The Mathematics of Financial Derivatives A Student Introduction 1st Edition by Paul Wilmott , Sam Howison, Jeff Dewynne ISBN 0521497892 978-0521497893
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ISBN 10: 0521497892
ISBN 13: 978-0521497893
Author:Paul Wilmott , Sam Howison, Jeff Dewynne
Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant “real-world” mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician’s viewpoint, from modeling to analysis to elementary computation. The authors present a unified approach to modeling derivative products as partial differential equations, using numerical solutions where appropriate. The authors assume some mathematical background, but provide clear explanations for material beyond elementary calculus, probability, and algebra. This volume will become the standard introduction for advanced undergraduate students to this exciting new field.
The Mathematics of Financial Derivatives A Student Introduction 1st Table of contents:
Part One: Basic Option Theory
1 An Introduction to Options and Markets
1.1 Introduction
1.2 What is an Option?
1.3 Reading the Financial Press
1.4 What are Options For?
1.5 Other Types of Option
1.6 Forward and Futures Contracts
1.7 Interest Rates and Present Value
2 Asset Price Random Walks
2.1 Introduction
2.2 A Simple Model for Asset Prices
2.3 Itô’s Lemma
2.4 The Elimination of Randomness
3 The Black–Scholes Model
3.1 Introduction
3.2 Arbitrage
3.3 Option Values, Payoffs and Strategies
3.4 Put-call Parity
3.5 The Black–Scholes Analysis
3.6 The Black–Scholes Equation
3.7 Boundary and Final Conditions
3.8 The Black–Scholes Formulæ
3.9 Hedging in Practice
3.10 Implied Volatility
4 Partial Differential Equations
4.1 Introduction
4.2 The Diffusion Equation
4.3 Initial and Boundary Conditions
4.4 Forward versus Backward
5 The Black–Scholes Formulæ
5.1 Introduction
5.2 Similarity Solutions
5.3 An Initial Value Problem
5.4 The Formulæ Derived
5.5 Binary Options
5.6 Risk Neutrality
6 Variations on the Black–Scholes Model
6.1 Introduction
6.2 Options on Dividend-paying Assets
6.3 Forward and Futures Contracts
6.4 Options on Futures
6.5 Time-dependent Parameters
7 American Options
7.1 Introduction
7.2 The Obstacle Problem
7.3 American Options as Free Boundary Problems
7.4 The American Put
7.5 Other American Options
7.6 Linear Complementarity Problems
7.7 The American Call with Dividends
Part Two: Numerical Methods
8 Finite-difference Methods
8.1 Introduction
8.2 Finite-difference Approximations
8.3 The Finite-difference Mesh
8.4 The Explicit Finite-difference Method
8.5 Implicit Finite-difference Methods
8.6 The Fully-implicit Method
8.7 The Crank–Nicolson Method
9 Methods for American Options
9.1 Introduction
9.2 Finite-difference Formulation
9.3 The Constrained Matrix Problem
9.4 Projected SOR
9.5 The Time-stepping Algorithm
9.6 Numerical Examples
9.7 Convergence of the Method
10 Binomial Methods
10.1 Introduction
10.2 The Discrete Random Walk
10.3 Valuing the Option
10.4 European Options
10.5 American Options
10.6 Dividend Yields
Part Three: Further Option Theory
11 Exotic and Path-dependent Options
11.1 Introduction
11.2 Compound Options: Options on Options
11.3 Chooser Options
11.4 Barrier Options
11.5 Asian Options
11.6 Lookback Options
12 Barrier Options
12.1 Introduction
12.2 Knock-outs
12.3 Knock-ins
13 A Unifying Framework for Path-dependent Options
13.1 Introduction
13.2 Time Integrals of the Random Walk
13.3 Discrete Sampling
14 Asian Options
14.1 Introduction
14.2 Continuously Sampled Averages
14.3 Similarity Reductions
14.4 The Average Strike Option
14.5 Average Rate Options
14.6 Discretely Sampled Averages
15 Lookback Options
15.1 Introduction
15.2 Continuous Sampling of the Maximum
15.3 Discrete Sampling of the Maximum
15.4 Similarity Reductions
15.5 Some Numerical Examples
15.6 Two ‘Perpetual Options’
16 Options with Transaction Costs
16.1 Introduction
16.2 Discrete Hedging
16.3 Portfolios of Options
Part Four: Interest Rate Derivative Products
17 Interest Rate Derivatives
17.1 Introduction
17.2 Basics of Bond Pricing
17.3 The Yield Curve
17.4 Stochastic Interest Rates
17.5 The Bond Pricing Equation
17.6 Solutions of the Bond Pricing Equation
17.7 The Extended Vasicek Model of Hull & White
17.8 Bond Options
17.9 Other Interest Rate Products
18 Convertible Bonds
18.1 Introduction
18.2 Convertible Bonds
18.3 Convertible Bonds with Random Inteterest Rate
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Paul Wilmott,Sam Howison,Jeff Dewynne,The Mathematics
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