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Related papers: Numerical methods for the L\'evy LIBOR model

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We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are non-negative, and the basic requirement from mathematical…

Pricing of Securities · Quantitative Finance 2015-03-13 Martin Keller-Ressel , Antonis Papapantoleon , Josef Teichmann

We introduce an algorithm for the pricing of finite expiry American options driven by L\'evy processes. The idea is to tweak Carr's `Canadisation' method, cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjusted algorithm…

Probability · Mathematics 2013-04-17 Florian Kleinert , Kees van Schaik

We describe a regression-based method, generally referred to as the Least Squares Monte Carlo (LSMC) method, to speed up exposure calculations of a portfolio. We assume that the portfolio contains several exotic derivatives that are priced…

Computational Finance · Quantitative Finance 2021-05-18 Yuriy Krepkiy , Asif Lakhany , Amber Zhang

Using a Levy process we generalize formulas in Bo et al.(2010) for the Esscher transform parameters for the log-normal distribution which ensure the martingale condition holds for the discounted foreign exchange rate. Using these values of…

Computational Finance · Quantitative Finance 2014-02-11 Anatoliy Swishchuk , Maksym Tertychnyi , Robert Elliott

In this paper we derive a efficient Monte Carlo approximation for the price of path-dependent derivatives under the multiscale stochastic volatility models of Fouque \textit{et al}. Using the formulation of this pricing problem under the…

Computational Finance · Quantitative Finance 2020-05-12 Yuri F. Saporito

In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman (1997) to price a $\pi$-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of…

Computational Finance · Quantitative Finance 2020-08-26 Zbigniew Palmowski , Tomasz Serafin

Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…

Numerical Analysis · Mathematics 2015-05-06 Desmond J. Higham

In this paper we propose a novel dual regression-based approach for pricing American options. This approach reduces the complexity of the nested Monte Carlo method and has especially simple form for time discretised diffusion processes. We…

Computational Finance · Quantitative Finance 2018-06-07 Denis Belomestny , Stefan Häfner , Mikhail Urusov

We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and…

Computational Finance · Quantitative Finance 2020-06-02 David Farahany , Kenneth Jackson , Sebastian Jaimungal

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-01-15 Qasim Nasar-Ullah

We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation.…

Probability · Mathematics 2018-11-16 Bruno Bouchard , Ki Chau , Arij Manai , Ahmed Sid-Ali

Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with…

Computational Finance · Quantitative Finance 2019-08-27 Kenji Nagami

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

Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general,…

Computation · Statistics 2016-08-12 Deborshee Sen , Ajay Jasra , Yan Zhou

Efficiently pricing multi-asset options is a challenging problem in quantitative finance. When the characteristic function is available, Fourier-based methods are competitive compared to alternative techniques because the integrand in the…

Computational Finance · Quantitative Finance 2024-01-17 Michael Samet , Christian Bayer , Chiheb Ben Hammouda , Antonis Papapantoleon , Raúl Tempone

An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and…

Statistical Mechanics · Physics 2009-11-07 G. Montagna , O. Nicrosini , N. Moreni

In this survey paper we discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations…

Mathematical Finance · Quantitative Finance 2016-07-19 Zuzana Buckova , Beata Stehlikova , Daniel Sevcovic

The problem of the construction of strong approximations with a given order of convergence for jump-diffusion equations is studied. General approximation schemes are constructed for L\'evy type stochastic differential equation. In…

Probability · Mathematics 2015-12-22 Michał Barski

This paper is a supplement to our recent paper ``Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models". We introduce the class of regime-switching L\'evy models with memory,…

Pricing of Securities · Quantitative Finance 2024-02-27 Svetlana Boyarchenko , Sergei Levendorskiĭ

A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n)…

Statistical Mechanics · Physics 2009-11-10 Cristian Predescu