Mathematical Models of Financial Derivatives

Overview

Financial Mathematics is one of the fastest growing research fields in applied mathematics. Leading edge banking and financial firms around the globe are hiring people who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks. Mathematical Models of Financial Derivatives serves this increasing demand, and is suitable as a textbook for degree programs in mathematical and computational finance. It models derivative products based mainly on the differential ...
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Overview

Financial Mathematics is one of the fastest growing research fields in applied mathematics. Leading edge banking and financial firms around the globe are hiring people who can use advanced analytical and numerical techniques to price financial derivatives and manage portfolio risks. Mathematical Models of Financial Derivatives serves this increasing demand, and is suitable as a textbook for degree programs in mathematical and computational finance. It models derivative products based mainly on the differential equation approach, together with numerical solution techniques when appropriate. Research results and concepts are made accessible to the student through extensive, well thought out exercises at the end of each chapter.
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Product Details

  • ISBN-13: 9789813083257
  • Publisher: Springer Singapore Pte. Limited
  • Publication date: 12/1/1998
  • Series: Finance Series
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 386
  • Product dimensions: 6.40 (w) x 9.57 (h) x 0.96 (d)

Table of Contents

Ch. 1 General Characteristics of Financial Derivative Models
1.1 Financial options and their trading strategies 2
1.2 Rational boundaries for option values 11
1.3 Asset price dynamics and stochastic processes 22
1.4 Black-Scholes formulation of option pricing 32
Ch. 2 Pricing Models for One-asset European Options
2.1 Black-Scholes pricing formulas and their properties 50
2.2 Extended option pricing models 68
2.3 Options on futures 82
Ch. 3 Pricing Models for Multi-asset European Options
3.1 Generalized multi-state Black-Scholes pricing models 97
3.2 Foreign currency option models 104
3.3 Options on the extremum of several risky assets 118
Ch. 4 American Options
4.1 Characterization of the optimal exercise boundaries 136
4.2 Analytic formulations of the American option pricing models 157
4.3 Approximate valuation methods for American options 165
Ch. 5 Numerical Schemes for Pricing Options
5.1 Principles of binomial pricing models 189
5.2 Extensions of the binomial pricing model 203
5.3 Finite difference algorithms 212
5.4 Monte Carlo simulation 224
Ch. 6 Path Dependent Options
6.1 Barrier options 246
6.2 Lookback options 267
6.3 Asian options 282
Ch. 7 Bonds and Interest Rate Derivatives
7.1 Bonds and interest rate models 314
7.2 No arbitrage interest rate models 331
7.3 Bond options and other interest rate derivatives 339
References 365
Author Index 375
Subject Index 379
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