series [9], [18], [3], and Functional data analysis with neural SDEs [6].…”

Section: Introductionmentioning

confidence: 99%