Second and Higher-Order Greeks with 3D Visualizations in Python with Option Chain IV скачать в хорошем качестве

Second and Higher-Order Greeks with 3D Visualizations in Python with Option Chain IV

🔍 This Jupyter Notebook explores advanced financial modeling concepts, focusing on the Greeks, which measure sensitivities in option pricing. Here's what you'll find: 1️⃣ Code and Explanation: Explore Espen Haug's analytical Greeks, including second and higher-order derivatives for the Generalized Black-Scholes models. Insightful problem statements and sanity checks to clarify and test financial applications. 2️⃣ 3D Visualizations: Stunning 3D plots of Delta, Gamma, Vega, and other Greeks using Python and Plotly. Interpolation of Option Chain Visual interpretations of gamma volatility surfaces and meshgrid data to enhance understanding. 3️⃣ Advanced Calculations: Numerical estimations for Delta and Gamma using 10,000-point grids. Code examples implementing Greek calculations with numpy, scipy, and plotly for professional-grade analysis. 📂 Sections Overview: Introduction to Higher-Order Greeks Analytical formulas and Python implementations Dynamic 3D visualizations of sensitivities in option pricing 👨‍💻 Programming Focus: Python (NumPy, SciPy, Plotly) 🌍 Audience: Quantitative analysts, finance professionals, and students seeking deeper insights into financial modeling. FRM, CFA, PRMIA, ACCA and Actuarial candidates The Professional Actuarial Exams also cover the Black-Scholes model and Greeks, particularly in the context of financial mathematics and risk management. CFA Curriculum: 1. Level I: Basic concepts of derivatives and options pricing. Little to no focus on Black-Scholes beyond intuition. 2. Level II: Introduction to the Black-Scholes-Merton (BSM) model. Basic understanding of Greeks for hedging (Delta, Gamma, Vega, Theta, Rho). Applications in equity and fixed-income derivatives. 3. Level III: Practical application of Greeks in portfolio risk management. Strategies for dynamic hedging using Greeks. --- PRMIA (PRM) Curriculum: 1. Exam II (Quantitative Finance) Rigorous mathematical derivation of Black-Scholes. Greeks discussed in detail, including their calculation and risk management uses. Applications to complex derivative structures. 2. Exam III (Financial Risk Management): Greeks applied in stress testing, sensitivity analysis, and VaR. Emphasis on dynamic hedging and volatility trading. --- FRM Curriculum: 1. Part I: Black-Scholes model introduced as a tool for valuing options. Greeks discussed in the context of sensitivity analysis for options portfolios. 2. Part II: Advanced applications of Black-Scholes for exotic options. Use of Greeks in scenario analysis, stress testing, and dynamic hedging. Risk-neutral pricing framework and practical risk management. --- Professional Actuarial Exams: Actuarial exams (e.g.*SOA*, *CAS*, and *IFoA*) cover Black-Scholes and Greeks extensively in financial mathematics and risk modeling. 1. SOA/CAS Exam IFM (Investment and Financial Markets): Black-Scholes model: Derivation, assumptions, and limitations. Applications to European options pricing. Greeks: Calculation and interpretation of Delta, Gamma, Vega, Theta, Rho. Use of Greeks for hedging and sensitivity analysis. Option strategies and risk-neutral valuation. 2. IFoA (Institute and Faculty of Actuaries) Exam CM2: Black-Scholes formula: PDE derivation and solution. Applications to vanilla and exotic options. Greeks: Full derivations and interpretations. Risk management using Greeks in dynamic hedging. Stochastic calculus: Integral to understanding Black-Scholes and its extensions. 3. SOA Exam QFI (Quantitative Finance and Investments): Advanced Black-Scholes applications. Greeks in portfolio optimization and risk management. Focus on practical implementation in financial risk and investment contexts.    • Constructing an Implied Volatility Surface 1      • Constructing an Implied Volatility Surface 2      • Constructing an Implied Volatility Surface 3      • Constructing an Implied Volatility Surface 4      • Constructing an Implied Volatility Surface 5      • Scrape option chain data using yfinance Py...   Google Colab Link: https://colab.research.google.com/dri... Useful Reference Books: 1. Espen Gaarder Haug The Complete Guide to Option Pricing Formulas (1st edition, 1997; 2nd edition, 2007) 2. Robert L. McDonald Derivatives Markets (1st edition, 2002; subsequent editions published, including the 3rd edition, 2013) https://sites.google.com/view/vinegar...