Theoretical foundations for quantitative finance / Luca Spadafora, Università Cattolica del Sacro Cuore, Italy, Gennady P. Berman, Los Alamos National Laboratory, USA & New Mexico Consortium, USA.

Format:

Book

Author/Creator:

Spadafora, Luca, author.

Berman, Gennady P., 1946- author.

Language:

English

Subjects (All):

Finance--Mathematical models.

Finance.

Investments--Mathematical models.

Investments.

Physical Description:

x, 213 pages ; 24 cm

Place of Publication:

New Jersey : World Scientific, [2017]

Summary:

This book provides simple introduction to quantitative finance for students and junior quants who want to approach the typical industry problems with practical but rigorous ambition. It shows a simple link between theoretical technicalities and practical solutions. Mathematical aspects are discussed from a practitioner perspective, with a deep focus on practical implications, favoring the intuition and the imagination. In addition, the new post-crisis paradigms, like multi-curves, x-value adjustments (xVA) and Counterparty Credit Risk are also discussed in a very simple framework. Finally, real world data and numerical simulations are compared in order to provide a reader with a simple and handy insight on the actual model performances. Book jacket.

Contents:

Chapter 1 Introduction 1

Chapter 2 All the Financial Math You Need to Survive with Interesting Applications 5

2.1 Introduction 5

2.2 Probability Space 5

2.2.1 Probability Measure and Random Variables 8

2.2.2 The Information Flow Through Time: The Role of the Filtration 11

2.3 How to Estimate a Random Variable - Expectations and Conditioning 13

2.4 Main Features of Probability Measure 19

2.5 Moments and Cumulants 21

2.6 Statistical Estimators 24

2.7 Probability Density Functions 25

2.7.1 Uniform Distribution 26

2.7.2 Bernoulli and Binomial Distributions 27

2.7.3 Normal Distribution 28

2.7.4 Empirical Distribution 28

2.7.5 Exponential Distribution and Student's t-Distribution 33

2.8 Central Limit Theorem 34

2.9 Stochastic Processes 37

2.10 Brownian Motion 39

2.11 Quadratic Variation 42

2.12 Martingale 43

2.13 Stochastic Differential Equations (SDEs) 44

2.14 Ito's Lemma 47

2.15 Some Very Useful Theorems 50

2.15.1 Martingale Representation Theorem 50

2.15.2 Feynman-Kac Theorem 52

2.15.3 Radon-Nikodym Theorem 53

2.15.4 Girsanov's Theorem 55

Chapter 3 The Pricing of Financial Derivatives - The Replica Approach 59

3.1 Introduction - The Pricing of Financial Derivatives 59

3.2 What Kind of Model are We Looking For? 60

3.2.1 Coherence of the Pricing Methodology 61

3.2.2 Hedging Strategies 63

3.3 Are We Able to do the Same? Replica Pricing 63

3.3.1 Bank Account 66

3.3.2 Self-Financing Strategies 70

3.3.3 Arbitrage 72

3.3.4 Replica Examples 74

3.3.4.1 Zero Coupon Bond 75

3.3.4.2 Depo Rates 77

3.3.4.3 Forward 77

3.3.4.4 Forward Rate Agreement 79

3.4 Derivatives: Call, Put and Digital Options 82

Chapter 4 Risk-Neutral Pricing 87

4.1 Introduction 87

4.1.1 Setting the Stage 89

4.1.2 Point One: Modeling the Underlying 91

4.1.3 Point Two: Guess a Pricing Formula 92

4.1.4 Point Three: Finding an Equivalent Martingale Measure 94

4.1.5 Point Four: Defining the Replica Strategy 96

4.1.6 Point Five: The Pricing Algorithm 98

Chapter 5 The Black and Scholes Framework and Its Extensions 101

5.1 Black-Scholes Model-Part I 101

5.2 BS Model - Part II - Girsanov is Back 106

5.3 Put-Call Parity 107

5.4 Implied Volatility and the Calibration Problem 109

5.5 Digital Options 115

5.6.1 The Forward Measure 122

5.7 Greeks 124

5.8 Heston Model 130

5.8.1 Incomplete Markets 130

5.8.2 Heston Model Equations 131

5.8.3 Heston Risk Neutral Model 132

5.8.4 Heston Pricing Formula 134

5.8.5 Heston Implied Volatility 136

Chapter 6 Risk Modeling 139

6.1 Introduction 139

6.2 Risk? What is Risk? 140

6.3 What Kind of Model are You Looking For? 140

6.4 Risk Measures: Value-at-Risk and Expected Shortfall 142

6.4.1 Some Caveats on VaR Estimation 146

6.4.1.1 Percentile Estimation 147

6.4.1.2 VaR Statistical Error 155

6.5 Real-World Measure 156

6.6 Market Risk Estimation 158

6.6.1 Historical Method 163

6.6.2 Parametric Method 166

6.6.3 Monte Carlo Method 171

6.7 Does it Really Work? The Backtesting Approach 172

6.8 From Theory to Practice 177

Chapter 7 The New Post-Crisis Paradigms 181

7.1 The Financial World After Financial Crisis 181

7.2 Multi-Curve Framework 183

7.3 Fair Value Adjustments 187

7.3.1 Credit Value Adjustment 187

7.4 Counterparty Credit Risk 192.

Notes:

Includes bibliographical references and index.

ISBN:

9789813202474

9813202475

OCLC:

972200527