Stochastic Finance with Python: Design Financial Models from Probabilistic Perspective

Table of Contents About the Author About the Technical Reviewer Introduction Chapter 1: Introduction What Is Quantitative Finance Why Stochastic What Is Special About Stochastic Methodologies Numerical Implementation Why Python The Approach of Pythonic Implementation Probabilistic and Numerical Programming Summary Chapter 2: Finance Basics and Data Sources Different Financial Assets Stocks Options Portfolio Basic Interest Theory Simple Interest Discrete Compound Interest Continuous Compound Interest Data Source Adapters for Financial Data Yahoo Financials Market Stack Returns Simple Return Multiperiod Simple Returns Log Returns Multiperiod Log Returns Summary Chapter 3: Probability The Inception of the Idea for Probability Theory Probability Space and Basic Definitions Definition of Probability Why Study Probability for Finance Set-Theoretic View of Probability Probability Space Independence and Conditional Probability Random Variable Discrete Random Variable Continuous Random Variable Probability Distributions Joint and Marginal Distribution Likelihood and Parameters Moments, Expectation, and Variance Variance Moments Moments Approximation Poisson Distribution Uniform Distribution Exponential Distribution Gaussian/Normal Distribution Characteristic Function Parameter Estimation Frequentist Method Maximum Likelihood Estimation (MLE) Log-Likelihood Function of Exponential and Gaussian Distribution Method of Moments Bayesian Method Bayes’ Theorem Parameter Estimation of Gaussian Distribution with Gaussian Prior Summary Chapter 4: Simulation Random Variable Generation Inverse Transform Method Change of Measure Inverse Method for PMF Acceptance/Rejection Method Monte Carlo Simulation Variance Reduction Antithetic Sampling Importance Sampling Summary Chapter 5: Stochastic Process Inception of Stochastic Process Random Walk Model Statistical Metrics of Symmetric Random Walk Model Quadratic Variation of Symmetric Random Walk Model Scaled Random Walk Model Brownian Motion Stochastic Calculus and Integrals – A Brief Introduction Stochastic Differential Equation – Financial Asset Dynamics Euler’s Method for Approximating SDE Basic Forecasting Theory and Monte Carlo Simulation Poisson Process Summary Chapter 6: Diffusion Model Modeling Financial Asset Price with SDE SDE-Based Model-Building Steps Formation of SDE – Log-Asset Price and Ito Lemma Ito Lemma Geometric Brownian Motion (GBM) Process and Euler Approximation Risk-Neutral Settings Estimation of PDF and Its Parameters Estimation of Parameters – Likelihood Function and MLE Numerical Estimation Under the Risk-Neutral Measure Closed-Form Estimation Under the Real-World Measure Inference Monte Carlo Simulation of Diffusion Model Time Unit Transformation Average Forecast – Mean Path Uncertainty Bounds Backtesting and RMSE Score Change of Frequency Computing Distributions of the Mean Path Comparison and Improvement Summary Chapter 7: Jump Models General Formation of Jump Model Ito Lemma for Jump Model Templates in Python for Parametric Jump-Diffusion Process Characteristic Function of Jump-Diffusion Model Merton Model Path Generation for Merton Model Parameter Estimation of Merton Model Density Recovery with Fourier Transform Recovery by FFT Method Recovery by COS Method Forecasting with Merton Model Kou Model Sampling Jumps from Asymmetric Double Exponential Distribution Stochastic Process for Kou Model and Path Generation Parameter Estimation of Kou Model Forecasting with Kou Model Methods to Improve the Result Nonparametric Models Brief Review of the Kernel Method Parameter Estimation Stochastic Process with Gaussian Jumps and Path Simulation Strategy for Selecting h and σY2(Y) Estimating h and σY2(Y) Summary Chapter 8: Options and Black- Scholes Model Options – Basics and Formulations Option Nomenclatures Payoff Function Put-Call Parity Black-Scholes Model Risk-Neutral Probability Method Greeks Delta (∆) Gamma (Γ) Theta (Θ) Vega (Κ) Rho (Ρ) Summary Chapter 9: PDE, Finite Difference, and Black-Scholes Model PDE – A Short Introduction Solution of PDE – Finite Difference Method (FDM) Explicit Method Python to Implement Explicit Method Stability Analysis Implicit Method Python to Implement Implicit Method Stability Analysis Crank-Nicolson Method Stability Analysis Black-Scholes PDE Implicit FDM for the Black-Scholes Model Integration with Diffusion Model and Python Implementation Summary Chapter 10: Portfolio Optimization Brief Idea About Portfolios The Mean-Variance Analysis Portfolio Simulation Minimum Variance Portfolio Additional Constraints Efficient Frontier Efficient Frontier Simulation Summary