Pricing Derivative Securities

    The development of successful techniques for valuing derivative assets is among the most influential achievements of economic science. Pricing Derivative Securities presents the theory of financial derivatives in a way that emphasizes both its mathematical foundations and its practical implementation. The book's organization reveals its three distinctive features. Part I surveys the necessary tools of analysis, probability theory, and stochastic calculus, thus making the book self-contained. The chapters in Part II, Pricing Theory, are organized around the dynamics of the price processes of underlying assets, progressing from simple models to those that require considerable mathematical sophistication. The last part of the book is devoted to the empirical implementation of the pricing formulas developed in Part II, offering a detailed survey of numerical methods and providing a collection of programs in FORTRAN and C++ that implement many of the techniques.

Preface
ⅠPreliminaries:
1 Introduction and Overview
1.1 A Tour of Derivatives and Markets
1.1.1 Forward Contracts
1.1.2 Futures
1.1.3 'Vanilla'Options
1.1.4 Other Derivative Products
1.2 An Overview of Derivatives Pricing
1.2.1 Replication:Static and Dynamic
1.2.2 Approaces to Valuation when Replication is Possible
1.2.3 Markets:Complete and Otherwise
1.2.4 Derivatives Pricing in Incomplete Markets
2 Mathematical Preparation
2.1 Analytical Tools
2.1.1 Order Notation
2.1.2 Series Expansions
2.1.3 Measures
2.1.4 Measurable Functions
2.1.5 Variation and Absolute Continuity of Functions
2.1.6 Integraton
2.1.7 Change of Measure:Radon-Nikodym Theorem
2.1.8 Special Functions and Integral Transforms
2.2 Probability
……
3 Tools for Continuous-Time Models
ⅡPricing Theory:
4 Dynamics-Free Pricing
5 Pricing Under Bernoulli Dynamics
6 Black-Scholes Dynamics
7 American Options and 'Exotics'
8 Models with Uncertain Volatility
9 Discontinuous Processes
10 Interest-Rate Dynamics
ⅢComputational Methods
11 Simulation
12 Solving PDEs Numerically
13 Programs
Bibliography
Index