MARTINGALE METHODS IN FINANCIAL MODELING

Le Monde En Tique

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Ouvrage 9783540614777 : MARTINGALE METHODS IN FINANCIAL MODELING
The book provides a comprehensive, self-contained
and up-to-date treatment of the main
topics in the theory of option pricing. The first
part of the text deals with simple discrete
models of financial markets, including the
Cox-Ross-Rubinstein binomial model. No
knowledge of probability and stochastic processes
is assumed at this stage, while most of
the concepts from modern mathematical finance are
explained at a very elementary
mathematical level. The passage from the discrete
to the continuous market models, done
in the Black-Scholes model setting, assumes
familiarity with basic ideas and results from
stochastic calculus such as Wiener process and Ito
formula; however, an appendix
containing all the necessary results is included.
The Black-Scholes setting is later
generalized to cover standard and exotic options
involving several assets and/or
currencies. Numerous examples of exotic options are
analysed. An outline of a general
theory of arbitrage pricing is presented. A very
substantial part of the text is devoted to
term structure modelling and to the pricing of
interest rate options. The HJM framework is
discussed in detail. Models based on the forward
LIBOR and forward swap rates are
introduced. The main emphasis is on models that can
be made consistent with the market
pricing practice.
Table of Contents
Preface
1
An Introduction to Financial Derivatives
3
2
The Cox-Ross-Rubinstein Model
33
3
Finite Security Markets
69
4
Market Imperfections
87
5
The Black-Scholes Model
109
6
Modifications of the Black-Scholes
Model
135
7
Foreign Market Derivatives
159
8
American Options
183
9
Exotic Options
205
10
Continuous-time Security Markets
229
11
Interest Rates and Related Contracts
265
12
Models of the Short-term Rate
281
13
Models of Instantaneous Forward Rates
303
14
Models of Bond Prices and LIBOR Rates
325
15
Option Valuation in Gaussian Models
357
16
Swap Derivatives
387
17
Cross-currency Derivatives
419
App. A
Conditional Expectations
455
App. B
Ito Stochastic Calculus
459
References
471
Index
507


Auteur : MUSIELA
Editeur : SPRINGER VERLAG
Nombre de pages : 512
Date de publication : 08 1997

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