Pricing Options in C++ using Monte Carlo Simulation

Jul 10, 2024

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

Introduction

  • Presenter: Jo Scors Channel (ethernet win)
  • Context: Continuation of C++ tutorials
  • Goal: To explain a C++ script for pricing options using Monte Carlo Simulation

Setup

  • Equipment: Laptop, camera, headphone, microphone
  • IDE: Visual Studio Code with a customized blue theme
  • Personal Note on Programming Languages:
    • C++ = icy blue
    • Python = orange/red
    • JavaScript = green
    • Java = yellow

Monte Carlo Simulation Explained

  • Concept: Relies on repeated random sampling from a distribution
  • Example: Estimating value of Pi using random points within a circle inscribed in a square
  • Formula: Pi ≈ (4 * number of points inside circle) / total number of points
  • Outcome: More points → Closer estimation to Pi (3.1415...)

About Option Pricing

  • Reference Model: Black-Scholes model
  • Components: Stock Price, Strike Price, Risk-Free Rate, Volatility, Expiry Date
  • Definition: An option is the right but not the obligation to buy/sell 100 shares at a specific price on a specific date
  • Challenge: Option pricing is complex; Black-Scholes is a simplified, widely-used but inherently flawed model

C++ Code Explanation

Helper Functions

  • Random Number Generator: Generates a random percentage move in stock price
  • Payoff Calculation: For European call/put option:
    • Call: Max(stock price - strike price, 0)
    • Put: Max(strike price - stock price, 0)

Monte Carlo Pricing Function

  • Variables: Initial stock price, strike price, risk-free rate, volatility, time to expiration, number of simulations, call/put option
  • Process:
    1. Initialize the sum of payoffs
    2. For each simulation:
      • Estimate stock price at option maturity using Euler’s formula and random percentage move
      • Calculate payoff (positive/zero) for call/put option
      • Aggregate payoffs
    3. Average the payoffs and discount to present value
  • Formula: Payoff sum * exp(- risk-free rate * time to maturity)

Compilation and Execution

  1. Compile: g++ filename -o outputfile
  2. Run: ./outputfile

Summary of Findings

  • Outputs: Estimated values of calls and puts
  • Interpretation of Results: Determine if the option is a good deal
  • Real-World Applicability: Adjusting risk-free rate and volatility for more dynamic and realistic simulations

Additional Points

  • Distribution: Normal distribution is a simplification; real markets often show skewed distributions
  • Final Thoughts: Option pricing models are essential yet approximate; success hinges on market willingness to pay expected prices

Links and Resources

  • Code Repository: GitHub link provided in the description
  • Pricing Simulation Resource: Link in the description
  • Prometheus Analytics: Company's website and TradingView scripts

Conclusion

  • Engagement: Encouraged viewers to comment and suggest future video topics
  • Next Video Idea: Correlation trading in stocks (e.g. pair trading)
  • Sign-Off: Farewell and encouragement to continue coding and exploring financial models