Related papers: A First Option Calibration of the GARCH Diffusion …
We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al.…
Diffusion models have shown remarkable performance in image synthesis by progressively estimating a smooth transition from a Gaussian distribution of noise to a real image. Unfortunately, their practical deployment is limited by slow…
This paper offers a new method for estimation and forecasting of the volatility of financial time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient…
We introduce a pricing kernel with time-varying volatility risk aversion to explain observed time variations in the shape of the pricing kernel. When combined with the Heston-Nandi GARCH model, this framework yields a tractable option…
In this article, we show how the scaling symmetry of the SABR model can be utilized to efficiently price European options. For special kinds of payoffs, the complexity of the problem is reduced by one dimension. For more generic payoffs,…
In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is…
In this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite…
The discontinuous Petrov Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan introduced in their first paper has been widely used for problems in computational mechanics. In this investigation, we propose the DPG method for option…
Stochastic variational inference algorithms are derived for fitting various heteroskedastic time series models. We examine Gaussian, t, and skew-t response GARCH models and fit these using Gaussian variational approximating densities. We…
This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston…
The latter author, together with collaborators, proposed a numerical scheme to calculate the price of barrier options. The scheme is based on a symmetrization of diffusion process. The present paper aims to give a mathematical credit to the…
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…
In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under…
Option pricing, a fundamental problem in finance, often requires solving non-linear partial differential equations (PDEs). When dealing with multi-asset options, such as rainbow options, these PDEs become high-dimensional, leading to…
Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…
This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To…
In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation…
We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…
We describe a high performance parallel implementation of a derivative pricing model, within which we introduce a new parallel method for the calibration of the industry standard SABR (stochastic-\alpha \beta \rho) stochastic volatility…
While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing…