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Related papers: Local Volatility Calibration by Optimal Transport

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Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…

Optimization and Control · Mathematics 2018-02-13 Laurent Pfeiffer

This paper presents simple formulae for the local variance gamma model of Carr and Nadtochiy, extended with a piecewise-linear local variance function. The new formulae allow to calibrate the model efficiently to market option quotes. On a…

Pricing of Securities · Quantitative Finance 2020-05-28 Fabien Le Floc'h

A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied…

Pricing of Securities · Quantitative Finance 2011-05-09 Peter Friz , Stefan Gerhold

While many questions in robust finance can be posed in the martingale optimal transport framework or its weak extension, others like the subreplication price of VIX futures, the robust pricing of American options or the construction of…

Probability · Mathematics 2023-04-20 Benjamin Jourdain , Gudmund Pammer

Local volatility is a versatile option pricing model due to its state dependent diffusion coefficient. Calibration is, however, non-trivial as it involves both proposing a hypothesis model of the latent function and a method for fitting it…

Mathematical Finance · Quantitative Finance 2021-12-08 Martin Tegner , Stephen Roberts

We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…

Machine Learning · Computer Science 2020-12-01 Nisan Chiprut , Amir Globerson , Ami Wiesel

The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…

Machine Learning · Computer Science 2024-07-04 Kirill Neklyudov , Rob Brekelmans , Alexander Tong , Lazar Atanackovic , Qiang Liu , Alireza Makhzani

We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…

Optimization and Control · Mathematics 2021-04-27 Jose Blanchet , Karthyek Murthy , Fan Zhang

We propose an optimal control method for simultaneous slewing and vibration control of flexible spacecraft. Considering dynamics on different time scales, the optimal control problem is discretized on micro and macro time grids using a…

Optimization and Control · Mathematics 2020-11-02 Yana Lishkova , Sina Ober-Blöbaum , Mark Cannon , Sigrid Leyendecker

We develop an optimization model and corresponding algorithm for the management of a demand-side platform (DSP), whereby the DSP aims to maximize its own profit while acquiring valuable impressions for its advertiser clients. We formulate…

Optimization and Control · Mathematics 2017-06-07 Paul Grigas , Alfonso Lobos , Zheng Wen , Kuang-chih Lee

We show the application of an optimal transportation approach to estimate stochastic volatility process by using the flow that optimally transports the set of particles from the prior to a posterior distribution. We also show how to direct…

Numerical Analysis · Mathematics 2017-09-06 Raphael Douady , Shohruh Miryusupov

Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…

Methodology · Statistics 2017-03-22 Hachem Saddiki , Andrew C. Trapp , Patrick Flaherty

We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the…

Analysis of PDEs · Mathematics 2015-05-08 Luigi De Pascale

We consider the problem of incentivization and optimal control of autonomous vehicles for improving traffic congestion. In our scenario, autonomous vehicles must be incentivized in order to participate in traffic improvement. Using the…

Optimization and Control · Mathematics 2020-06-18 Uroš Kalabić , Piyush Grover , Shuchin Aeron

The paper proposes an expanded version of the Local Variance Gamma model of Carr and Nadtochiy by adding drift to the governing underlying process. Still in this new model it is possible to derive an ordinary differential equation for the…

Computational Finance · Quantitative Finance 2018-12-27 Peter Carr , Andrey Itkin

Executing even moderately large derivatives orders can be expensive and risky; it's hard to balance the uncertainty of working an order over time versus paying a liquidity premium for immediate execution. Here, we introduce the Time Is…

Mathematical Finance · Quantitative Finance 2021-04-14 Kevin Patrick Darby

In this work we present a numerical method for the Optimal Mass Transportation problem. Optimal Mass Transportation (OT) is an active research field in mathematics.It has recently led to significant theoretical results as well as…

Numerical Analysis · Mathematics 2013-08-06 Jean-David Benamou , Brittany D. Froese , Adam M. Oberman

Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…

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

We present a numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices up to a finite horizon under convex transaction costs and convex trading constraints. This approach can then be…

Computational Finance · Quantitative Finance 2021-07-15 Hans Buehler , Phillip Murray , Mikko S. Pakkanen , Ben Wood

We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…

Optimization and Control · Mathematics 2018-05-24 Chuanye Gu , Zhiyou Wu , Jueyou Li