Lecture Notes: Pricing Options in C++ using Monte Carlo Simulation

Introduction

• Presenter: Jo Scors, Ethernet Win Channel
• Topic: C++ Script for Pricing Options using Monte Carlo Simulation
• Background: Continuing from a previous popular C++ video

Setup

• Using VS Code with icy blue theme for C++ coding
• Hardware: Laptop, Camera, Headphone, Microphone

Personal Note on Colors

• Jo associates languages/subjects with colors:
  • C++: Icy blue
  • Python: Orange/Red
  • JavaScript: Green
  • Java: Yellow
• Comparison with School notebooks' color-coding for subjects

Main Topic: Pricing Options with Monte Carlo Simulation

Monte Carlo Simulation Basics

• Core Idea: Repeated random sampling to estimate outcomes
• *Example of Estimating Pi:
  • Randomly distributing points within a square and circle
  • Using the ratio of points within the circle to estimate Pi*

Options Pricing and The Black-Scholes Model

• Options Pricing Model: Black-Scholes
  • Parameters: stock price, strike price, risk-free rate, volatility, expiration time
  • Option: Right but not obligation to buy/sell 100 shares
  • Call Options: Buy 100 shares at strike price (appreciates if stock price rises)
  • Model’s Limitations: Simplifications and agreed-upon inaccuracies

Helper Functions Overview

• Helper Function (Random Number Generator):

  • Generates random numbers with specified mean and standard deviation
  • Example usage: Mean = 0, Standard Deviation = 1

• Market Normal Distribution:

  • Normal Distribution assumption is incorrect; real markets do not follow this
  • Example: Abnormal market moves (City group trading dollar/Yen spreads)

Main Simulation Function

• Variables: stock price, strike price, risk-free rate, volatility, expiration, number of simulations, option type
• Steps in the simulation:
  • Generating a random price path using Euler’s formula
  • Calculating payoff based on the stock and strike prices for both call and put options
  • Summing and averaging out the payoffs
  • Discounting the average payoff to present value using Euler's number formula

Practical Application and Customization

• Dynamic Parameters: Volatility and risk-free rate can change over time
• Running the Simulation: Command Line Instructions
  • Use g++ to compile and run the script

Overview of the Script Output

• Displays the average payoff for call and put options
• Importance of evaluating if the option contract is a good deal based on pay off

Final Takeaways

• In-depth understanding of Option Pricing Models
  • Acknowledge assumptions and simplifications in models like Black-Scholes
  • Look out for ‘fat tails’ in market moves (extreme rare events)
• Importance of Simulation in Trading
  • Evaluation of risk and potential pay off

Additional Resources and Links

• GitHub: Code for the presented script
• Link to Monte Carlo Simulation tool
• Prometheus Analytics: Presenter’s company (indicators and alerts)
• Personal and Business Twitter accounts

Future Video Ideas

• Correlation Trading and Pairs Trading
• Viewer suggestions and comments are encouraged

Conclusion

• Encourage viewers to experiment and code along
• Open for ideas and suggestions from viewers