How to Price Options with Monte Carlo Simulation

Описание: 🚀 Master Quantitative Skills with Quant Guild
https://quantguild.com

📅 Meet with me 1:1
https://calendly.com/quantguild-support

📈 Interactive Brokers for Algorithmic Trading
https://www.interactivebrokers.com/mk...

👾 Join the Quant Guild Discord server here
  / discord  
___________________________________________
🪐 Jupyter Notebook
https://github.com/romanmichaelpaoluc...

*TL;DW Executive Summary*
The Black-Scholes portfolio replication argument is precisely the arbitrage free price implied by the Fundamental Theorem of Asset Pricing proven by the Feynman-Kac Theorem
We thus have two ways to solve for an option price: solving (analytically or numerically) a pricing PDE or by solve for (analytically or numerically) an expectation
Since we are dealing with stable underlying distributions we can approxoimate the expectation via Monte Carlo simulation and the Law of Large Numbers (LLN) to produce the necessary expectation corresponding to the option price
After discounting the simulated expectation back to the present we will find the price of the option consistent with the replication argument
This recipe is how the fair (mid) price is approximated by large institutions every day before adjustments, quoting a two-way, and hedging as I discuss in my video on Algorithmic Market-Making

I hope you enjoyed!

Roman
___________________________________________
📖 Chapters:
00:00 - How and Why Monte Carlo Pricing Works
03:14 - Black-Scholes and No-Arbitrage Pricing
06:15 - Visualizing the Discrete Expectation
07:57 - Discrete Law of Large Numbers (LLN)
09:11 - Visualizing the Continuous Expectation
10:29 - Continuous Law of Large Numbers (LLN)
11:39 - Extension to Distributions of Stochastic Processes
12:28 - Why This is Necessary for Pricing Options
13:58 - Why Simulation Works to Price Option
15:46 - Recipe for Simulating Option Prices
16:50 - Pricing a (Best-of Call) Rainbow Option
19:15 - TL;DW Executive Summary
___________________________________________
🗣️ Shout Outs

A special thank you to my members on YouTube for supporting my channel and enabling me to continue to create videos just like this one!

⭐ Quant Guild Directors
Dr. Jason Pirozzolo
___________________________________________
▶️ Related Videos

Referenced Videos 👉
How Physics Accidentally Proved the Black-Scholes Model
   • How Physics Accidentally Proved the Black-...  

How to Price Exotic Options
   • How to Price Exotic Options  

Quant Explains Algorithmic Market-Making
   • Quant Explains Algorithmic Market-Making  

Markov Chains for Quant Finance
   • Markov Chains for Quant Finance  

Hidden Markov Models for Quant Finance
   • Hidden Markov Models for Quant Finance  

Quant Builds 🔨
How to Build a Markov Chain Regime Switching Bot in Python with Interactive Brokers | Part 1
   • How to Build a Markov Chain Regime Switchi...  

Probability, Statistics, and Stochastic Calculus Applied to Pricing 📈
Why Monte Carlo Simulation Works
   • Why Monte Carlo Simulation Works  

Finite Differences Option Pricing for Quant Finance
   • Finite Differences Option Pricing for Quan...  

Brownian Motion for Quant Finance
   • Brownian Motion for Quant Finance  

How Physics Accidentally Proved the Black-Scholes Model
   • How Physics Accidentally Proved the Black-...  
___________________________________________
🗂️ 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  
___________________________________________