Non-Gaussian Merton-Black-Scholes theory
Svetlana I. Boyarchenko, Sergei Z. Levendorskiĭ.
Bok Engelsk 2002 · Electronic books.
| Utgitt | Singapore ; River Edge, NJ : : World Scientific, , 2002.
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| Omfang | 1 online resource (421 p.)
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| Opplysninger | Description based upon print version of record.. - Contents ; Preface ; 0.0.1 General notation ; Chapter 1 Introduction ; 1.1 The Gaussian Merton-Black-Scholes theory ; 1.2 Regular Levy Processes of Exponential type ; 1.3 Pricing of contingent claims ; 1.4 The Generalized Black-Scholes equation. - 1.5 Analytical methods used in the book 1.6 An overview of the results covered in the book ; 1.7 Commentary ; Chapter 2 Levy processes ; 2.1 Basic notation and definitions ; 2.2 Levy processes: general definitions ; 2.3 Levy processes as Markov processes. - 2.4 Boundary value problems for the Black-Scholes-type equation 2.5 Commentary ; Chapter 3 Regular Levy Processes of Exponential type in 1D ; 3.1 Model Classes ; 3.2 Two definitions of Regular Levy Processes of Exponential type. - 3.3 Properties of the characteristic exponents and probability densities of RLPE 3.4 Properties of the infinitesimal generators ; 3.5 A ""naive approach"" to the construction of RLPE or why they are natural from the point of view of the theory of PDO ; 3.6 The Wiener-Hopf factorization. - 4.3 Generalized Black-Scholes equation and its properties for different RLPE and different choices of EMM and implications for parameter fitting. - Chapter 4 Pricing and hedging of contingent claims of European type 4.1 Equivalent Martingale Measures in a Levy market ; 4.2 Pricing of European options and the generalized Black-Scholes formula. - This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory. The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferentia
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| Sjanger | |
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| ISBN | 9810249446
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