Finite Differences Option Pricing for Quant Finance скачать в хорошем качестве

Finite Differences Option Pricing for Quant Finance

🚀 Master Quantitative Skills with Quant Guild https://quantguild.com 📈 Interactive Brokers for Algorithmic Trading https://www.interactivebrokers.com/mk... 👾 Join the Quant Guild Discord server here   / discord   ___________________________________________ 🪐 Jupyter Notebook https://github.com/romanmichaelpaoluc... *Roman's Overview of Option Pricing Methodology* When we go about pricing options the first step is to select a model framework and accept the associated assumptions: Black-Scholes, Heston, the list goes on... The goal in this capacity is to capture as much variation observed empirically while saying as little as possible about the true distribution observed of corresponding market prices. We aim to price consistently and efficiently - we can't subject our quotes to arbitrage and need to select a reasonable model capable of producing quotes consistent with a market implied volatility surface. Once we select a model we can develop prices in several ways: A.) Develop and Analytically Solve a Pricing Partial Differential Equation B.) Develop and Numerically Solve a Pricing Partial Differential Equation (Finite Differences) C.) Leverage the Law of Large Numbers (LLN) and Risk-Neutrality to Simulate Prices via Monte Carlo Simulation The instrument you are pricing and the model framework you select will largely dictate which technique you will use to go about developing prices. In some cases we can produce prices slowly and consistently with models that perhaps better capture the dynamics observed in the market (i.e. the Rough Model Family) though there is literature and conjecture about the efficacy of rough volatility, neural networks and other machine learning techniques make it possible to provide quotes for such models in an effective manner - a video for another day! I hope you enjoyed, this was a long one! Roman ___________________________________________ 📖 Chapters: 00:00 - Introduction 03:39 - Pricing Differential Equations 04:37 - Understanding Pricing Differential Equation 06:38 - Why Finite Differences is Necessary 07:50 - Understanding and Approximating Derivatives 12:00 - Why Finite Differences Works 14:21 - Visualizing Finite Differences (2D) 16:02 - Extrapolation and Interpolation with Finite Differences 17:32 - Finite Differences 18:48 - Example: Finite Differences, Ordinary Differential Equation 21:20 - Coding: Finite Differences, Ordinary Differential Equation 24:48 - Partial Differential Equations, 1-D Heat Equation 26:40 - Visualizing Finite Differences (3D) 27:27 - Example: Finite Differences, Partial Differential Equation 30:31 - Coding: Finite Differences, Partial Differential Equation 39:23 - Finite Differences Applied to the Black-Scholes Equation 41:28 - Closing Thoughts and Future Topics ___________________________________________ ▶️ Related Videos Ito's Lemma Clearly and Visually Explained    • Ito's Lemma Clearly and Visually Explained   Ito Integration Clearly and Visually Explained    • Ito Integration Clearly and Visually Expla...   Stochastic Differential Equations for Quant Finance    / qdaesc40zj   Monte Carlo Simulation and Black-Scholes for Pricing Options    • Monte Carlo Simulation and Black-Scholes f...   Why Monte Carlo Simulation Works    • Why Monte Carlo Simulation Works   Expected Stock Returns Don't Exist    • Expected Stock Returns Don't Exist   How to Trade    • How to Trade   How to Trade with an Edge    • How to Trade with an Edge   ___________________________________________ 🗂️ Resources 📚 Quant Guild Library: https://github.com/romanmichaelpaoluc... 🌎 GitHub: https://github.com/RomanMichaelPaolucci https://github.com/Quant-Guild 📝 Medium (Blog):   / quantguild     / quant   ___________________________________________ 🛠️ Projects The Gaussian Cookbook: https://gaussiancookbook.com Recipes for simulating stochastic processes: https://papers.ssrn.com/sol3/papers.c... ___________________________________________ 💬 Socials TikTok:   / quantguild   Instagram:   / quantguild   X/Twitter: https://x.com/quantguild/ LinkedIn (personal):   / rmp99   LinkedIn (company):   / quant-guild   ___________________________________________