Numerical Methods For Pricing American Put Options Under Stochastic Volatility
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Author | : Dominique Joubert |
Publisher | : |
Total Pages | : 0 |
Release | : 2013 |
Genre | : Electronic dissertations |
ISBN | : |
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.
Author | : Dominique Joubert |
Publisher | : |
Total Pages | : 144 |
Release | : 2013 |
Genre | : Electronic dissertations |
ISBN | : |
Author | : Carl Chiarella |
Publisher | : World Scientific |
Total Pages | : 223 |
Release | : 2014-10-14 |
Genre | : Options (Finance) |
ISBN | : 9814452629 |
The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers'' experiences with these approaches over the years. Contents: Introduction; The Merton and Heston Model for a Call; American Call Options under Jump-Diffusion Processes; American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics OCo The Transform Approach; Representation and Numerical Approximation of American Option Prices under Heston; Fourier Cosine Expansion Approach; A Numerical Approach to Pricing American Call Options under SVJD; Conclusion; Bibliography; Index; About the Authors. Readership: Post-graduates/ Researchers in finance and applied mathematics with interest in numerical methods for American option pricing; mathematicians/physicists doing applied research in option pricing. Key Features: Complete discussion of different numerical methods for American options; Able to handle stochastic volatility and/or jump diffusion dynamics; Able to produce hedge ratios efficiently and accurately"
Author | : Samuli Ikonen |
Publisher | : |
Total Pages | : 26 |
Release | : 2005 |
Genre | : |
ISBN | : 9789513923495 |
Author | : Yves Achdou |
Publisher | : SIAM |
Total Pages | : 308 |
Release | : 2005-07-18 |
Genre | : Technology & Engineering |
ISBN | : 0898715733 |
This book allows you to understand fully the modern tools of numerical analysis in finance.
Author | : Lishang Jiang |
Publisher | : World Scientific Publishing Company |
Total Pages | : 343 |
Release | : 2005-07-18 |
Genre | : Business & Economics |
ISBN | : 9813106557 |
From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to 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. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
Author | : LEVEQUE |
Publisher | : Birkhäuser |
Total Pages | : 221 |
Release | : 2013-11-11 |
Genre | : Science |
ISBN | : 3034851162 |
These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
Author | : Ibtissam Medarhri |
Publisher | : |
Total Pages | : |
Release | : 2017 |
Genre | : |
ISBN | : 9783841673442 |
Author | : Lishang Jiang |
Publisher | : World Scientific |
Total Pages | : 344 |
Release | : 2005 |
Genre | : Science |
ISBN | : 9812563695 |
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.
Author | : Conall O'Sullivan |
Publisher | : |
Total Pages | : 41 |
Release | : 2010 |
Genre | : |
ISBN | : |
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.