You Need to Learn Importance Sampling NOW | Deep Out of the Money Options

In this tutorial we discuss Monte Carlo convergence and how we can more effectively value a deep out of the money option. In previous tutorials will discusses the benefits of combining Monte Carlo Variance Reduction techniques such as antithetic and control variate methods to reduce the standard error of our simulation. We demonstrate the effectiveness of using Importance Sampling by comparing the convergence on a pricing a European Call Option by monte carlo simulation using normal risk-neutral dynamics compared to using a change of measure. Method of Importance Sampling involes a change of distribution using the Radon-Nikodym derivative. So we conductr a simulation under a new probability measure and then multiply by the ratio of the two probability density functions (the old over the new), or the Radon Nikodym derivative of one process with respect to the other. For more complicated processes and derivatives one need to use the densities given by Girsanovs Theorem within the monte carlo simulation. References: https://sas.uwaterloo.ca/~dlmcleis/s906/chapt5.pdf ★ ★ Code Available on GitHub ★ ★ GitHub: https://github.com/TheQuantPy Specific Tutorial Link: https://github.com/TheQuantPy/youtube-tutorials/blob/8e64e19629cee840928b51baf4660e5c777e87e7/2022/002%20Apr-Jun/2022-05-30%20You%20Need%20to%20Learn%20Importance%20Sampling%20NOW%20_%20Deep%20Out%20of%20the%20Money%20Options.ipynb ★ ★ QuantPy GitHub ★ ★ Collection of resources used on QuantPy YouTube channel. https://github.com/thequantpy ★ ★ Discord Community ★ ★ Join a small niche community of like-minded quants on discord. https://discord.com/invite/aY2Af4CxHP ★ ★ Support our Patreon Community ★ ★ Get access to Jupyter Notebooks that can run in the browser without downloading python. https://www.patreon.com/quantpy ★ ★ ThetaData API ★ ★ ThetaData's API provides both realtime and historical options data for end-of-day, and intraday trades and quotes. Use coupon 'QPY1' to receive 20% off on your first month. https://www.thetadata.net/ ★ ★ Online Quant Tutorials ★ ★ WEBSITE: https://quantpy.com.au ★ ★ Contact Us ★ ★ EMAIL: [email protected] Disclaimer: All ideas, opinions, recommendations and/or forecasts, expressed or implied in this content, are for informational and educational purposes only and should not be construed as financial product advice or an inducement or instruction to invest, trade, and/or speculate in the markets. Any action or refraining from action; investments, trades, and/or speculations made in light of the ideas, opinions, and/or forecasts, expressed or implied in this content, are committed at your own risk an consequence, financial or otherwise. As an affiliate of ThetaData, QuantPy Pty Ltd is compensated for any purchases made through the link provided in this description.