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Option Valuation: A First Course in Financial Mathematics [Kõva köide]

(The George Washington University, Washington, D.C., USA)
  • Formaat: Hardback, 266 pages, kõrgus x laius: 235x156 mm, kaal: 499 g, 500+; 9 Tables, black and white; 10 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Financial Mathematics Series
  • Ilmumisaeg: 23-Nov-2011
  • Kirjastus: Taylor & Francis Inc
  • ISBN-10: 1439889112
  • ISBN-13: 9781439889114
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Option Valuation: A First Course in Financial MathematicsSuurem pilt
  • Formaat: Hardback, 266 pages, kõrgus x laius: 235x156 mm, kaal: 499 g, 500+; 9 Tables, black and white; 10 Illustrations, black and white
  • Sari: Chapman & Hall/CRC Financial Mathematics Series
  • Ilmumisaeg: 23-Nov-2011
  • Kirjastus: Taylor & Francis Inc
  • ISBN-10: 1439889112
  • ISBN-13: 9781439889114
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781439889114.html
Märksõnad:
Option Valuation: A First Course in Financial Mathematics provides a straightforward introduction to the mathematics and models used in the valuation of financial derivatives. It examines the principles of option pricing in detail via standard binomial and stochastic calculus models. Developing the requisite mathematical background as needed, the text presents an introduction to probability theory and stochastic calculus suitable for undergraduate students in mathematics, economics, and finance.









The first nine chapters of the book describe option valuation techniques in discrete time, focusing on the binomial model. The author shows how the binomial model offers a practical method for pricing options using relatively elementary mathematical tools. The binomial model also enables a clear, concrete exposition of fundamental principles of finance, such as arbitrage and hedging, without the distraction of complex mathematical constructs. The remaining chapters illustrate the theory in continuous time, with an emphasis on the more mathematically sophisticated Black-Scholes-Merton model.









Largely self-contained, this classroom-tested text offers a sound introduction to applied probability through a mathematical finance perspective. Numerous examples and exercises help students gain expertise with financial calculus methods and increase their general mathematical sophistication. The exercises range from routine applications to spreadsheet projects to the pricing of a variety of complex financial instruments. Hints and solutions to odd-numbered problems are given in an appendix and a full solutions manual is available for qualifying instructors.

Arvustused

"a suitable text for an advanced undergraduate or graduate-level course in option valuation via the binomial model and the BlackScholesMerton model." International Statistical Review, 2013



"The text provides an introduction to classical material of mathematical finance, i.e. the notions of arbitrage, replication, and option pricing in the context of the discrete-time Cox-Ross-Rubinstein and the continuous-time Black-Scholes model, respectively. The book sticks out by not assuming any background in stochastics. All necessary concepts of probability theory, martingales, and Itō calculus are provided " Jan Kallsen, Zentralblatt MATH 1247

Preface xi
1 Interest and Present Value
1(12)
1.1 Compound Interest
1(2)
1.2 Annuities
3(3)
1.3 Bonds
6(1)
1.4 Rate of Return
7(2)
1.5 Exercises
9(4)
2 Probability Spaces
13(14)
2.1 Sample Spaces and Events
13(1)
2.2 Discrete Probability Spaces
14(2)
2.3 General Probability Spaces
16(4)
2.4 Conditional Probability
20(2)
2.5 Independence
22(2)
2.6 Exercises
24(3)
3 Random Variables
27(16)
3.1 Definition and General Properties
27(2)
3.2 Discrete Random Variables
29(3)
3.3 Continuous Random Variables
32(2)
3.4 Joint Distributions
34(1)
3.5 Independent Random Variables
35(3)
3.6 Sums of Independent Random Variables
38(3)
3.7 Exercises
41(2)
4 Options and Arbitrage
43(16)
4.1 Arbitrage
44(2)
4.2 Classification of Derivatives
46(1)
4.3 Forwards
46(2)
4.4 Currency Forwards
48(1)
4.5 Futures
49(1)
4.6 Options
50(3)
4.7 Properties of Options
53(2)
4.8 Dividend-Paying Stocks
55(2)
4.9 Exercises
57(2)
5 Discrete-Time Portfolio Processes
59(8)
5.1 Discrete-Time Stochastic Processes
59(2)
5.2 Self-Financing Portfolios
61(3)
5.3 Option Valuation by Portfolios
64(2)
5.4 Exercises
66(1)
6 Expectation of a Random Variable
67(10)
6.1 Discrete Case: Definition and Examples
67(1)
6.2 Continuous Case: Definition and Examples
68(1)
6.3 Properties of Expectation
69(2)
6.4 Variance of a Random Variable
71(2)
6.5 The Central Limit Theorem
73(2)
6.6 Exercises
75(2)
7 The Binomial Model
77(12)
7.1 Construction of the Binomial Model
77(3)
7.2 Pricing a Claim in the Binomial Model
80(3)
7.3 The Cox-Ross-Rubinstein Formula
83(3)
7.4 Exercises
86(3)
8 Conditional Expectation and Discrete-Time Martingales
89(12)
8.1 Definition of Conditional Expectation
89(3)
8.2 Examples of Conditional Expectation
92(2)
8.3 Properties of Conditional Expectation
94(2)
8.4 Discrete-Time Martingales
96(2)
8.5 Exercises
98(3)
9 The Binomial Model Revisited
101(18)
9.1 Martingales in the Binomial Model
101(2)
9.2 Change of Probability
103(2)
9.3 American Claims in the Binomial Model
105(3)
9.4 Stopping Times
108(3)
9.5 Optimal Exercise of an American Claim
111(3)
9.6 Dividends in the Binomial Model
114(1)
9.7 The General Finite Market Model
115(2)
9.8 Exercises
117(2)
10 Stochastic Calculus
119(22)
10.1 Differential Equations
119(1)
10.2 Continuous-Time Stochastic Processes
120(2)
10.3 Brownian Motion
122(1)
10.4 Variation of Brownian Paths
123(3)
10.5 Riemann-Stieltjes Integrals
126(1)
10.6 Stochastic Integrals
126(5)
10.7 The Ito-Doeblin Formula
131(5)
10.8 Stochastic Differential Equations
136(3)
10.9 Exercises
139(2)
11 The Black-Scholes-Merton Model
141(10)
11.1 The Stock Price SDE
141(1)
11.2 Continuous-Time Portfolios
142(1)
11.3 The Black-Scholes-Merton PDE
143(3)
11.4 Properties of the BSM Call Function
146(3)
11.5 Exercises
149(2)
12 Continuous-Time Martingales
151(12)
12.1 Conditional Expectation
151(1)
12.2 Martingales: Definition and Examples
152(2)
12.3 Martingale Representation Theorem
154(2)
12.4 Moment Generating Functions
156(2)
12.5 Change of Probability and Girsanov's Theorem
158(3)
12.6 Exercises
161(2)
13 The BSM Model Revisited
163(10)
13.1 Risk-Neutral Valuation of a Derivative
163(2)
13.2 Proofs of the Valuation Formulas
165(2)
13.3 Valuation under P
167(1)
13.4 The Feynman-Kac Representation Theorem
168(3)
13.5 Exercises
171(2)
14 Other Options
173(36)
14.1 Currency Options
173(2)
14.2 Forward Start Options
175(1)
14.3 Chooser Options
176(1)
14.4 Compound Options
177(1)
14.5 Path-Dependent Derivatives
178(17)
14.5.1 Barrier Options
179(6)
14.5.2 Lookback Options
185(6)
14.5.3 Asian Options
191(4)
14.6 Quantos
195(2)
14.7 Options on Dividend-Paying Stocks
197(3)
14.7.1 Continuous Dividend Stream
197(1)
14.7.2 Discrete Dividend Stream
198(2)
14.8 American Claims in the BSM Model
200(3)
14.9 Exercises
203(6)
A Sets and Counting 209(6)
B Solution of the BSM PDE 215(4)
C Analytical Properties of the BSM Call Function 219(6)
D Hints and Solutions to Odd-Numbered Problems 225(22)
Bibliography 247(2)
Index 249
Hugo D. Junghenn is a professor of mathematics at the George Washington University. His research interests include functional analysis and semigroups.