OPUS – Option Pricing & Uncertainty Sensitivities

OPUS is a modular and interactive Streamlit-based application for pricing European, American, and Asian call and put options using Black-Scholes, Binomial Tree, and Monte Carlo Simulation models. It also provides analytical insights into first- and second-order option sensitivities (the Greeks).

Supported Models

Model	European	American	Asian	Notes
Black-Scholes	✅	❌	❌	Closed-form solution for European only
Binomial Tree	✅	✅	❌	American via early exercise handling
Monte Carlo	✅	❌	✅	Suitable for path-dependent options

Features

• Black-Scholes: Closed-form pricing and Greeks for European call options
• Binomial Tree: Recombining lattice supporting early exercise for American calls
• Monte Carlo: Supports both European and Asian options via path-averaging
• Computed Greeks:
  • Delta (Δ)
  • Gamma (Γ)
  • Theta (Θ)
  • Vega (𝜈)
  • Rho (ρ)
• Real-time LaTeX-rendered formulas
• Flexible user-defined inputs: spot price, strike, volatility, time to maturity, number of steps, and simulation paths
• Structured user interface with model separation via Streamlit tab navigation

Installation

Clone the repository and install dependencies:

git clone https://github.com/julgas/opus.git
cd opus
pip install -r requirements.txt
streamlit run opus.py