Related papers: Smile with the Gaussian term structure model
We analyse the behaviour of the implied volatility smile for options close to expiry in the exponential L\'evy class of asset price models with jumps. We introduce a new renormalisation of the strike variable with the property that the…
We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the…
We propose a non-parametric extension with leverage functions to the Andersen commodity curve model. We calibrate this model to market data for WTI and NG including option skew at the standard maturities. While the model can be calibrated…
The mathematical formulation of sign-changing problems involves a linear second-order partial differential equation in the divergence form, where the coefficient can assume positive and negative values in different subdomains. These…
Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…
Discovering materials with desirable properties in an efficient way remains a significant problem in materials science. Many studies have tackled this problem by using different sets of information available about the materials. Among them,…
A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the…
This paper develops and estimates a multivariate affine GARCH(1,1) model with Normal Inverse Gaussian innovations that captures time-varying volatility, heavy tails, and dynamic correlation across asset returns. We generalize the…
We construct a gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition at a rigid, regular, codimension one configuration. This construction plays an important role in establishing the relation…
In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian…
Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…
Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…
Language models for agglutinative languages have always been hindered in past due to myriad of agglutinations possible to any given word through various affixes. We propose a method to diminish the problem of out-of-vocabulary words by…
Continuous-time state estimation is gaining in popularity due to its abilities to provide smooth solutions, handle asynchronous sensors, and interpolate between data points. While there are two main paradigms, parametric (e.g., temporal…
Volatility Skew and Smile of Interest Rate products (Swaption and Caplet) are represented by SABR (Stochastic Alpha Beta Rho model). So, the Interest Rate derivatives model for pricing the callable exotic swaps should be comparable to the…
We consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Lo\`{e}ve expansion for the…
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…
Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…
Large Language Models (LLMs) demonstrate potential to estimate the probability of uncertain events, by leveraging their extensive knowledge and reasoning capabilities. This ability can be applied to support intelligent decision-making…
Advances in neural variational inference have facilitated the learning of powerful directed graphical models with continuous latent variables, such as variational autoencoders. The hope is that such models will learn to represent rich,…