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High Order Compact Finite Difference Scheme For Option Pricing In Stochastic Volatility Models
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Book Synopsis High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Models by : Bertram Düring
Download or read book High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Models written by Bertram Düring and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann are presented. Where the analysis becomes too involved we validate our findings by a numerical study. Numerical experiments for the European option pricing problem are presented. We observe fourth order convergence for non-smooth payoff.
Book Synopsis High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility With Contemporaneous Jump Models by : Bertram Düring
Download or read book High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility With Contemporaneous Jump Models written by Bertram Düring and published by . This book was released on 2018 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend the scheme developed in B. Düring, A. Pitkin, ”High-order compact finite difference scheme for option pricing in stochastic volatility jump models”, 2017, to the so-called stochastic volatility with contemporaneous jumps (SVCJ) model, derived by Duffie, Pan and Singleton. The performance of the scheme is assessed through a number of numerical experiments, using comparisons against a standard second-order central difference scheme. We observe that the new high-order compact scheme achieves third order convergence alongside improvements in efficiency and computation time.
Book Synopsis High-Order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Models on Non-Uniform Grids by : Bertram Düring
Download or read book High-Order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Models on Non-Uniform Grids written by Bertram Düring and published by . This book was released on 2014 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical study we obtain high-order numerical convergence also for non-zero correlation and non-smooth payoffs which are typical in option pricing. In all numerical experiments a comparative standard second-order discretisation is significantly outperformed. We conduct a numerical stability study which indicates unconditional stability of the scheme.
Book Synopsis High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Jump Models by : Bertram Düring
Download or read book High-Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Jump Models written by Bertram Düring and published by . This book was released on 2017 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential equation. The scheme is fourth order accurate in space and second order accurate in time. Numerical experiments for the European option pricing problem are presented. We validate the stability of the scheme numerically and compare its efficiency and hedging performance to standard finite difference methods. The new scheme outperforms a standard discretisation based on a second-order central finite difference approximation in all our experiments. At the same time, it is very efficient, requiring only one initial LU-factorisation of a sparse matrix to perform the option price valuation. It can also be useful to upgrade existing implementations based on standard finite differences in a straightforward manner to obtain a highly efficient option pricing code.
Book Synopsis High-order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Jump-diffusion Models by : Alexander Pitkin
Download or read book High-order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Jump-diffusion Models written by Alexander Pitkin and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Essentially High-Order Compact Schemes with Application to Stochastic Volatility Models on Non-Uniform Grids by : Bertram Düring
Download or read book Essentially High-Order Compact Schemes with Application to Stochastic Volatility Models on Non-Uniform Grids written by Bertram Düring and published by . This book was released on 2016 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of stochastic volatility models. We use a non-uniform grid with more grid-points around the strike price. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numerical convergence study we achieve fourth-order accuracy also for non-zero correlation. A combination of Crank-Nicolson and BDF-4 discretisation is applied in time. Numerical examples confirm that a standard, second-order finite difference scheme is significantly outperformed.
Book Synopsis High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models by : Bertram Düring
Download or read book High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models written by Bertram Düring and published by . This book was released on 2015 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer's ADI time-stepping method, to obtain an efficient method which is fourth-order accurate in space and second-order accurate in time. Numerical experiments for the European put option pricing problem using Heston's stochastic volatility model confirm the high-order convergence.
Book Synopsis Novel Methods in Computational Finance by : Matthias Ehrhardt
Download or read book Novel Methods in Computational Finance written by Matthias Ehrhardt and published by Springer. This book was released on 2017-09-19 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector. The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models. In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry. Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.
Book Synopsis Computational Sciences - Modelling, Computing and Soft Computing by : Ashish Awasthi
Download or read book Computational Sciences - Modelling, Computing and Soft Computing written by Ashish Awasthi and published by Springer Nature. This book was released on 2021-07-27 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes revised and selected papers of the First International Conference on Computational Sciences - Modelling, Computing and Soft Computing, held in Kozhikode, Kerala, India, in September 2020. The 15 full papers and 6 short papers presented were thoroughly reviewed and selected from the 150 submissions. They are organized in the topical secions on computing; soft computing; general computing; modelling.
Book Synopsis Pricing Derivatives in Stochastic Volatility Models Using the Finite Difference Method by :
Download or read book Pricing Derivatives in Stochastic Volatility Models Using the Finite Difference Method written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Heston stochastic volatility model is one extension of the Black-Scholes model which describes the money markets more accurately so that more realistic prices for derivative products are obtained. From the stochastic differential equation of the underlying financial product a partial differential equation (p.d.e.) for the value function of an option can be derived. This p.d.e. can be solved with the finite difference method (f.d.m.). The stability and consistency of the method is examined. Furthermore a boundary condition is proposed to reduce the numerical error. Finally a non uniform structured grid is derived which is fairly optimal for the numerical result in the most interesting point.
Book Synopsis Recent Advances in Mathematical and Statistical Methods by : D. Marc Kilgour
Download or read book Recent Advances in Mathematical and Statistical Methods written by D. Marc Kilgour and published by Springer. This book was released on 2018-11-04 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the recent development of methodologies and computation methods in mathematical and statistical modelling, computational science and applied mathematics. It emphasizes the development of theories and applications, and promotes interdisciplinary endeavour among mathematicians, statisticians, scientists, engineers and researchers from other disciplines. The book provides ideas, methods and tools in mathematical and statistical modelling that have been developed for a wide range of research fields, including medical, health sciences, biology, environmental science, engineering, physics and chemistry, finance, economics and social sciences. It presents original results addressing real-world problems. The contributions are products of a highly successful meeting held in August 2017 on the main campus of Wilfrid Laurier University, in Waterloo, Canada, the International Conference on Applied Mathematics, Modeling and Computational Science (AMMCS-2017). They make this book a valuable resource for readers interested not only in a broader overview of the methods, ideas and tools in mathematical and statistical approaches, but also in how they can attain valuable insights into problems arising in other disciplines.
Book Synopsis Pricing Options Under Heston's Stochastic Volatility Model Via Accelerated Explicit Finite Differencing Methods by : Conall O'Sullivan
Download or read book Pricing Options Under Heston's Stochastic Volatility Model Via Accelerated Explicit Finite Differencing Methods written by Conall O'Sullivan and published by . This book was released on 2010 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an acceleration technique, effective for explicit finite difference schemes describing diffusive processes with nearly symmetric operators, called Super-Time-Stepping (STS). The technique is applied to the two-factor problem of option pricing under stochastic volatility. It is shown to significantly reduce the severity of the stability constraint known as the Courant-Friedrichs-Lewy condition whilst retaining the simplicity of the chosen underlying explicit method. For European and American put options under Heston's stochastic volatility model we demonstrate degrees of acceleration over standard explicit methods sufficient to achieve comparable, or superior, efficiencies to a benchmark implicit scheme. We conclude that STS is a powerful tool for the numerical pricing of options and propose them as the method-of-choice for exotic financial instruments in two and multi-factor models.
Book Synopsis Progress in Industrial Mathematics at ECMI 2021 by : Matthias Ehrhardt
Download or read book Progress in Industrial Mathematics at ECMI 2021 written by Matthias Ehrhardt and published by Springer Nature. This book was released on 2022-11-25 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers peer-reviewed contributions submitted to the 21st European Conference on Mathematics for Industry, ECMI 2021, which was virtually held online, hosted by the University of Wuppertal, Germany, from April 13th to April 15th, 2021. The works explore mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Topics covered include: Applied Physics, Biology and Medicine, Cybersecurity, Data Science, Economics, Finance and Insurance, Energy, Production Systems, Social Challenges, and Vehicles and Transportation. The goal of the European Consortium for Mathematics in Industry (ECMI) conference series is to promote interaction between academia and industry, leading to innovations in both fields. These events have attracted leading experts from business, science and academia, and have promoted the application of novel mathematical technologies to industry. They have also encouraged industrial sectors to share challenging problems where mathematicians can provide fresh insights and perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.
Book Synopsis Progress in Industrial Mathematics at ECMI 2010 by : Michael Günther
Download or read book Progress in Industrial Mathematics at ECMI 2010 written by Michael Günther and published by Springer Science & Business Media. This book was released on 2012-04-05 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: ECMI, the European Consortium for Mathematics in Industry, is the European brand associated with applied mathematics for industry and organizes highly successful biannual conferences. In this series, the ECMI 2010, the 16th European Conference on Mathematics for Industry, was held in the historic city hall of Wuppertal in Germany. It covered the mathematics of a wide range of applications and methods, from circuit and electromagnetic device simulation to model order reduction for chip design, uncertainties and stochastics, production, fluids, life and environmental sciences, and dedicated and versatile methods. These proceedings of ECMI 2010 emphasize mathematics as an innovation enabler for industry and business, and as an absolutely essential pre-requiste for Europe on its way to becoming the leading knowledge-based economy in the world.
Book Synopsis Progress in Industrial Mathematics at ECMI 2014 by : Giovanni Russo
Download or read book Progress in Industrial Mathematics at ECMI 2014 written by Giovanni Russo and published by Springer. This book was released on 2017-09-04 with total page 1139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of papers emphasizing applications of mathematical models and methods to real-world problems of relevance for industry, life science, environment, finance and so on. The biannual Conference of ECMI (the European Consortium of Mathematics in Industry) held in 2014 focused on various aspects of industrial and applied mathematics. The five main topics addressed at the conference were mathematical models in life science, material science and semiconductors, mathematical methods in the environment, design automation and industrial applications, and computational finance. Several other topics have been treated, such as, among others, optimization and inverse problems, education, numerical methods for stiff pdes, model reduction, imaging processing, multi physics simulation, mathematical models in textile industry. The conference, which brought together applied mathematicians and experts from industry, provided a unique opportunity to exchange ideas, problems and methodologies, bridging the gap between mathematics and industry and contributing to the advancement of science and technology. The conference has included a presentation of EU-Maths-In (European Network of Mathematics for Industry and Innovation), a recent joint initiative of ECMI and EMS. The proceedings from this conference represent a snapshot of the current activity in industrial mathematics in Europe, and are highly relevant to anybody interested in the latest applications of mathematics to industrial problems.
Book Synopsis Progress in Industrial Mathematics at ECMI 2018 by : István Faragó
Download or read book Progress in Industrial Mathematics at ECMI 2018 written by István Faragó and published by Springer Nature. This book was released on 2019-11-22 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. The book gathers 81 contributions submitted to the 20th European Conference on Mathematics for Industry, ECMI 2018, which was held in Budapest, Hungary in June 2018. The application areas include: Applied Physics, Biology and Medicine, Cybersecurity, Data Science, Economics, Finance and Insurance, Energy, Production Systems, Social Challenges, and Vehicles and Transportation. In turn, the mathematical technologies discussed include: Combinatorial Optimization, Cooperative Games, Delay Differential Equations, Finite Elements, Hamilton-Jacobi Equations, Impulsive Control, Information Theory and Statistics, Inverse Problems, Machine Learning, Point Processes, Reaction-Diffusion Equations, Risk Processes, Scheduling Theory, Semidefinite Programming, Stochastic Approximation, Spatial Processes, System Identification, and Wavelets. The goal of the European Consortium for Mathematics in Industry (ECMI) conference series is to promote interaction between academia and industry, leading to innovations in both fields. These events have attracted leading experts from business, science and academia, and have promoted the application of novel mathematical technologies to industry. They have also encouraged industrial sectors to share challenging problems where mathematicians can provide fresh insights and perspectives. Lastly, the ECMI conferences are one of the main forums in which significant advances in industrial mathematics are presented, bringing together prominent figures from business, science and academia to promote the use of innovative mathematics in industry.
Book Synopsis Mathematical Modeling and Methods of Option Pricing by : Lishang Jiang
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
