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Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia.
Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.
Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia.
Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.
Dr. Michael Konikov is an Executive Director and Head of Quantitative Development at Numerix, where he manages a team responsible for the development and delivery of models in Numerix software. Previously, he worked at Citigroup, Barclays and Bloomberg in quantitative research and desk quant roles. He completed his PhD in mathematical finance at the University of Maryland College Park, concentrating in particular on the application of pure jump processes to option pricing. Dr. Konikov's publications cover diverse asset classes ranging from equity to interest rates and credit.
Dr. Michael Spector, Director of Quantitative Research, received his PhD in theoretical physics from the Budker Institute of Nuclear Physics, Novosibirsk. He has worked at research centers and universities in Russia, Israel, and the US and is the author of multiple publications on plasma physics, hydrodynamics, turbulence, nonlinear wave dynamics and mathematical finance. He joined the Numerix quantitative research team in 2006, working on the valuation of various exotic options (Asians, lookbacks, barriers), and has lately concentrated on the development of stochastic volatility models for interest rates and equity.
Unifies scattered modern SABR analytics in the same text
Intuitive but still rigorous explanation of complicated probabilistic concepts
Numerous numerical results for both analytics and simulations which can serve as benchmarks
1 Introduction.- 1.1 Introduction.- 1.2 Wide popularity of the SABR.- 1.3 Simple derivation.- 1.4 Modifications and extensions of the SABR.- 1.5 CMS and the SABR.- 1.6 Approximation accuracy and its improvements.- 1.7 About this book.- 2 Exact Solutions to CEV Model with Stochastic Volatility.- 2.1 Introduction.- 2.2 Transforming CEV Process into the Bessel One.- 2.3 Solution behavior near singular point x = 0, integrability, flux.- 2.4 Laplace Transform.- 2.5 Probability distributions.- 2.6 Back to CEV model.- 2.6.1 Option pricing through Chi Square distributions.- 2.7 Alternative expressions for CEV option values.- 2.8 CEV Model with Stochastic Volatility.- 2.9 Conclusion.- 3 Classic SABR Model: Exactly Solvable Cases.- 3.1 Introduction.- 3.2 Probability Density Functions for the Free Normal and Log-Normal SABR, Probabilistic Approach.- 3.3 Deriving PDFs using Kolmogorov equations.- 3.4 Option Value for the Free Normal SABR.- 3.5 OptionValue for the Lognormal SABR.- 3.6 The Zero Correlation case.- 4 Classic SABR Model: Heat Kernel Expansion and Projection on Solvable Models.- 4.1 Introduction.- 4.2 Invariant forms of Diffusion Equations.- 4.3 Heat Kernel Expansion.- 4.4 Non-Zero Correlation General Case.- 4.5 Conclusion.- References.
| Erscheinungsjahr: | 2019 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Recht, Sozialwissenschaften, Wirtschaft |
| Rubrik: | Recht & Wirtschaft |
| Medium: | Taschenbuch |
| Inhalt: |
ix
127 S. 1 s/w Illustr. 14 farbige Illustr. 127 p. 15 illus. 14 illus. in color. |
| ISBN-13: | 9783030106553 |
| ISBN-10: | 3030106551 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-10655-3 |
| Einband: | Kartoniert / Broschiert |
| Autor: |
Antonov, Alexandre
Konikov, Michael Spector, Michael |
| Hersteller: |
Springer
Palgrave Macmillan Springer International Publishing AG |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 235 x 155 x 8 mm |
| Von/Mit: | Alexandre Antonov (u. a.) |
| Erscheinungsdatum: | 02.05.2019 |
| Gewicht: | 0,224 kg |