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Introducing Financial Mathematics: Theory, Binomial Models, and Applications [Hardback]

  • Formāts: Hardback, 292 pages, height x width: 234x156 mm, weight: 562 g, 10 Tables, black and white; 6 Line drawings, color; 13 Line drawings, black and white; 19 Illustrations, black and white
  • Sērija : Chapman and Hall/CRC Financial Mathematics Series
  • Izdošanas datums: 09-Nov-2022
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1032359854
  • ISBN-13: 9781032359854
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  • Cena: 109,33 €
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Introducing Financial Mathematics: Theory, Binomial Models, and ApplicationsPalielināt
  • Formāts: Hardback, 292 pages, height x width: 234x156 mm, weight: 562 g, 10 Tables, black and white; 6 Line drawings, color; 13 Line drawings, black and white; 19 Illustrations, black and white
  • Sērija : Chapman and Hall/CRC Financial Mathematics Series
  • Izdošanas datums: 09-Nov-2022
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1032359854
  • ISBN-13: 9781032359854
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781032359854.html
Keywords:
"This book seeks to replace existing books with a more rigorous stand-alone text that covers fewer examples but with more proofs, and also provides example computer programs, mainly in Octave/Matlab but also as spreadsheets and Macsyma scripts, with which students may experiment on real data"--

This book seeks to replace existing books with a more rigorous stand-alone text that covers fewer examples but with more proofs, and also provides example computer programs, mainly in Octave/Matlab but also as spreadsheets and Macsyma scripts, with which students may experiment on real data.

Introducing Financial Mathematics: Theory, Binomial Models, and Applications seeks to replace existing books with a rigorous stand-alone text that covers fewer examples in greater detail with more proofs. The book uses the fundamental theorem of asset pricing as an introduction to linear algebra and convex analysis. It also provides
example computer programs, mainly Octave/MATLAB functions but also spreadsheets and Macsyma scripts, with which students may experiment on real data.The text's unique coverage is in its contemporary combination of
discrete and continuous models to compute implied volatility and fit models to market data. The goal is to bridge the large gaps among nonmathematical finance texts, purely theoretical economics texts, and specific software-focused engineering texts.
Preface xi
1 Basics
1(22)
1.1 Assets and Portfolios
1(3)
1.1.1 Stocks and Bonds
1(1)
1.1.2 Foreign Exchange
2(1)
1.1.3 Derivatives
2(1)
1.1.4 Riskless Return
2(1)
1.1.5 Interest Rates and Present Value
2(2)
1.2 Payoff and Profit Graphs
4(2)
1.2.1 Payoff Graphs for Forward Contracts
4(1)
1.2.2 Payoff and Profit Graphs for Options
4(2)
1.2.3 Payoff and Profit Graphs for Contingent Options
6(1)
1.3 Arbitrage
6(6)
1.3.1 Random Variables and Stochastic Processes
7(3)
1.3.2 Deterministic Arbitrages
10(1)
1.3.3 Arbitrage and Expected Value
11(1)
1.4 No Arbitrage and Its Consequences
12(8)
1.4.1 Hedging
13(1)
1.4.2 Martingales and Fair Prices
14(1)
1.4.3 No-Arbitrage Price Equalities
15(4)
1.4.4 No-Arbitrage Inequalities
19(1)
1.5 Exercises
20(2)
1.6 Further Reading
22(1)
2 Continuous Models
23(26)
2.1 Some Facts from Probability Theory
23(1)
2.2 Understanding Brownian Motion
24(3)
2.3 The Black-Scholes Formula
27(7)
2.3.1 Option Pricing
29(2)
2.3.2 Historical Note
31(1)
2.3.3 Black-Scholes Greeks
32(2)
2.4 Implementation
34(12)
2.4.1 Numerical Differentiation
35(2)
2.4.2 Interpolation
37(3)
2.4.3 Regression
40(6)
2.5 Exercises
46(1)
2.6 Further Reading
47(2)
3 Discrete Models
49(38)
3.1 One-Step, Two-State Models
49(10)
3.1.1 Risk Neutral Probabilities
50(1)
3.1.2 Pricing Derivatives by Hedging
51(4)
3.1.3 Pricing Foreign Exchange Derivatives by Hedging
55(2)
3.1.4 Zero-Coupon Bonds of Different Maturity
57(2)
3.2 One-Step, Multistate Models
59(2)
3.3 Multistep Binomial Models
61(12)
3.3.1 Recombining Models
62(1)
3.3.2 Generalized Backward Induction Pricing
63(3)
3.3.3 Arrow-Debreu Securities
66(2)
3.3.4 Jamshidian's Forward Induction Formula
68(3)
3.3.5 Zero-Coupon Bonds and Interest Rate Constraints
71(2)
3.4 The Cox-Ross-Rubinstein Model
73(11)
3.4.1 Arrow-Debreu Decomposition in CRR
74(4)
3.4.2 Limit of CRR as N → θ
78(4)
3.4.3 CRR Greeks
82(2)
3.5 Exercises
84(2)
3.6 Further Reading
86(1)
4 Exotic Options
87(42)
4.1 Recombining Binomial Tree Prices
87(17)
4.1.1 European-Style Options in CRR
88(1)
4.1.2 American-Style Options in CRR
89(1)
4.1.3 Binary Options in CRR
90(2)
4.1.4 Compound Options in CRR
92(1)
4.1.5 Chooser Options in CRR
93(1)
4.1.6 Forward Start Options in CRR
94(2)
4.1.7 Barrier Options
96(6)
4.1.8 Booster Options
102(2)
4.2 Path Dependent Prices
104(22)
4.2.1 Efficient Data Structures
104(4)
4.2.2 Paths in Recombining Trees
108(3)
4.2.3 Path Dependent Arrow-Debreu Securities
111(2)
4.2.4 Asian-Style Options
113(7)
4.2.5 Floating Strike Options
120(2)
4.2.6 Lookback Options
122(2)
4.2.7 Ladder Options
124(2)
4.3 Exercises
126(1)
4.4 Further Reading
127(2)
5 Forwards and Futures
129(16)
5.1 Discrete Models for Forwards
129(2)
5.1.1 No-Arbitrage Forwards Values
130(1)
5.1.2 Binomial Models for Forwards Prices
131(1)
5.2 Discrete Models for Futures
131(11)
5.2.1 Binomial Models for Futures Prices
133(3)
5.2.2 No-Arbitrage Futures Values
136(3)
5.2.3 Margin Calls and Defaults
139(3)
5.3 Exercises
142(1)
5.4 Further Reading
143(2)
6 Dividends and Interest
145(30)
6.1 Stocks with Dividends
145(16)
6.1.1 Effects on Forwards
146(3)
6.1.2 Effects on American Call Options
149(2)
6.1.3 Dividends as Cash Flows
151(10)
6.2 Interest Rates
161(11)
6.2.1 Zero-Coupon Bonds
162(1)
6.2.2 Coupon Bonds
163(3)
6.2.3 Cash Flow Swaps
166(3)
6.2.4 Benchmarks
169(3)
6.3 Exercises
172(2)
6.4 Further Reading
174(1)
7 Implied Volatility
175(16)
7.1 The Inverse Problem for Volatility
175(2)
7.2 Implied Volatility Surfaces
177(3)
7.3 Implied Binomial Trees
180(8)
7.3.1 Path Independent Probabilities
181(1)
7.3.2 Jackwerth's Generalization
182(3)
7.3.3 Rubinstein's One-Two-Three Algorithm
185(3)
7.4 Exercises
188(1)
7.5 Further Reading
189(2)
8 Fundamental Theorems
191(26)
8.1 Finite Financial Models
191(4)
8.1.1 Arbitrage and Positivity
194(1)
8.1.2 Fundamental Theorems of Asset Pricing
195(1)
8.2 Applications of the Fundamental Theorems
195(8)
8.2.1 Hedges
196(1)
8.2.2 Complete Markets
197(2)
8.2.3 Incomplete Markets
199(4)
8.3 Cones, Convexity, and Duals
203(11)
8.3.1 Open and Closed Sets
205(2)
8.3.2 Dual Cones and Double Duals
207(3)
8.3.3 Proofs of the Fundamental Theorems
210(1)
8.3.4 Farkas's Lemma
211(1)
8.3.5 Hyperplane Separation
212(2)
8.4 Exercises
214(2)
8.5 Further Reading
216(1)
9 Project Suggestions
217(2)
A Answers
219(70)
A.1 To
Chapter 1 Exercises
219(8)
A.2 To
Chapter 2 Exercises
227(12)
A.3 To
Chapter 3 Exercises
239(10)
A.4 To
Chapter 4 Exercises
249(9)
A.5 To
Chapter 5 Exercises
258(6)
A.6 To
Chapter 6 Exercises
264(9)
A.7 To
Chapter 7 Exercises
273(6)
A.8 To
Chapter 8 Exercises
279(10)
Index 289
Mladen Victor Wickerhauser is professor of mathematics and statistics at Washington University, St. Louis. He holds a PhD from Yale University. Professor Wickerhausers research interests include harmonic analysis, wavelets, and numerical algorithms for data compression. He has six US patents and 118 publications, one of which led to an algorithm used by the FBI to encode fingerprint images.