CiNii 図書 - An introduction to the mathematics of financial derivatives

An Introduction to the Mathematics of Financial Derivatives, Second Edition, introduces the mathematics underlying the pricing of derivatives. The increased interest in dynamic pricing models stems from their applicability to practical situations: with the freeing of exchange, interest rates, and capital controls, the market for derivative products has matured and pricing models have become more accurate. This updated edition has six new chapters and chapter-concluding exercises, plus one thoroughly expanded chapter. The text answers the need for a resource targeting professionals, Ph.D. students, and advanced MBA students who are specifically interested in financial derivatives. This edition is also designed to become the main text in first year masters and Ph.D. programs for certain courses, and will continue to be an important manual for market professionals and professionals with mathematical, technical, or physics backgrounds.

Financial Derivatives
A Primer on Arbitrage Theorem
Calculus in Deterministic and Stochastic Environments
Pricing Derivatives: Models and Notation
Tools in Probability Theory
Martingales and Martingale Representations
Differentiation in Stochastic Environments
The Wiener Process and Rare Events in Financial Markets
Integration in Stochastic Environments
The Dynamics of Derivative Prices
Pricing Derivative Products
The Black-Scholes PDE
Pricing Derivative Products
Equivalent Martingale Measures
New Results and Tools for Interest Sensitive Securities
Arbitrage Theorem in a New Setting: Normalization and Random Interest Rates
Modeling Term Structure and Related Concepts
Classical and HJM Approaches to Fixed Income
Classical PDE Analysis for Interest Rate Derivatives
Relating Conditional Expectations to PDEs
Stopping Times and American-Type Securities
Bibliography
Index.

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An introduction to the mathematics of financial derivatives

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