Related papers: Exact Simulation of the 3/2 Model
We employ adaptive mesh refinement, implicit time stepping, a nonlinear multigrid solver and parallel computation, to solve a multi-scale, time dependent, three dimensional, nonlinear set of coupled partial differential equations for three…
We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed L\'evy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of…
An important family of stochastic processes arising in many areas of applied probability is the class of L\'evy processes. Generally, such processes are not simulatable especially for those with infinite activity. In practice, it is common…
Energy companies need efficient procedures to perform market calibration of stochastic models for commodities. If the Black framework is chosen for option pricing, the bottleneck of the market calibration is the computation of the variance…
We construct realistic spot and equity option market simulators for a single underlying on the basis of normalizing flows. We address the high-dimensionality of market observed call prices through an arbitrage-free autoencoder that…
A high-fidelity kinetic Monte Carlo (KMC) simulation method (T. Treeratanaphitak, M. Pritzker, N. M. Abukhdeir, Electrochim. Acta 121 (2014) 407--414) using the semi-empirical multi-body embedded-atom method (EAM) potential has been…
Diagrammatic Monte Carlo -- the technique for numerically exact summation of all Feynman diagrams to high orders -- offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the…
In this work we illustrate our novel quantitative simulation approach for dense amorphous polymer systems, as discussed in our previous work[Kulkarni et al., A Novel Approach for Lattice Simulations of Polymer Chains in Dense Amorphous…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in…
This paper explores stochastic modeling approaches to elucidate the intricate dynamics of stock prices and volatility in financial markets. Beginning with an overview of Brownian motion and its historical significance in finance, we delve…
In this paper, we extend the 3/2-model for VIX studied by Goard and Mazur (2013) and introduce the generalized 3/2 and 1/2 classes of volatility processes. Under these models, we study the pricing of European and American VIX options and,…
Mean field-like approximations (including naive mean field, Bethe and Kikuchi and more general Cluster Variational Methods) are known to stabilize ordered phases at temperatures higher than the thermodynamical transition. For example, in…
The ability to construct a realistic simulator of financial exchanges, including reproducing the dynamics of the limit order book, can give insight into many counterfactual scenarios, such as a flash crash, a margin call, or changes in…
Existing variance reduction techniques used in stochastic simulations for rare event analysis still require a substantial number of model evaluations to estimate small failure probabilities. In the context of complex, nonlinear finite…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
This paper introduces a drift optimization model of stochastic optimization problems driven by regulated stochastic processes. A broad range of problems across operations research, machine learning, and statistics can be viewed as…
A rigourous Monte Carlo method for protein folding simulation on lattice model is introduced. We show that a parameter which can be seen as the rigidity of the conformations has to be introduced in order to satisfy the detailed balance…
L\'{e}vy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on L\'{e}vy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse…
Variance reduction techniques are of crucial importance for the efficiency of Monte Carlo simulations in finance applications. We propose the use of neural SDEs, with control variates parameterized by neural networks, in order to learn…