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Found 23 papers, 4 papers with code
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.
Unsupervised Random Quantum Networks for PDEs
On the theoretical side, we develop a complexity analysis of this approach, and show numerically that random quantum networks can outperform more traditional quantum networks as well as random classical networks.
Natural Language Processing for Financial Regulation
This article provides an understanding of Natural Language Processing techniques in the framework of financial regulation, more specifically in order to perform semantic matching search between rules and policy when no dataset is available for supervised learning.
Quantum Computing for Financial Mathematics
Quantum computing has recently appeared in the headlines of many scientific and popular publications.
Interest rate convexity in a Gaussian framework
The contributions of this paper are twofold: we define and investigate the properties of a short rate model driven by a general Gaussian Volterra process and, after defining precisely a notion of convexity adjustment, derive explicit formulae for it.
Propagation of a carbon price in a credit portfolio through macroeconomic factors
We adapt a stochastic multisectoral model to take into account the greenhouse gases (GHG) emissions costs of both sectoral firms' production and consumption, as well as sectoral household's consumption.
Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest.
Random neural networks for rough volatility
The reservoir approach allows us to formulate the optimisation problem as a simple least-square regression for which we prove theoretical convergence properties.
Rough multifactor volatility for SPX and VIX options
We provide explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions.
Portfolio optimisation with options
We develop a new analysis for portfolio optimisation with options, tackling the three fundamental issues with this problem: asymmetric options' distributions, high dimensionality and dependence structure.
Large and moderate deviations for importance sampling in the Heston model
We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models.
A Quantum Generative Adversarial Network for distributions
Generative Adversarial Networks are becoming a fundamental tool in Machine Learning, in particular in the context of improving the stability of deep neural networks.
Market regime classification with signatures
We provide a data-driven algorithm to classify market regimes for time series.
Functional quantization of rough volatility and applications to volatility derivatives
We develop a product functional quantization of rough volatility.
The Log Moment formula for implied volatility
As a byproduct, we relax the moment assumptions on the stock price to provide a new proof of the notorious Gatheral-Fukasawa formula expressing variance swaps in terms of the implied volatility.
A theoretical analysis of Guyon's toy volatility model
We provide a thorough analysis of the path-dependent volatility model introduced by Guyon \cite{G17}, proving existence and uniqueness of a strong solution, characterising its behaviour at boundary points, providing asymptotic closed-form option prices as well as deriving small-time behaviour estimates.
A Quantum algorithm for linear PDEs arising in Finance
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model.
Anomalous diffusions in option prices: connecting trade duration and the volatility term structure
We show here that anomalous diffusions are able to reproduce the market behaviour of the implied volatility more consistently than usual L\'evy or stochastic volatility models.
Deep Curve-dependent PDEs for affine rough volatility
We introduce a new deep-learning based algorithm to evaluate options in affine rough stochastic volatility models.
Perturbation analysis of sub/super hedging problems
We investigate the links between various no-arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein.
Volatility options in rough volatility models
We discuss the pricing and hedging of volatility options in some rough volatility models.
Functional central limit theorems for rough volatility
The non-Markovian nature of rough volatility processes makes Monte Carlo methods challenging and it is in fact a major challenge to develop fast and accurate simulation algorithms.
Probability Pricing of Securities 60F17, 60F05, 60G15, 60G22, 91G20, 91G60, 91B25
Shapes of implied volatility with positive mass at zero
We study the shapes of the implied volatility when the underlying distribution has an atom at zero and analyse the impact of a mass at zero on at-the-money implied volatility and the overall level of the smile.
