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Quantitative Modeling of Derivative Securities: From Theory To Practice [Mīkstie vāki]

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(Courant Institute, New York, New York, USA), (Universita di Roma, Italy)
  • Formāts: Paperback / softback, 322 pages, height x width: 246x174 mm, weight: 616 g
  • Izdošanas datums: 30-Jun-2020
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 0367579146
  • ISBN-13: 9780367579142
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Quantitative Modeling of Derivative Securities: From Theory To PracticePalielināt
  • Formāts: Paperback / softback, 322 pages, height x width: 246x174 mm, weight: 616 g
  • Izdošanas datums: 30-Jun-2020
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 0367579146
  • ISBN-13: 9780367579142
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780367579142.html
Keywords:
Quantitative Modeling of Derivative Securities demonstrates how to take the basic ideas of arbitrage theory and apply them - in a very concrete way - to the design and analysis of financial products. Based primarily (but not exclusively) on the analysis of derivatives, the book emphasizes relative-value and hedging ideas applied to different financial instruments. Using a "financial engineering approach," the theory is developed progressively, focusing on specific aspects of pricing and hedging and with problems that the technical analyst or trader has to consider in practice.

More than just an introductory text, the reader who has mastered the contents of this one book will have breached the gap separating the novice from the technical and research literature.

Recenzijas

"This fine treatment of the arbitrage pricing of derivatives will become a standard. Avellaneda and Laurence have brought their extensive combined knowledge in [ a treatment] mathematics that financial analysts will find both concrete and authoritative." -Darrell Duffie, Professor of Finance, Graduate School of Business, Stanford University

"I learned a great deal of what I know of mathematics finance from Marco Avellaneda - and I know I will learn a lot more. Not only is he a great scholar, but he is a superb pedagogue, capable to cut to the chase and avoid needless complications - with the ease and simplicity of those who truly master the subject. I am glad this book by Avellaneda and Laurence is out so more people can share his knowledge." -Nassim Taleb, Trader, Paribas Capital Markets

"Written by two of the field's leading experts, this book stands out from the crowd of recent books on derivatives pricing theory. I recommend it to anyone interested in this fascinating field." -Peter Carr, Principal, Bank of America Securities

"This is a textbook, though it contains no exercises, on the theory underlying the modeling and risk management of financial derivatives. The authors attempt to link theory with practice, not flinching from pointing out that the theory does no have all the answers. The mathematical style is informal, assuming an understanding of linear algebra and elementary probability, but not requiring a grasp of measure theory. It introduces stochastic calculus.

"Despite the recent publicity concerning how physics PhDs can find highly remunerative employment in this area, the authors point out that "financial modeling is very different from modeling in the natural sciences. Unlike physics, where we deal with reproducible experiments with well-defined initial conditions, the models and ideas presented in this book deal with phenomena for which we have only limited information and that are not necessarily reproducible

Introduction ix
1 Arbitrage Pricing Theory: The One-Period Model 1(20)
1.1 The Arrow-Debreu Model
2(6)
1.2 Security-Space Diagram: A Geometric Interpretation of Theorem 1.1
8(3)
1.3 Replication
11(2)
1.4 The Binomial Model
13(1)
1.5 Complete and Incomplete Markets
14(2)
1.6 The One-Period Trinomial Model
16(2)
1.7 Exercises
18(1)
References and Further Reading
19(2)
2 The Binomial Option Pricing Model 21(20)
2.1 Recursion Relation for Pricing Contingent Claims
22(2)
2.2 Delta-Hedging and the Replicating Portfolio
24(2)
2.3 Pricing European Puts and Calls
26(2)
Portfolio Delta
27(1)
Money-Market Account
27(1)
Puts
28(1)
2.4 Relation Between the Parameters of the Tree and the Stock Price Fluctuations
28(6)
Calibration of the Volatility Parameter
31(1)
Expected Growth Rate
32(1)
Implementation of Binomial Trees
33(1)
2.5 The Limit for dt right arrow 0: Log-Normal Approximation
34(1)
2.6 The Black-Scholes Formula
35(4)
References and Further Reading
39(2)
3 Analysis of the Black-Scholes Formula 41(16)
3.1 Delta
42(3)
Option Deltas
44(1)
3.2 Practical Delta Hedging
45(3)
3.3 Gamma: The Convexity Factor
48(3)
3.4 Theta: The Time-Decay Factor
51(3)
3.5 The Binomial Model as a Finite-Difference Scheme for the Black-Scholes Equation
54(1)
References and Further Reading
55(2)
4 Refinements of the Binomial Model 57(20)
4.1 Term-Structure of Interest Rates
57(6)
4.2 Constructing a Risk-Neutral Measure with Time-Dependent Volatility
63(3)
4.3 Deriving a Volatility Term-Structure from Option Market Data
66(4)
4.4 Underlying Assets That Pay Dividends
70(3)
4.5 Futures Contracts as the Underlying Security
73(2)
4.6 Valuation of a Stream of Uncertain Cash Flows
75(1)
References and Further Reading
76(1)
5 American-Style Options, Early Exercise, and Time-Optionality 77(16)
5.1 American-Style Options
77(1)
5.2 Early-Exercise Premium
78(2)
5.3 Pricing American Options Using the Binomial Model: The Dynamic Programming Equation
80(2)
5.4 Hedging
82(1)
5.5 Characterization of the Solution for dt 1: Free-Boundary Problem for the Black-Scholes Equation
82(6)
References and Further Reading
88(1)
A A PDE Approach to the Free-Boundary Condition
89(4)
A.1 A Proof of the Free Boundary Condition
90(3)
6 Trinomial Model and Finite-Difference Schemes 93(14)
6.1 Trinomial Model
93(2)
6.2 Stability Analysis
95(1)
6.3 Calibration of the Model
96(4)
6.4 "Tree-Trimming" and Far-Field Boundary Conditions
100(3)
6.5 Implicit Schemes
103(3)
References and Further Reading
106(1)
7 Brownian Motion and Ito Calculus 107(20)
7.1 Brownian Motion
107(2)
7.2 Elementary Properties of Brownian Paths
109(2)
7.3 Stochastic Integrals
111(6)
7.4 Ito's Lemma
117(3)
7.5 Ito Processes and Ito Calculus
120(2)
References and Further Reading
122(1)
A Properties of the Ito Integral
123(4)
8 Introduction to Exotic Options: Digital and Barrier Options 127(34)
8.1 Digital Options
128(11)
European Digitals
128(7)
American Digitals
135(4)
8.2 Barrier Options
139(7)
Pricing Barrier Options Using Trees or Lattices
141(1)
Closed-Form Solutions
142(3)
Hedging Barrier Options
145(1)
8.3 Double Barrier Options
146(4)
Range Discount Note
147(1)
Range Accruals
148(2)
Double Knock-out Options
150(1)
References and Further Reading
150(11)
A Proofs of Lemmas 8.1 and 8.2
151(4)
A.1 A Consequence of the Invariance of Brownian Motion Under Reflections
151(2)
A.2 The Case µ not = to 0
153(2)
B Closed-Form Solutions for Double-Barrier Options
155(41)
B.1 Exit Probabilities of a Brownian Trajectory from a Strip -B < Z <a; A
155(3)
B.2 Applications to Pricing Barrier Options
158(3)
9 Ito Processes, Continuous-Time Martingales, and Girsanov's Theorem 161(10)
9.1 Martingales and Doob-Meyer Decomposition
161(2)
9.2 Exponential Martingales
163(2)
9.3 Girsanov's Theorem
165(3)
References and Further Reading
168(1)
A Proof of Equation (9.11)
169(2)
10 Continuous-Time Finance: An Introduction 171(12)
10.1 The Basic Model
171(2)
10.2 Trading Strategies
173(3)
10.3 Arbitrage Pricing Theory
176(5)
References and Further Reading
181(2)
11 Valuation of Derivative Securities 183(16)
11.1 The General Principle
183(2)
11.2 Black-Scholes Model
185(4)
11.3 Dynamic Hedging and Dynamic Completeness
189(4)
11.4 Fokker-Planck Theory: Computing Expectations Using PDEs
193(3)
References and Further Reading
196(3)
A Proof of Proposition 11.5
197(2)
12 Fixed-Income Securities and the Term-Structure of Interest Rates 199(30)
12.1 Bonds
199(7)
12.2 Duration
206(3)
12.3 Term Rates, Forward Rates, and Futures-Implied Rates
209(3)
12.4 Interest-Rate Swaps
212(5)
12.5 Caps and Floors
217(1)
12.6 Swaptions and Bond Options
218(3)
12.7 Instantaneous Forward Rates: Definition
221(3)
12.8 Building an Instantaneous Forward-Rate Curve
224(3)
References and Further Reading
227(2)
13 The Heath-Jarrow-Morton Theorem and Multidimensional Term-Structure Models 229(24)
13.1 The Heath-Jarrow-Morton Theorem
230(4)
13.2 The Ho-Lee Model
234(3)
13.3 Mean Reversion: The Modified Vasicek or Hull-White Model
237(2)
13.4 Factor Analysis of the Term-Structure
239(6)
13.5 Example: Construction of a Two-Factor Model with Parametric Components
245(3)
13.6 More General Volatility Specifications in the HJM Equation
248(3)
References and Further Reading
251(2)
14 Exponential-Affine Models 253(26)
14.1 A Characterization of EA Models
255(3)
14.2 Gaussian State-Variables: General Formulas
258(3)
14.3 Gaussian Models: Explicit Formulas
261(3)
14.4 Square-Root Processes and the Non-Central Chi-Squared Distribution
264(4)
14.5 One-Factor Square-Root Model: Discount Factors and Forward Rates
268(4)
References and Further Reading
272(7)
A Behavior of Square-Root Processes for Large Times
273(2)
B Characterization of the Probability Density Function of Square-Root Processes
275(2)
C The Square-Root Diffusion with v = 1
277(2)
15 Interest-Rate Options 279(34)
15.1 Forward Measures
279(3)
Definition and Examples
279(3)
15.2 Commodity Options with Stochastic Interest Rate
282(1)
15.3 Options on Zero-Coupon Bonds
283(2)
15.4 Money-Market Deposits with Yield Protection
285(4)
Forward Rates and Forward Measures
286(3)
15.5 Pricing Caps
289(10)
General Considerations
289(3)
Cap Pricing with Gaussian Models
292(1)
Cap Pricing with Square-Root Models
293(4)
Cap Pricing and Implied Volatilities
297(2)
15.6 Bond Options and Swaptions
299(9)
General Pricing Relations
299(2)
Jamshidian's Theorem
301(2)
Volatility Analysis
303(5)
15.7 Epilogue: The Brace-Gatarek-Musiela model
308(4)
References and Further Reading
312(1)
Index 313
Marco Avellaneda, Peter Laurence