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El. knyga: Introduction to Financial Derivatives with Python

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, (Universitat Pompeu Frabra, Spain)
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"Introduction to Financial Derivatives with Python is an ideal textbook for an undergraduate course on derivatives, whether on a finance, economics, or financial mathematics programme. As well as covering all of the essential topics one would expect to be covered, the book also includes the basis of the numerical techniques most used in the financial industry, and their implementation in Python. Features Connected to a Github repository with the codes in the book. The repository can be accessed at https://bit.ly/3bllnuf Suitable for undergraduate students, as well as anyone who wants a gentle introduction to the principles of quantitative finance No pre-requisites required for programming or advanced mathematics beyond basic calculus"--

This textbook is ideal for an undergraduate course on derivatives in a finance, economics, or financial mathematics programme. As well as covering all of the essential topics, the book also includes the basis of the numerical techniques most used in the financial industry, and their implementation in Python.

List of Figures
xiii
Foreword xvii
Preface xxi
Chapter 1 Introduction
1(8)
1.1 Financial Markets
1(1)
1.2 Derivatives
1(1)
1.3 Time Has A Value
2(3)
1.4 No-Arbitrage Principle
5(2)
1.5
Chapter's Digest
7(1)
1.6 Exercises
7(2)
Chapter 2 Futures and Forwards
9(16)
2.1 Forward Contracts: Definitions
9(2)
2.2 Futures
11(3)
2.3 Why To Use Forwards And Futures?
14(1)
2.4 The Fair Delivery Price: The Forward Price
15(8)
2.4.1 The General Approach
15(2)
2.4.2 Some Special Cases
17(1)
2.4.2.1 Assets that Provide a Known Income
17(2)
2.4.2.2 Assets that Provide an Income Proportional to Its Price
19(2)
2.4.3 The Price of a Forward Contract
21(1)
2.4.4 The general case
21(1)
2.4.4.1 The Case of a Known Income
22(1)
2.4.4.2 Assets that Provide an Income Proportional to Its Price
22(1)
2.5
Chapter's Digest
23(1)
2.6 Exercises
23(2)
Chapter 3 Options
25(20)
3.1 Call And Put Options
25(2)
3.2 The Intrinsic Value of An Option
27(1)
3.3 Some Properties Of Option Prices
27(6)
3.3.1 The Price of an Option vs the Price of an Asset
28(1)
3.3.2 The Role of the strike price
29(1)
3.3.3 The Role of the Price of the Underlying Asset
29(1)
3.3.4 The Role of Interest Rates
30(1)
3.3.5 The Role of Volatility
31(1)
3.3.6 The Role of Time to Maturity
31(1)
3.3.7 The Put-Call Parity
32(1)
3.4 Speculation With Options
33(2)
3.5 Some Classical Strategies
35(2)
3.5.0.1 Bull Spread
35(1)
3.5.0.2 Bear Spread
36(1)
3.6 Draw Your Strategy With Python
37(5)
3.7
Chapter's Digest
42(1)
3.8 Exercises
43(2)
Chapter 4 Exotic Options
45(10)
4.1 Binary Options
45(1)
4.2 Forward Start Options
46(1)
4.2.1 Compound Options
47(1)
4.3 Path-Dependent Options
47(5)
4.3.1 Barrier Options
48(2)
4.3.2 Lookback Options
50(1)
4.3.3 Asian Options
51(1)
4.4 Spread and Basket Options
52(1)
4.5 Bermuda Options
53(1)
4.6
Chapter's Digest
53(1)
4.7 Exercises
53(2)
Chapter 5 The Binomial Model
55(54)
5.1 The Single-Period Binomial Model
55(14)
5.1.1 Relationship between European Options and Their Underlying in the Binomial Model
59(1)
5.1.2 Replication Portfolio for European Options
60(4)
5.1.3 The Risk-neutral Valuation
64(3)
5.1.4 Link the Model to the Market
67(2)
5.2 The Multi-Period Binomial Model
69(18)
5.2.1 Adjusting the Parameters
72(2)
5.2.2 Pricing a European Option
74(1)
5.2.2.1 Extended Framework
74(10)
5.2.2.2 Simplified Framework
84(1)
5.2.3 Early Exercise
84(3)
5.3 The Greeks In The Binomial Model
87(6)
5.3.1 Delta
90(1)
5.3.2 Gamma
90(1)
5.3.3 Theta
91(1)
5.3.4 Vega
91(1)
5.3.5 Rho
92(1)
5.3.6 Approximating the Price Function
92(1)
5.4 Coding The Binomial Model
93(12)
5.5
Chapter's Digest
105(1)
5.6 Exercises
106(3)
Chapter 6 A Continuous-time Pricing Model
109(38)
6.1 Creating Some Intuition
109(4)
6.2 The Black-Scholes-Merton Framework
113(1)
6.3 The Black-Scholes-Merton Equation
114(2)
6.4 The Black-Scholes-Merton Formula
116(4)
6.5 The Black-Scholes-Merton Model From a Probabilistic Perspective
120(6)
6.6 The Black-Scholes-Merton Price and the Binomial Price
126(1)
6.7 The Greeks in the Black-Scholes-Merton Model
127(12)
6.7.1 Delta
128(4)
6.7.2 Theta
132(2)
6.7.3 Gamma
134(3)
6.7.4 Vega
137(2)
6.8 Other Assets
139(2)
6.8.1 Black-Scholes-Merton with Dividends
140(1)
6.8.2 Black-Scholes-Merton for Foreign-Exchange
140(1)
6.8.3 Black-scholes-Merton for Futures
141(1)
6.9 Drawbacks of the Black-Scholes-Merton Model
141(2)
6.10
Chapter's Digest
143(1)
6.11 Exercises
143(4)
Chapter 7 Monte Carlo Methods
147(22)
7.1 The Need of General Option Pricing Tools
147(1)
7.2 Mathematical Foundations of Monte Carlo Methods
148(7)
7.2.1 Sample Means as Estimators of Theoretical Expectations
150(1)
7.2.2 The Laws of Large Numbers
151(3)
7.2.3 The Central Limit Theorem
154(1)
7.3 Option Pricing With Monte Carlo Methods
155(7)
7.3.1 European Options that Depend Only on the Final Value of the Asset
156(2)
7.3.2 European Options that Depend on the Path of Asset Prices
158(4)
7.4 European Options That Depend on the Final Price of Two Assets
162(3)
7.5
Chapter's Digest
165(1)
7.6 Exercises
165(4)
Chapter 8 The Volatility
169(8)
8.1 Historical Volatilities
169(2)
8.2 The Spot Volatility
171(1)
8.3 The Implied Volatility
172(2)
8.4
Chapter's Digest
174(1)
8.5 Exercises
175(2)
Chapter 9 Replicating Portfolios
177(14)
9.1 Replicating Portfolios for the Binomial Model
177(4)
9.2 Replicating Portfolios for the Black-Scholes-Merton Mode
181(6)
9.3
Chapter's Digest
187(1)
9.4 Exercises
188(3)
Appendix A Introduction to Python
191(18)
A.1 Basic Operations
191(1)
A.2 Data Types
192(1)
A.3 Variables
193(1)
A.4 Print
194(1)
A.5 Packages
195(1)
A.6 Rocking Like A Data Scientist
195(11)
A.6.1 Import Data
196(1)
A.6.2 Using Dataframes
197(4)
A.6.3 Make Plot
201(5)
A.7
Chapter's Digest
206(1)
A.8 Exercises
207(2)
Appendix B Introduction to Coding in Python
209(16)
B.1 Define Your Own Functions
209(2)
B.2 If
211(4)
B.3 For
215(2)
B.4 Creating Matrices
217(5)
B.5
Chapter's Digest
222(1)
B.6 Exercises
223(2)
Bibliography 225(2)
Index 227
Elisa Alņs holds a Ph.D. in Mathematics from the University of Barcelona. She is an Associate Professor in the Department of Economics and Business at Universitat Pompeu Fabra (UPF) and a Barcelona GSE Affiliated Professor. Her research focus has been on the applications of the Malliavin calculus and the fractional Brownian motion in mathematical finance and volatility modelling since he past fourteen years.

Raśl Merino has been working full-time in the industry as Risk Quant since 2008. He is also an Associate Professor at Pompeu Fabra University (UPF) where he teaches the course "Financial Derivatives and Risk Management". Raul holds a Ph.D. in Mathematics from the University of Barcelona. In his Ph.D. he studied the use of decomposition formulas in stochastic volatility models. His research interests are stochastic analysis and applied mathematics, with a special focus on applications to mathematical finance.
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