Related papers: A gradient based calibration method for the Heston…
This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and…
We present an analytic approach to solve a degenerate parabolic problem associated to the Heston model, which is widely used in mathematical finance to derive the price of an European option on an risky asset with stochastic volatility. We…
Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…
We propose a gradient-based deep learning framework to calibrate the Heston option pricing model (Heston, 1993). Our neural network, henceforth deep differential network (DDN), learns both the Heston pricing formula for plain-vanilla…
American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to the higher flexibility in comparison to European…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
Several convex formulation methods have been proposed previously for statistical estimation with structured sparsity as the prior. These methods often require a carefully tuned regularization parameter, often a cumbersome or heuristic…
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…
We propose an extension of the anisotropic interaction model which allows for collision avoidance in pairwise interactions by a rotation of forces \cite{arXiv:1912.04234} by including the agents' body size. The influence of the body size on…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
Many real-world problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns in the field of computer vision. Recently, the alignment problem…
Dealing with planning problems with both logical relations and numeric changes in real-world dynamic environments is challenging. Existing numeric planning systems for the problem often discretize numeric variables or impose convex…
In the present work, the European option pricing SWIFT method is extended for Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The…
Many modern machine learning applications, such as multi-task learning, require finding optimal model parameters to trade-off multiple objective functions that may conflict with each other. The notion of the Pareto set allows us to focus on…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
We evaluate a co-evolutionary calibration framework for the Heston model in which a genetic algorithm (GA) over parameters is coupled to an evolving neural inverse map from option surfaces to parameters. While GA-history sampling can reduce…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…