Monte Carlo Simulation with Multiple Factors | European spread options with stochastic volatility

One of the main benefits of Monte Carlo simulations is to price options under multiple factors. By this I refer to multiple underlying asset prices or stochastic volatility or even changing interest rates. In this tutorial we will explore the pricing of a European Spread Call Option on the difference between two stock indices the Nasdaq and SP500 following a more general stochastic process. The SDE's will have stochastic volatility as described under the Heston Model (1993). The Monte Carlo procedure is exactly the same for a spread call option except the correlation matrix between Wiener processes is larger, as in we have four correlated normal variates to simulate the four processes. This will require the use of Cholesky decomposition to simulate correlated wiener variables for each factor within our monte carlo simulation. We develop two monte carlo methods, one that is termed the slow implementation where we step through each time step and simulation path to explain the calculations that are occuring elementwise. The next is the fast implementation where we vectorize the code. ★ ★ Code Available on GitHub ★ ★ GitHub: https://github.com/TheQuantPy Specific Tutorial Link: https://github.com/TheQuantPy/youtube-tutorials/blob/8e64e19629cee840928b51baf4660e5c777e87e7/2022/002%20Apr-Jun/2022-04-08%20Monte%20Carlo%20Simulation%20with%20Multiple%20Factors%20_%20European%20spread%20options%20with%20stochastic%20volatility.ipynb 00:00 Intro 00:40 Heston Model Dynamics 04:20 Nasdaq vs SP500 Index Spread 05:10 Slow Implementation 10:10 Fast Implementation ★ ★ 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.