# Problems and Solutions in Mathematical Finance

Equity Derivatives, Volume 2

Wiley (Verlag)
• erschienen am 4. Januar 2017
• |
• 856 Seiten

 E-Book | ePUB mit Adobe-DRM | Systemvoraussetzungen
978-1-119-96611-1 (ISBN)

Detailed guidance on the mathematics behind equityderivatives
Problems and Solutions in Mathematical Finance Volume IIis an innovative reference for quantitative practitioners andstudents, providing guidance through a range of mathematicalproblems encountered in the finance industry. This volume focusessolely on equity derivatives problems, beginning with basicproblems in derivatives securities before moving on to moreadvanced applications, including the construction of volatilitysurfaces to price exotic options. By providing a methodology forsolving theoretical and practical problems, whilst explaining thelimitations of financial models, this book helps readers to developthe skills they need to advance their careers. The text covers awide range of derivatives pricing, such as European, American,Asian, Barrier and other exotic options. Extensive appendicesprovide a summary of important formulae from calculus, theory ofprobability, and differential equations, for the convenience ofreaders.
As Volume II of the four-volume Problems and Solutions inMathematical Finance series, this book provides clearexplanation of the mathematics behind equity derivatives, in orderto help readers gain a deeper understanding of their mechanics anda firmer grasp of the calculations.
* Review the fundamentals of equity derivatives
* Work through problems from basic securities to advanced exoticspricing
* Examine numerical methods and detailed derivations ofclosed-form solutions
* Utilise formulae for probability, differential equations, andmore
Mathematical finance relies on mathematical models, numericalmethods, computational algorithms and simulations to make trading,hedging, and investment decisions. For the practitioners andgraduate students of quantitative finance, Problems andSolutions in Mathematical Finance Volume II provides essentialguidance principally towards the subject of equity derivatives.
 Reihe: Auflage: 1. Auflage Sprache: Englisch Verlagsort: New York | Großbritannien Verlagsgruppe: John Wiley & Sons Dateigröße: 20,44 MB Schlagworte: ISBN-13: 978-1-119-96611-1 (9781119966111)
weitere Ausgaben werden ermittelt
Preface ix
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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