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Problems and Solutions in Mathematical Finance. Equity Derivatives, Volume 2. The Wiley Finance Series

  • ID: 2586595
  • Book
  • 856 Pages
  • John Wiley and Sons Ltd
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Problems and Solutions in Mathematical Finance

VOLUME 2

Equity Derivatives

Eric Chin, Dian Nel and Sverrir Ólafsson

The quantitative methods required for the pricing and hedging of a range of financial securities are drawn from mathematical finance, an important and rapidly growing discipline. In an increasingly complex financial world, the role of mathematical finance is indispensable. It follows that successful financial engineers or quants need to have an excellent grasp of all the major technicalities of mathematical finance to master its diverse applications in the financial industry.

Problems and Solutions in Mathematical Finance Volume 2: Equity Derivatives is the second of a four–volume set of books focusing on problems and solutions in mathematical finance.

The first volume in the series introduced the reader to all the important concepts in probability and stochastic calculus. The second volume covers a broad area of equity derivative contracts, ranging from vanilla options to various more complex options such as time dependent American, compound, barrier and volatility options. The theoretical presentation and its effective integration with a wide range of problems is clear and to the point. This approach brings the student quickly to the forefront of the modern practice of mathematical finance.

This series is unique as it provides the student with rigorous but yet intuitive explanations of some highly technical material further deepened by extensive real–world examples.

Written mainly for students, industry practitioners and those involved in teaching in this field of study, Equity Derivatives provides a valuable reference book to complement one′s further understanding of mathematical finance.

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Preface ix

About the Authors xi

1 Basic Equity Derivatives Theory 1

1.1 Introduction 1

1.2 Problems and Solutions 8

1.2.1 Forward and Futures Contracts 8

1.2.2 Options Theory 15

1.2.3 Hedging Strategies 27

2 European Options 63

2.1 Introduction 63

2.2 Problems and Solutions 74

2.2.1 Basic Properties 74

2.2.2 Black Scholes Model 89

2.2.3 Tree–Based Methods 190

2.2.4 The Greeks 218

3 American Options 267

3.1 Introduction 267

3.2 Problems and Solutions 271

3.2.1 Basic Properties 271

3.2.2 Time–Independent Options 292

3.2.3 Time–Dependent Options 305

4 Barrier Options 351

4.1 Introduction 351

4.2 Problems and Solutions 357

4.2.1 Probabilistic Approach 357

4.2.2 Reflection Principle Approach 386

4.2.3 Further Barrier–Style Options 408

5 Asian Options 439

5.1 Introduction 439

5.2 Problems and Solutions 443

5.2.1 Discrete Sampling 443

5.2.2 Continuous Sampling 480

6 Exotic Options 531

6.1 Introduction 531

6.2 Problems and Solutions 532

6.2.1 Path–Independent Options 532

6.2.2 Path–Dependent Options 586

7 Volatility Models 647

7.1 Introduction 647

7.2 Problems and Solutions 652

7.2.1 Historical and Implied Volatility 652

7.2.2 Local Volatility 685

7.2.3 Stochastic Volatility 710

7.2.4 Volatility Derivatives 769

A Mathematics Formulae 787

B Probability Theory Formulae 797

C Differential Equations Formulae 813

Bibliography 821

Notation 825

Index 829

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Eric Chin
Dian Nel
Sverrir Ólafsson
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