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Financial Derivative and Energy Market Valuation: Theory and Implementation in MATLAB

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

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Chapter 1: Financial Models
  6. 1.1 Introduction
  7. 1.2 Geometric Brownian Motion
  8. 1.3 Expected Value, Variance, and Moments of Lognormal Distribution
  9. 1.4 Fitting Geometric Brownian Motion
  10. 1.5 Mean Price Simulation
  11. 1.6 Mean Reversion Models
  12. 1.7 Solving the Ornstein–Uhlenbeck Process
  13. 1.8 Simulating the Ornstein–Uhlenbeck Process
  14. 1.9 Calibrating the Ornstein–Uhlenbeck Process
  15. 1.10 Least Squares Fitting
  16. 1.11 Maximum Likelihood
  17. Summary
  18. Chapter 2: Jump Models
  19. 2.1 Introduction
  20. 2.2 Jump-Diffusion Model
  21. 2.3 Probability Functions
  22. 2.4 Least-Squares Estimation
  23. 2.5 Basic Moments
  24. 2.6 The Kolmogorov-Smirnov Test
  25. 2.7 Multinomial Estimation
  26. 2.8 Alternate Jump Models
  27. Summary
  28. Chapter 3: Options
  29. 3.1 Introduction
  30. 3.2 Capital Asset Pricing Model
  31. 3.3 Equivalent Martingale Measure
  32. 3.4 Money Market Numeraire
  33. 3.5 Zero-Coupon Bond Numeraire
  34. 3.6 Derivation of Black-Scholes Equation
  35. 3.7 Option Greeks
  36. 3.8 Binary Options
  37. 3.9 Merton Jump-Diffusion Option Price
  38. 3.10 Merton Option in a Hedged Portfolio
  39. 3.11 Martingale Derivation of Merton Option Price
  40. 3.12 Heston's Stochastic Volatility Model
  41. 3.13 PDE for Heston Probabilities
  42. 3.14 Characteristic Functions of the Heston Probabilities
  43. 3.15 Decoupled Green Function Approach to the Heston Model
  44. 3.16 Fourier Space Terminal Payoff
  45. 3.17 Green Function for Heston
  46. 3.18 Heston Greeks
  47. Summary
  48. Chapter 4: Binomial Trees
  49. 4.1 Introduction
  50. 4.2 Risk-Neutral Valuation
  51. 4.3 Delta Hedge Portfolio
  52. 4.4 Variance Matching
  53. 4.5 Recursive Binomial Tree
  54. 4.6 Futures Option Tree
  55. 4.7 Memory and CPU Improvements
  56. 4.8 Smile and Smirk
  57. 4.9 Implied Local Volatility
  58. Summary
  59. Chapter 5: Trinomial Trees
  60. 5.1 Introduction
  61. 5.2 Trinomial Tree Derivation
  62. 5.3 Calibrating the Trinomial Tree
  63. 5.4 Hull–White Calibration Step One
  64. 5.5 Reversion at Edge of Tree
  65. 5.6 Hull–White Calibration Step Two
  66. 5.7 Spot Price Stochastic Differential Equation
  67. 5.8 Tree-Based Futures Options Under Mean Reversion
  68. 5.9 Analytical European Futures Option Under Mean Reversion
  69. Summary
  70. Chapter 6: Finite Difference Methods
  71. 6.1 Introduction
  72. 6.2 Black–Scholes Differential Equation
  73. 6.3 Finite Difference Grid
  74. 6.4 Partial Derivative Representation
  75. 6.5 Explicit (Forward in Time) Finite Difference
  76. 6.6 European Option Boundary Conditions
  77. 6.7 Log-Price Explicit Finite Difference Equation
  78. 6.8 Implicit (Backward in Time) Finite Difference Equation
  79. 6.9 Crank–Nicolson Method
  80. 6.10 Tridiagonal Gaussian Elimination
  81. 6.11 Successive Overrelation Technique
  82. 6.12 Gauss–Seidel Technique
  83. 6.13 Crank–Nicolson for American Options
  84. 6.14 Option Greeks
  85. 6.15 Multidimensional Pde
  86. 6.16 Heston Model Stochastic Differential Equations
  87. 6.17 Heston Partial Differential Equation
  88. 6.18 Log-Price Heston Pde
  89. 6.19 Explicit Heston Finite Difference Approach
  90. 6.20 Explicit Stability Limit
  91. 6.21 Heston Finite Difference Boundary Conditions
  92. 6.22 Implicit Finite Difference Heston
  93. Summary
  94. Chapter 7: Kalman Filter
  95. 7.1 Introduction
  96. 7.2 Kalman Filter Derivation
  97. 7.3 Key Kalman Filter Equations
  98. 7.4 Multivariate Distribution
  99. 7.5 Kalman Filter of Spot Mean Reversion Process
  100. Summary
  101. Chapter 8: Futures and Forwards
  102. 8.1 Introduction
  103. 8.2 Fair Value
  104. 8.3 Forward and Futures Terminology
  105. 8.4 Capital Asset Pricing Model
  106. 8.5 Forward Price Differential Equation
  107. 8.6 Mean Reversion One-Factor Model
  108. 8.7 Kalman Filtration of One-Factor Model
  109. 8.8 Convenience Yield
  110. 8.9 Forward Price Differential Equation with a Fixed Convenience Yield
  111. 8.10 Forward Price Differential Equation with Stochastic Convenience Yield
  112. 8.11 Two-Factor Schwartz Stochastic Convenience Yield Model
  113. 8.12 Joseph Form of the Error Covariance Update
  114. 8.13 Filtering Vector Measurements with Uncorrelated Errors as Scalars
  115. 8.14 Square Root Filtering
  116. 8.15 Squaring/Square Root Filter
  117. Summary
  118. Chapter 9: Nonlinear and Non-Gaussian Kalman Filter
  119. 9.1 Introduction
  120. 9.2 Extended Kalman Filter
  121. 9.3 Extended Kalman Filter of Black–Scholes Model
  122. 9.4 General Transition Functions
  123. 9.5 Gauss–Hermite Quadrature Kalman Filter
  124. 9.6 Weights and Roots of Gauss–Hermite Quadratutre
  125. 9.7 Gauss–Hermite Quadrature
  126. 9.8 Gauss–Hermite Filter with Additive Gaussian Noise
  127. 9.9 Unscented Transform
  128. 9.10 Scaled Unscented Transform
  129. 9.11 Unscented Transform Kalman Filter of Black–Scholes Model
  130. 9.12 Unscented Transform Kalman Filter of Heston Model
  131. 9.13 Scaled Unscented Transform Kalman Filter
  132. 9.14 Monte Carlo Numerical Integration
  133. 9.15 Nonlinear Monte Carlo Kalman Filter with Additive Noise
  134. 9.16 Importance Sampling
  135. 9.17 Sequential Importance Sampling
  136. 9.18 Inverse Transform Resampling
  137. 9.19 Bootstrap Particle Filter
  138. 9.20 Particle Filter of the Heston Model
  139. Summary
  140. Chapter 10: Short-Term Deviation/Long-Term Equilibrium Model
  141. 10.1 Introduction
  142. 10.2 Schwartz and Smith Model
  143. Summary
  144. Chapter 11: Futures and Forwards Options
  145. 11.1 Introduction
  146. 11.2 Futures Price Process
  147. 11.3 Futures Risk Neutral Behavior
  148. 11.4 Futures Contract for Constant Interest Rate
  149. 11.5 Futures Options
  150. 11.6 European Put–Call Parity
  151. 11.7 American Put–Call Parity
  152. 11.8 Black's Model
  153. 11.9 Black Model Greeks
  154. 11.10 American Options
  155. 11.11 American Option Derivation
  156. 11.12 Barone-Adesi–Whaley Quadratic Approximation
  157. 11.13 American Call Quadratic Approximation
  158. 11.14 American Put Quadratic Approximation
  159. 11.15 Critical Asset Price Search
  160. 11.16 Futures Option Quadratic Approximation
  161. Summary
  162. Chapter 12: Fourier Transform
  163. 12.1 Introduction
  164. 12.2 Basic Fourier Transform Equations
  165. 12.3 Fourier Transform Processing
  166. 12.4 Absolutely Integrable Function
  167. 12.5 Square Integrable Function
  168. 12.6 Discrete Fourier Transform
  169. 12.7 Fourier Matrix
  170. 12.8 Fast Fourier Transform
  171. 12.9 Zero Padding the Fast Fourier Transform
  172. 12.10 Bluestein Fft
  173. 12.11 Chirp Z-Transform
  174. 12.12 Fractional Fast Fourier Transform
  175. 12.13 Taylor Series Approximation
  176. 12.14 Hermite Polynomials
  177. 12.15 Summary
  178. Chapter 13: Fundamentals of Characteristic Functions
  179. 13.1 Introduction
  180. 13.2 Characteristic Function
  181. 13.3 Moment Generating Function
  182. 13.4 Taylor Series oF Characteristic Function
  183. 13.5 Characteristic Function of a Gaussian Probability Distribution
  184. 13.6 Summation of Random Variables
  185. 13.7 Summary
  186. Chapter 14: Application of Characteristic Functions
  187. 14.1 Introduction
  188. 14.2 Levy Theorem
  189. 14.3 Relating Characteristic and Cumulative Distribution Functions
  190. 14.4 Symmetry of Characteristic Function
  191. 14.5 Probability Density Function by Inversion
  192. 14.6 Cumulative Distribution Function by Inversion
  193. 14.7 Probability Density Function from Fourier Inversion
  194. 14.8 Probability Density Function by FFT of Characteristic Function
  195. 14.9 Probability Density Function by Fractional FFT of Characteristic Function
  196. 14.10 Cumulative Distribution Function by FFT of Characteristic Function
  197. 14.11 α-Stable Number Generation
  198. 14.12 Fitting an α-Stable Distribution
  199. 14.13 Summary
  200. Chapter 15: Levy Processes
  201. 15.1 Introduction
  202. 15.2 Levy-Khintchine Formula
  203. 15.3 Infinite Versus Finite Variation
  204. 15.4 Infinite Versus Finite Activity Processes
  205. 15.5 Finite Activity Levy Process
  206. 15.6 Infinite Activity Levy Processes
  207. 15.7 Levy Process with Drift
  208. 15.8 Ito's Lemma for Finite and Infinite Activity Processes
  209. 15.9 Risk-Neutral Characteristic Function
  210. 15.10 Non-Levy Processes
  211. Summary
  212. Chapter 16: Fourier-Based Option Analysis
  213. 16.1 Introduction
  214. 16.2 Risk-Neutral Valuation
  215. 16.3 Delta Probability Decomposition for the Black–Scholes form
  216. 16.4 FFT-Based Option Valuation
  217. 16.5 Implementation of the FFT Call Price
  218. 16.6 Fractional FFT-Based Option Valuation
  219. 16.7 Time Value Method
  220. 16.8 Greeks
  221. 16.9 Lewis Fundamental Transform Method
  222. Summary
  223. Chapter 17: Fundamentals of Stochastic Finance
  224. 17.1 Introduction
  225. 17.2 Risk-Neutral Pricing
  226. 17.3 Expected Price
  227. 17.4 Martingales
  228. 17.5 Futures Contract Valuation Basics
  229. 17.6 Forward Contract Valuation Basics
  230. 17.7 Dynamics of Bond Prices
  231. 17.8 Vasicek Model
  232. 17.9 Kolmogorov's Backward Equation
  233. 17.10 The Feynman–Kac Formula
  234. 17.11 Multiple Ito Diffusions
  235. Summary
  236. Chapter 18: Affine Jump-Diffusion Processes
  237. 18.1 Introduction
  238. 18.2 Affine Mean Reversion Process
  239. 18.3 Transform Analysis
  240. 18.4 Transform Analysis Derivation
  241. 18.5 Two-Factor Model: Affine Pricing
  242. 18.6 Nomikos and Soldatos Three-Factor Model
  243. 18.7 Kalman Filter for the Nomikos Three-Factor Model
  244. 18.8 Exponential Jump-Size Distribution
  245. 18.9 Villaplana Log Price Jump-Diffusion Two-Factor Model
  246. 18.10 Extended Transform
  247. 18.11 Extended Transform Derivation
  248. 18.12 Villaplana Linear Price Jump-Diffusion Two-Factor Model
  249. Summary
  250. Index