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Introduction to Financial Mathematics: Option Valuation 2nd edition [Kõva köide]

(The George Washington University, Washington, D.C., USA)
  • Formaat: Hardback, 304 pages, kõrgus x laius: 234x156 mm, kaal: 489 g, 8 Tables, black and white; 38 Illustrations, black and white
  • Sari: Chapman and Hall/CRC Financial Mathematics Series
  • Ilmumisaeg: 08-Mar-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367208822
  • ISBN-13: 9780367208820
Teised raamatud teemal:
Introduction to Financial Mathematics: Option Valuation 2nd editionSuurem pilt
  • Formaat: Hardback, 304 pages, kõrgus x laius: 234x156 mm, kaal: 489 g, 8 Tables, black and white; 38 Illustrations, black and white
  • Sari: Chapman and Hall/CRC Financial Mathematics Series
  • Ilmumisaeg: 08-Mar-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367208822
  • ISBN-13: 9780367208820
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367208820.html
Märksõnad:
Introduction to Financial Mathematics: Option Valuation, Second Edition is a well-rounded primer to the mathematics and models used in the valuation of financial derivatives. The book consists of ?fteen chapters, the ?rst ten of which develop option valuation techniques in discrete time, the last ?ve describing the theory in continuous time. The first half of the textbook develops basic finance and probability. The author then treats the binomial model as the primary example of discrete-time option valuation. The final part of the textbook examines the Black-Scholes model. The book is written to provide a straightforward account of the principles of option pricing and examines these principles in detail using standard discrete and stochastic calculus models. Additionally, the second edition has new exercises and examples, and includes many tables and graphs generated by over 30 MS Excel VBA modules available on the author’s webpage https://home.gwu.edu/~hdj/. 
Preface xi
1 Basic Finance
1(16)
1.1 Interest
1(2)
*1.2 Inflation
3(1)
1.3 Annuities
4(6)
1.4 Bonds
10(1)
*1.5 Internal Rate of Return
11(2)
1.6 Exercises
13(4)
2 Probability Spaces
17(18)
2.1 Sample Spaces and Events
17(1)
2.2 Discrete Probability Spaces
18(3)
2.3 General Probability Spaces
21(5)
2.4 Conditional Probability
26(4)
2.5 Independence
30(1)
2.6 Exercises
31(4)
3 Random Variables
35(20)
3.1 Introduction
35(2)
3.2 General Properties of Random Variables
37(1)
3.3 Discrete Random Variables
38(4)
3.4 Continuous Random Variables
42(2)
3.5 Joint Distributions of Random Variables
44(2)
3.6 Independent Random Variables
46(2)
3.7 Identically Distributed Random Variables
48(1)
3.8 Sums of Independent Random Variables
48(3)
3.9 Exercises
51(4)
4 Options and Arbitrage
55(24)
4.1 The Price Process of an Asset
55(1)
4.2 Arbitrage
56(2)
4.3 Classification of Derivatives
58(1)
4.4 Forwards
59(1)
4.5 Currency Forwards
60(1)
4.6 Futures
61(2)
*4.7 Equality of Forward and Future Prices
63(1)
4.8 Call and Put Options
64(3)
4.9 Properties of Options
67(2)
4.10 Dividend-Paying Stocks
69(1)
4.11 Exotic Options
70(3)
*4.12 Portfolios and Payoff Diagrams
73(3)
4.13 Exercises
76(3)
5 Discrete-Time Portfolio Processes
79(12)
5.1 Discrete Time Stochastic Processes
79(4)
5.2 Portfolio Processes and the Value Process
83(1)
5.3 Self-Financing Trading Strategies
84(1)
5.4 Equivalent Characterizations of Self-Financing
85(2)
5.5 Option Valuation by Portfolios
87(1)
5.6 Exercises
88(3)
6 Expectation
91(16)
6.1 Expectation of a Discrete Random Variable
91(2)
6.2 Expectation of a Continuous Random Variable
93(2)
6.3 Basic Properties of Expectation
95(1)
6.4 Variance of a Random Variable
96(2)
6.5 Moment Generating Functions
98(1)
6.6 The Strong Law of Large Numbers
99(1)
6.7 The Central Limit Theorem
100(2)
6.8 Exercises
102(5)
7 The Binomial Model
107(18)
7.1 Construction of the Binomial Model
107(4)
7.2 Completeness and Arbitrage in the Binomial Model
111(4)
7.3 Path-Independent Claims
115(4)
*7.4 Path-Dependent Claims
119(2)
7.5 Exercises
121(4)
8 Conditional Expectation
125(10)
8.1 Definition of Conditional Expectation
125(1)
8.2 Examples of Conditional Expectations
126(2)
8.3 Properties of Conditional Expectation
128(2)
8.4 Special Cases
130(2)
*8.5 Existence of Conditional Expectation
132(2)
8.6 Exercises
134(1)
9 Martingales in Discrete Time Markets
135(12)
9.1 Discrete Time Martingales
135(2)
9.2 The Value Process as a Martingale
137(1)
9.3 A Martingale View of the Binomial Model
138(2)
9.4 The Fundamental Theorems of Asset Pricing
140(2)
*9.5 Change of Probability
142(2)
9.6 Exercises
144(3)
1 American Claims in Discrete-Time Markets
147(12)
10.1 Hedging an American Claim
147(2)
10.2 Stopping Times
149(2)
10.3 Submartingales and Supermartingales
151(1)
10.4 Optimal Exercise of an American Claim
152(2)
10.5 Hedging in the Binomial Model
154(1)
10.6 Optimal Exercise in the Binomial Model
155(1)
10.7 Exercises
156(3)
1 Stochastic Calculus
159(24)
11.1 Continuous-Time Stochastic Processes
159(1)
11.2 Brownian Motion
160(4)
11.3 Stochastic Integrals
164(6)
11.4 The Ito-Doeblin Formula
170(6)
11.5 Stochastic Differential Equations
176(4)
11.6 Exercises
180(3)
1 The Black-Scholes-Merton Model
183(14)
12.1 The Stock Price SDE
183(1)
12.2 Continuous-Time Portfolios
184(1)
12.3 The Black-Scholes Formula
185(3)
12.4 Properties of the Black-Scholes Call Function
188(3)
*12.5 The BS Formula as a Limit of CR.R Formulas
191(3)
12.6 Exercises
194(3)
1 Martingales in the Black-Scholes-Merton Model
197(16)
13.1 Continuous-Time Martingales
197(4)
13.2 Change of Probability and Girsanov's Theorem
201(3)
13.3 Risk-Neutral Valuation of a Derivative
204(1)
13.4 Proofs of the Valuation Formulas
205(3)
*13.5 Valuation under P
208(1)
*13.6 The Feynman-Kac Representation Theorem
209(2)
13.7 Exercises
211(2)
1 Path-Independent Options
213(16)
14.1 Currency Options
213(3)
14.2 Forward Start Options
216(1)
14.3 Chooser Options
216(2)
14.4 Compound Options
218(1)
14.5 Quantos
219(2)
14.6 Options on Dividend-Paying Stocks
221(3)
14.7 American Claims
224(2)
14.8 Exercises
226(3)
1 Path-Dependent Options
229(68)
15.1 Barrier Options
229(5)
15.2 Lookback Options
234(6)
15.3 Asian Options
240(3)
15.4 Other Options
243(1)
15.5 Exercises
244(5)
A Basic Combinatorics
249(6)
B Solution of the BSM PDE
255(4)
C Properties of the BSM Call Function
259(6)
D Solutions to Odd-Numbered Problems
265(32)
Bibliography 297(2)
Index 299
Hugo D. Junghenn is Professor of Mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including A Course in Real Analysis and Principles of Analysis: Measure, Integration, Functional Analysis, and Applications. His research interests include functional analysis, semigroups, and probability.