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Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that…
We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most…
We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…
This paper presents simple formulae for the local variance gamma model of Carr and Nadtochiy, extended with a piecewise-linear local variance function. The new formulae allow to calibrate the model efficiently to market option quotes. On a…
We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended…
Sparse variational Gaussian process (SVGP) methods are a common choice for non-conjugate Gaussian process inference because of their computational benefits. In this paper, we improve their computational efficiency by using a dual…
Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled \emph{with} replacement. In practice, however, sampling \emph{without} replacement is very common, easier to…
In a recent paper "Deep Learning Volatility" a fast 2-step deep calibration algorithm for rough volatility models was proposed: in the first step the time consuming mapping from the model parameter to the implied volatilities is learned by…
In this paper we use Gaussian Process (GP) regression to propose a novel approach for predicting volatility of financial returns by forecasting the envelopes of the time series. We provide a direct comparison of their performance to…
We present a neural network based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models…
Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…
Gaussian Processes (GPs) are a popular approach to predict the output of a parameterized experiment. They have many applications in the field of Computer Experiments, in particular to perform sensitivity analysis, adaptive design of…
The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their…
The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalised to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options…
We introduce a novel procedure that, given sparse data generated from a stationary deterministic nonlinear dynamical system, can characterize specific local and/or global dynamic behavior with rigorous probability guarantees. More…
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a…
This paper generalizes the local variance gamma model of Carr and Nadtochiy, to a piecewise quadratic local variance function. The formulation encompasses the piecewise linear Bachelier and piecewise linear Black local variance gamma…
We introduce a stochastic variational inference procedure for training scalable Gaussian process (GP) models whose per-iteration complexity is independent of both the number of training points, $n$, and the number basis functions used in…