
- 420 pages
- English
- PDF
- Available on iOS & Android
Non-gaussian Merton-black-scholes Theory
About this book
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 pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
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Information
Table of contents
- Contents
- Preface
- Chapter 1 Introduction
- Chapter 2 Levy processes
- Chapter 3 Regular Levy Processes of Exponential type in 1D
- Chapter 4 Pricing and hedging of contingent claims of European type
- Chapter 5 Perpetual American options
- Chapter 6 American options: finite time horizon
- Chapter 7 First-touch digitals
- Chapter 8 Barrier options
- Chapter 9 Multi-asset contracts
- Chapter 10 Investment under uncertainty and capital accumulation
- Chapter 11 Endogenous default and pricing of the corporate debt
- Chapter 12 Fast pricing of European options
- Chapter 13 Discrete time models
- Chapter 14 Feller processes of normal inverse Gaussian type
- Chapter 15 Pseudo-differential operators with constant symbols
- Chapter 16 Elements of calculus of pseudodifferential operators
- Bibliography
- Index