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Pricing Options Under Hestons Stochastic Volatility Model Via Accelerated Explicit Finite Differencing Methods
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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 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 Numerical Methods for Pricing American Put Options Under Stochastic Volatility by : Dominique Joubert
Download or read book Numerical Methods for Pricing American Put Options Under Stochastic Volatility written by Dominique Joubert and published by . This book was released on 2013 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Pricing American Put Options Under Stochastic Volatility by : Dominique Joubert
Download or read book Numerical Methods for Pricing American Put Options Under Stochastic Volatility written by Dominique Joubert and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early exercise boundary -- Free boundary value problem -- Linear complimentary problem -- Crank-Nicolson finite difference method -- Projected Over-Relaxation method (PSOR) -- Stochastic volatility -- Heston stochastic volatility model -- Vroeë uitoefengrens -- Vrye grenswaardeprobleem -- Linêere komplimentêre probleem -- Crank-Nicolson eindige differensiemetode -- Geprojekteerde oorverslappingsmetode (PSOR) -- Stogastiese volatiliteit -- Heston stogastiese volatiliteitsmodel.
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 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 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 The Evaluation of American Compound Option Prices under Stochastic Volatility Using the Sparse Grid Approach by : Carl Chiarella
Download or read book The Evaluation of American Compound Option Prices under Stochastic Volatility Using the Sparse Grid Approach written by Carl Chiarella and published by . This book was released on 2009 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a partial differential equation (PDE) approach to pricing American-type compound options where the underlying dynamics follow Heston's stochastic volatility model. This price is formulated as the solution to a two-pass free boundary PDE problem. A modified sparse grid approach is implemented to solve the PDEs, which is shown to be accurate and efficient compared with the results from Monte Carlo simulation combined with the Method of Lines.
Book Synopsis On the Valuation of Fader and Discrete Barrier Options in Heston's Stochastic Volatility Model by : Susanne Griebsch
Download or read book On the Valuation of Fader and Discrete Barrier Options in Heston's Stochastic Volatility Model written by Susanne Griebsch and published by . This book was released on 2010 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We focus on closed-form option pricing in Heston's stochastic volatility model, where closed-form formulas exist only for a few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this closed-form approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times.
Book Synopsis Exotic Option Pricing in Heston's Stochastic Volatility Model by : Susanne A. Griebsch
Download or read book Exotic Option Pricing in Heston's Stochastic Volatility Model written by Susanne A. Griebsch and published by . This book was released on 2008 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Acceleration of Explicit Finite Difference Methods for Option Pricing by : Stephen O'Sullivan
Download or read book On the Acceleration of Explicit Finite Difference Methods for Option Pricing written by Stephen O'Sullivan and published by . This book was released on 2016 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implicit finite difference methods are conventionally preferred over their explicit counterparts for the valuation of options. In large part the reason for this is a severe stability constraint known as the Courant-Friedrichs-Lewy (CFL) condition which limits the latters' efficiencies. Implicit methods, however, are difficult to implement for all but the most simple of pricing models whereas explicit techniques are easily adapted to complex problems. In this work we present an acceleration technique for explicit finite difference schemes called Super-Time-Stepping (STS) for the first time in a financial context. Furthermore, we introduce a novel method for describing the efficiencies of finite difference schemes as semi-empirical power laws relating the minimal walltime W required to attain a solution with an error of magnitude E. For European and American put option test cases we demonstrate degrees of acceleration over standard explicit methods resulting in efficiencies comparable, or superior, to a set of implicit scheme benchmarks. We conclude that STS is a powerful tool for the numerical pricing of options and propose it as the method-of-choice for exotic financial intruments such as those requiring multi-dimensional descriptions on adaptive meshes.
Book Synopsis The Heston Model and its Extensions in Matlab and C# by : Fabrice D. Rouah
Download or read book The Heston Model and its Extensions in Matlab and C# written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2013-08-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.
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 Option Pricing Under Stochastic Volatility by : Martin Jan Andersen
Download or read book Option Pricing Under Stochastic Volatility written by Martin Jan Andersen and published by . This book was released on 2015 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis High-Performance Computing Using FPGAs by : Wim Vanderbauwhede
Download or read book High-Performance Computing Using FPGAs written by Wim Vanderbauwhede and published by Springer Science & Business Media. This book was released on 2013-08-23 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-Performance Computing using FPGA covers the area of high performance reconfigurable computing (HPRC). This book provides an overview of architectures, tools and applications for High-Performance Reconfigurable Computing (HPRC). FPGAs offer very high I/O bandwidth and fine-grained, custom and flexible parallelism and with the ever-increasing computational needs coupled with the frequency/power wall, the increasing maturity and capabilities of FPGAs, and the advent of multicore processors which has caused the acceptance of parallel computational models. The Part on architectures will introduce different FPGA-based HPC platforms: attached co-processor HPRC architectures such as the CHREC’s Novo-G and EPCC’s Maxwell systems; tightly coupled HRPC architectures, e.g. the Convey hybrid-core computer; reconfigurably networked HPRC architectures, e.g. the QPACE system, and standalone HPRC architectures such as EPFL’s CONFETTI system. The Part on Tools will focus on high-level programming approaches for HPRC, with chapters on C-to-Gate tools (such as Impulse-C, AutoESL, Handel-C, MORA-C++); Graphical tools (MATLAB-Simulink, NI LabVIEW); Domain-specific languages, languages for heterogeneous computing(for example OpenCL, Microsoft’s Kiwi and Alchemy projects). The part on Applications will present case from several application domains where HPRC has been used successfully, such as Bioinformatics and Computational Biology; Financial Computing; Stencil computations; Information retrieval; Lattice QCD; Astrophysics simulations; Weather and climate modeling.
Book Synopsis Pricing Multi-windowed Barrier Options Using Finite Element Method by : Chengshi Ai
Download or read book Pricing Multi-windowed Barrier Options Using Finite Element Method written by Chengshi Ai and published by . This book was released on 2013 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study pricing multi-windowed barrier options under three different models: Black-Scholes' model, Heston model, and the multi-dimensional Heston model proposed by De Col, Gnoatto and Grasselli. The PDE approach is employed where the option price is deemed as the solution of a partial differential equation. The PDEs arising in the area of option pricing are most parabolic equations. The interesting questions are a) how to deal with the semi-infinite boundary; b) how to determine the boundary conditions when the domain changes with time. Especially we also consider the situation where the Feller condition is violated in the foreign exchange markets, which gives degenerate parabolic equations. We use the finite element method to obtain the numerical results of the PDEs. It is implemented by C++. The main result of this thesis provides a practical scheme in pricing options in a real market scenario. All the coefficients used in the multi-dimensional Heston model can be calibrated once for all according to the real markets. Then the model dimension can be reduced when different types of options are priced.
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:
