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We propose a multi-scale stochastic volatility model in which a fast mean-reverting factor of volatility is built on top of the Heston stochastic volatility model. A singular pertubative expansion is then used to obtain an approximation for…

Pricing of Securities · Quantitative Finance 2012-05-15 Jean-Pierre Fouque , Matthew Lorig

We investigate the statistical evidence for the use of `rough' fractional processes with Hurst exponent $H< 0.5$ for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-parametric method for…

Statistical Finance · Quantitative Finance 2023-07-11 Rama Cont , Purba Das

This article addresses the problem of approximating the price of options on discrete and continuous arithmetic average of the underlying, i.e. discretely and continuously monitored Asian options, in local volatility models. A…

Computational Finance · Quantitative Finance 2018-08-13 Louis-Pierre Arguin , Nien-Lin Liu , Tai-Ho Wang

We construct estimators for the parameters of a parabolic SPDE with one spatial dimension based on discrete observations of a solution in time and space on a bounded domain. We establish central limit theorems for a high-frequency…

Statistics Theory · Mathematics 2025-04-23 Markus Bibinger , Patrick Bossert

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting.…

Pricing of Securities · Quantitative Finance 2012-05-15 Matthew Lorig

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

Machine Learning · Statistics 2014-02-21 Keisuke Yamazaki

In this paper we study the small noise asymptotic expansions for certain classes of local volatility models arising in finance. We provide explicit expressions for the involved coefficients as well as accurate estimates on the remainders.…

Probability · Mathematics 2018-09-19 Sergio ALbeverio , Francesco Cordoni , Luca Di Persio , Gregorio Pellegrini

We introduce Stochastic Asymptotical Regularization (SAR) methods for the uncertainty quantification of the stable approximate solution of ill-posed linear-operator equations, which are deterministic models for numerous inverse problems in…

Numerical Analysis · Mathematics 2022-12-21 Ye Zhang , Chuchu Chen

We consider the pricing of derivatives written on the discretely sampled realized variance of an underlying security. In the literature, the realized variance is usually approximated by its continuous-time limit, the quadratic variation of…

Pricing of Securities · Quantitative Finance 2010-11-24 Martin Keller-Ressel , Johannes Muhle-Karbe

This paper investigates asymptotically optimal importance sampling (IS) schemes for pricing European call options under the Heston stochastic volatility model. We focus on two distinct rare-event regimes where standard Monte Carlo methods…

Mathematical Finance · Quantitative Finance 2025-11-26 Yun-Feng Tu , Chuan-Hsiang Han

We propose a novel time discretization for the log-normal SABR model which is a popular stochastic volatility model that is widely used in financial practice. Our time discretization is a variant of the Euler-Maruyama scheme. We study its…

Mathematical Finance · Quantitative Finance 2021-10-18 Dan Pirjol , Lingjiong Zhu

Techniques from deep learning play a more and more important role for the important task of calibration of financial models. The pioneering paper by Hernandez [Risk, 2017] was a catalyst for resurfacing interest in research in this area. In…

Mathematical Finance · Quantitative Finance 2019-08-26 Christian Bayer , Blanka Horvath , Aitor Muguruza , Benjamin Stemper , Mehdi Tomas

The purpose of this article is to solve rough differential equations with the theory of regularity structures. These new tools recently developed by Martin Hairer for solving semi-linear partial differential stochastic equations were…

Probability · Mathematics 2019-10-15 Antoine Brault

This work extends the variance reduction method for the pricing of possibly path-dependent derivatives, which was developed in (Genin and Tankov, 2016) for exponential L\'evy models, to affine stochastic volatility models (Keller-Ressel,…

Probability · Mathematics 2018-09-18 Zorana Grbac , David Krief , Peter Tankov

The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the…

Pricing of Securities · Quantitative Finance 2014-09-19 José Da Fonseca , Claude Martini

We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for…

Optimization and Control · Mathematics 2022-01-19 Daniel Bartl , Samuel Drapeau , Jan Obloj , Johannes Wiesel

In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains…

Pricing of Securities · Quantitative Finance 2013-05-16 Jacek Jakubowski , Maciej Wisniewolski

We study Euler-type discrete-time schemes for the rough Heston model, which can be described by a stochastic Volterra equation (with non-Lipschtiz coefficient functions), or by an equivalent integrated variance formulation. Using weak…

Numerical Analysis · Mathematics 2022-03-08 Alexandre Richard , Xiaolu Tan , Fan Yang

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…

Statistics Theory · Mathematics 2013-10-30 Peter Bickel , David Choi , Xiangyu Chang , Hai Zhang

We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works…

Risk Management · Quantitative Finance 2016-08-17 Adrien Genin , Peter Tankov