Novel methods in computational finance

Description

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. Front Matter ....Pages i-xviii Front Matter ....Pages 1-1 Nonlinear Parabolic Equations Arising in Mathematical Finance (Daniel Ševčovič)....Pages 3-15 Modeling of Herding and Wealth Distribution in Large Markets (Ansgar Jüngel, Lara Trussardi)....Pages 17-29 Indifference Pricing in a Market with Transaction Costs and Jumps (Nicola Cantarutti, João Guerra, Manuel Guerra, Maria do Rosário Grossinho)....Pages 31-46 Negative Rates: New Market Practice (Jörg Kienitz)....Pages 47-63 Accurate Vega Calculation for Bermudan Swaptions (Mark Beinker, Sebastian Schlenkrich)....Pages 65-82 Modelling and Calibration of Stochastic Correlation in Finance (Long Teng, Matthias Ehrhardt, Michael Günther)....Pages 83-105 Front Matter ....Pages 107-107 Lie Group Analysis of Nonlinear Black-Scholes Models (Ljudmila A. Bordag, Ivan P. Yamshchikov)....Pages 109-128 Analytical and Numerical Results for American Style of Perpetual Put Options Through Transformation into Nonlinear Stationary Black-Scholes Equations (Maria do Rosário Grossinho, Yaser Faghan, Daniel Ševčovič)....Pages 129-142 Stochastic Dynamic Programming and Control of Markov Processes (Manuel Guerra)....Pages 143-167 Front Matter ....Pages 169-169 Numerical Analysis of Novel Finite Difference Methods (Rafael Company, Vera N. Egorova, Mohamed El Fakharany, Lucas Jódar, Fazlollah Soleymani)....Pages 171-214 Modified Barrier Penalization Method for Pricing American Options (Miglena N. Koleva, Radoslav L. Valkov)....Pages 215-226 Front Matter ....Pages 227-227 Newton-Based Solvers for Nonlinear PDEs in Finance (Shih-Hau Tan, Choi-Hong Lai)....Pages 229-242 Implicit-Explicit Schemes for European Option Pricing with Liquidity Shocks (Walter Mudzimbabwe, Lubin Vulkov)....Pages 243-251 A Highly Efficient Numerical Method for the SABR Model (Álvaro Leitao, Lech A. Grzelak, Cornelis W. Oosterlee)....Pages 253-263 PDE Methods for SABR (Jörg Kienitz, Thomas McWalter, Roelof Sheppard)....Pages 265-291 Front Matter ....Pages 293-293 Sparse Grid High-Order ADI Scheme for Option Pricing in Stochastic Volatility Models (Bertram Düring, Christian Hendricks, James Miles)....Pages 295-312 Essentially High-Order Compact Schemes with Application to Stochastic Volatility Models on Non-Uniform Grids (Bertram Düring, Christof Heuer)....Pages 313-319 High Order Compact Schemes for Option Pricing with Liquidity Shocks (Miglena N. Koleva, Walter Mudzimbabwe, Lubin G. Vulkov)....Pages 321-331 Alternating Direction Explicit Methods for Linear, Nonlinear and Multi-Dimensional Black-Scholes Models (Zuzana Bučková, Matthias Ehrhardt, Michael Günther, Pedro Pólvora)....Pages 333-371 Numerical Study of Splitting Methods for American Option Valuation (Karel in ’t Hout, Radoslav L. Valkov)....Pages 373-398 High-Order-Compact ADI Schemes for Pricing Basket Options in the Combination Technique (Christian Hendricks, Christof Heuer, Matthias Ehrhardt, Michael Günther)....Pages 399-405 Front Matter ....Pages 407-407 Splitting Methods for Fokker-Planck Equations Related to Jump-Diffusion Processes (Beatrice Gaviraghi, Mario Annunziato, Alfio Borzì)....Pages 409-422 A Fokker-Planck Based Approach to Control Jump Processes (Beatrice Gaviraghi, Mario Annunziato, Alfio Borzì)....Pages 423-439 Proper Orthogonal Decomposition in Option Pricing (José P. Silva, E. Jan W. ter Maten, Michael Günther, Matthias Ehrhardt)....Pages 441-452 Front Matter ....Pages 453-453 Alternative Parallel Strategies for Linear and Nonlinear PDEs in Option Pricing (Choi-Hong Lai, André M. S. Ribeiro, Natkunam Kokulan)....Pages 455-463 Modern Monte Carlo Methods and GPU Computing (Álvaro Leitao, Cornelis W. Oosterlee)....Pages 465-476 Sparse Grid Combination Technique for Hagan SABR/LIBOR Market Model (José Germán López-Salas, Carlos Vázquez Cendón)....Pages 477-500 Front Matter ....Pages 501-501 Stochastic Filtering Methods in Electronic Trading (Paul Bilokon, James Gwinnutt, Daniel Jones)....Pages 503-542 Using Python to Analyse Financial Markets (Saeed Amen)....Pages 543-559 The STRIKE Computational Finance Toolbox (Christof Heuer, Pedro Pólvora, José Silva, Matthias Ehrhardt, Michael Günther, E. Jan W. ter Maten)....Pages 561-601 Back Matter ....Pages 603-606