## Book description

**A road map for implementing quantitative financial models**

Financial Derivative and Energy Market Valuation brings the application of financial models to a higher level by helping readers capture the true behavior of energy markets and related financial derivatives. The book provides readers with a range of statistical and quantitative techniques and demonstrates how to implement the presented concepts and methods in Matlab.

Featuring an unparalleled level of detail, this unique work provides the underlying theory and various advanced topics without requiring a prior high-level understanding of mathematics or finance. In addition to a self-contained treatment of applied topics such as modern Fourier-based analysis and affine transforms, Financial Derivative and Energy Market Valuation also:

Provides the derivation, numerical implementation, and documentation of the corresponding Matlab for each topic

Extends seminal works developed over the last four decades to derive and utilize present-day financial models

Shows how to use applied methods such as fast Fourier transforms to generate statistical distributions for option pricing

Includes all Matlab code for readers wishing to replicate the figures found throughout the book

Thorough, practical, and easy to use, *Financial Derivative and Energy Market Valuation* is a first-rate guide for readers who want to learn how to use advanced numerical methods to implement and apply state-of-the-art financial models. The book is also ideal for graduate-level courses in quantitative finance, mathematical finance, and financial engineering.

## Table of contents

- Cover
- Title Page
- Copyright
- Preface
- Chapter 1: Financial Models
- 1.1 Introduction
- 1.2 Geometric Brownian Motion
- 1.3 Expected Value, Variance, and Moments of Lognormal Distribution
- 1.4 Fitting Geometric Brownian Motion
- 1.5 Mean Price Simulation
- 1.6 Mean Reversion Models
- 1.7 Solving the Ornstein–Uhlenbeck Process
- 1.8 Simulating the Ornstein–Uhlenbeck Process
- 1.9 Calibrating the Ornstein–Uhlenbeck Process
- 1.10 Least Squares Fitting
- 1.11 Maximum Likelihood
- Summary
- Chapter 2: Jump Models
- 2.1 Introduction
- 2.2 Jump-Diffusion Model
- 2.3 Probability Functions
- 2.4 Least-Squares Estimation
- 2.5 Basic Moments
- 2.6 The Kolmogorov-Smirnov Test
- 2.7 Multinomial Estimation
- 2.8 Alternate Jump Models
- Summary
- Chapter 3: Options
- 3.1 Introduction
- 3.2 Capital Asset Pricing Model
- 3.3 Equivalent Martingale Measure
- 3.4 Money Market Numeraire
- 3.5 Zero-Coupon Bond Numeraire
- 3.6 Derivation of Black-Scholes Equation
- 3.7 Option Greeks
- 3.8 Binary Options
- 3.9 Merton Jump-Diffusion Option Price
- 3.10 Merton Option in a Hedged Portfolio
- 3.11 Martingale Derivation of Merton Option Price
- 3.12 Heston's Stochastic Volatility Model
- 3.13 PDE for Heston Probabilities
- 3.14 Characteristic Functions of the Heston Probabilities
- 3.15 Decoupled Green Function Approach to the Heston Model
- 3.16 Fourier Space Terminal Payoff
- 3.17 Green Function for Heston
- 3.18 Heston Greeks
- Summary
- Chapter 4: Binomial Trees
- 4.1 Introduction
- 4.2 Risk-Neutral Valuation
- 4.3 Delta Hedge Portfolio
- 4.4 Variance Matching
- 4.5 Recursive Binomial Tree
- 4.6 Futures Option Tree
- 4.7 Memory and CPU Improvements
- 4.8 Smile and Smirk
- 4.9 Implied Local Volatility
- Summary
- Chapter 5: Trinomial Trees
- 5.1 Introduction
- 5.2 Trinomial Tree Derivation
- 5.3 Calibrating the Trinomial Tree
- 5.4 Hull–White Calibration Step One
- 5.5 Reversion at Edge of Tree
- 5.6 Hull–White Calibration Step Two
- 5.7 Spot Price Stochastic Differential Equation
- 5.8 Tree-Based Futures Options Under Mean Reversion
- 5.9 Analytical European Futures Option Under Mean Reversion
- Summary
- Chapter 6: Finite Difference Methods
- 6.1 Introduction
- 6.2 Black–Scholes Differential Equation
- 6.3 Finite Difference Grid
- 6.4 Partial Derivative Representation
- 6.5 Explicit (Forward in Time) Finite Difference
- 6.6 European Option Boundary Conditions
- 6.7 Log-Price Explicit Finite Difference Equation
- 6.8 Implicit (Backward in Time) Finite Difference Equation
- 6.9 Crank–Nicolson Method
- 6.10 Tridiagonal Gaussian Elimination
- 6.11 Successive Overrelation Technique
- 6.12 Gauss–Seidel Technique
- 6.13 Crank–Nicolson for American Options
- 6.14 Option Greeks
- 6.15 Multidimensional Pde
- 6.16 Heston Model Stochastic Differential Equations
- 6.17 Heston Partial Differential Equation
- 6.18 Log-Price Heston Pde
- 6.19 Explicit Heston Finite Difference Approach
- 6.20 Explicit Stability Limit
- 6.21 Heston Finite Difference Boundary Conditions
- 6.22 Implicit Finite Difference Heston
- Summary
- Chapter 7: Kalman Filter
- 7.1 Introduction
- 7.2 Kalman Filter Derivation
- 7.3 Key Kalman Filter Equations
- 7.4 Multivariate Distribution
- 7.5 Kalman Filter of Spot Mean Reversion Process
- Summary
- Chapter 8: Futures and Forwards
- 8.1 Introduction
- 8.2 Fair Value
- 8.3 Forward and Futures Terminology
- 8.4 Capital Asset Pricing Model
- 8.5 Forward Price Differential Equation
- 8.6 Mean Reversion One-Factor Model
- 8.7 Kalman Filtration of One-Factor Model
- 8.8 Convenience Yield
- 8.9 Forward Price Differential Equation with a Fixed Convenience Yield
- 8.10 Forward Price Differential Equation with Stochastic Convenience Yield
- 8.11 Two-Factor Schwartz Stochastic Convenience Yield Model
- 8.12 Joseph Form of the Error Covariance Update
- 8.13 Filtering Vector Measurements with Uncorrelated Errors as Scalars
- 8.14 Square Root Filtering
- 8.15 Squaring/Square Root Filter
- Summary
- Chapter 9: Nonlinear and Non-Gaussian Kalman Filter
- 9.1 Introduction
- 9.2 Extended Kalman Filter
- 9.3 Extended Kalman Filter of Black–Scholes Model
- 9.4 General Transition Functions
- 9.5 Gauss–Hermite Quadrature Kalman Filter
- 9.6 Weights and Roots of Gauss–Hermite Quadratutre
- 9.7 Gauss–Hermite Quadrature
- 9.8 Gauss–Hermite Filter with Additive Gaussian Noise
- 9.9 Unscented Transform
- 9.10 Scaled Unscented Transform
- 9.11 Unscented Transform Kalman Filter of Black–Scholes Model
- 9.12 Unscented Transform Kalman Filter of Heston Model
- 9.13 Scaled Unscented Transform Kalman Filter
- 9.14 Monte Carlo Numerical Integration
- 9.15 Nonlinear Monte Carlo Kalman Filter with Additive Noise
- 9.16 Importance Sampling
- 9.17 Sequential Importance Sampling
- 9.18 Inverse Transform Resampling
- 9.19 Bootstrap Particle Filter
- 9.20 Particle Filter of the Heston Model
- Summary
- Chapter 10: Short-Term Deviation/Long-Term Equilibrium Model
- 10.1 Introduction
- 10.2 Schwartz and Smith Model
- Summary
- Chapter 11: Futures and Forwards Options
- 11.1 Introduction
- 11.2 Futures Price Process
- 11.3 Futures Risk Neutral Behavior
- 11.4 Futures Contract for Constant Interest Rate
- 11.5 Futures Options
- 11.6 European Put–Call Parity
- 11.7 American Put–Call Parity
- 11.8 Black's Model
- 11.9 Black Model Greeks
- 11.10 American Options
- 11.11 American Option Derivation
- 11.12 Barone-Adesi–Whaley Quadratic Approximation
- 11.13 American Call Quadratic Approximation
- 11.14 American Put Quadratic Approximation
- 11.15 Critical Asset Price Search
- 11.16 Futures Option Quadratic Approximation
- Summary
- Chapter 12: Fourier Transform
- 12.1 Introduction
- 12.2 Basic Fourier Transform Equations
- 12.3 Fourier Transform Processing
- 12.4 Absolutely Integrable Function
- 12.5 Square Integrable Function
- 12.6 Discrete Fourier Transform
- 12.7 Fourier Matrix
- 12.8 Fast Fourier Transform
- 12.9 Zero Padding the Fast Fourier Transform
- 12.10 Bluestein Fft
- 12.11 Chirp Z-Transform
- 12.12 Fractional Fast Fourier Transform
- 12.13 Taylor Series Approximation
- 12.14 Hermite Polynomials
- 12.15 Summary
- Chapter 13: Fundamentals of Characteristic Functions
- 13.1 Introduction
- 13.2 Characteristic Function
- 13.3 Moment Generating Function
- 13.4 Taylor Series oF Characteristic Function
- 13.5 Characteristic Function of a Gaussian Probability Distribution
- 13.6 Summation of Random Variables
- 13.7 Summary
- Chapter 14: Application of Characteristic Functions
- 14.1 Introduction
- 14.2 Levy Theorem
- 14.3 Relating Characteristic and Cumulative Distribution Functions
- 14.4 Symmetry of Characteristic Function
- 14.5 Probability Density Function by Inversion
- 14.6 Cumulative Distribution Function by Inversion
- 14.7 Probability Density Function from Fourier Inversion
- 14.8 Probability Density Function by FFT of Characteristic Function
- 14.9 Probability Density Function by Fractional FFT of Characteristic Function
- 14.10 Cumulative Distribution Function by FFT of Characteristic Function
- 14.11 α-Stable Number Generation
- 14.12 Fitting an α-Stable Distribution
- 14.13 Summary
- Chapter 15: Levy Processes
- 15.1 Introduction
- 15.2 Levy-Khintchine Formula
- 15.3 Infinite Versus Finite Variation
- 15.4 Infinite Versus Finite Activity Processes
- 15.5 Finite Activity Levy Process
- 15.6 Infinite Activity Levy Processes
- 15.7 Levy Process with Drift
- 15.8 Ito's Lemma for Finite and Infinite Activity Processes
- 15.9 Risk-Neutral Characteristic Function
- 15.10 Non-Levy Processes
- Summary
- Chapter 16: Fourier-Based Option Analysis
- 16.1 Introduction
- 16.2 Risk-Neutral Valuation
- 16.3 Delta Probability Decomposition for the Black–Scholes form
- 16.4 FFT-Based Option Valuation
- 16.5 Implementation of the FFT Call Price
- 16.6 Fractional FFT-Based Option Valuation
- 16.7 Time Value Method
- 16.8 Greeks
- 16.9 Lewis Fundamental Transform Method
- Summary
- Chapter 17: Fundamentals of Stochastic Finance
- 17.1 Introduction
- 17.2 Risk-Neutral Pricing
- 17.3 Expected Price
- 17.4 Martingales
- 17.5 Futures Contract Valuation Basics
- 17.6 Forward Contract Valuation Basics
- 17.7 Dynamics of Bond Prices
- 17.8 Vasicek Model
- 17.9 Kolmogorov's Backward Equation
- 17.10 The Feynman–Kac Formula
- 17.11 Multiple Ito Diffusions
- Summary
- Chapter 18: Affine Jump-Diffusion Processes
- 18.1 Introduction
- 18.2 Affine Mean Reversion Process
- 18.3 Transform Analysis
- 18.4 Transform Analysis Derivation
- 18.5 Two-Factor Model: Affine Pricing
- 18.6 Nomikos and Soldatos Three-Factor Model
- 18.7 Kalman Filter for the Nomikos Three-Factor Model
- 18.8 Exponential Jump-Size Distribution
- 18.9 Villaplana Log Price Jump-Diffusion Two-Factor Model
- 18.10 Extended Transform
- 18.11 Extended Transform Derivation
- 18.12 Villaplana Linear Price Jump-Diffusion Two-Factor Model
- Summary
- Index

## Product information

- Title: Financial Derivative and Energy Market Valuation: Theory and Implementation in MATLAB
- Author(s):
- Release date: March 2013
- Publisher(s): Wiley
- ISBN: 9781118487716

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