numerical-option-pricing-duke-energy

Methods and code to study numerical option pricing using Duke Energy Corporation (DUK) daily closing prices. We developed an end‑to‑end methodology to price European call options under the Black–Scholes framework, validating GBM assumptions before pricing. Besides, data provided contains closing prices of different companies which follow GBM assumptions.

This repository accompanies an academic project. It focuses on methodology and reproducibility rather than business KPIs.

Project Structure

numerical-option-pricing-duke-energy/
├─ code/
│ └─ matlab/
│ └─ Proyecto_EstocasticosII_AreizaParraSerna.mlx
├─ data/
│ └─ raw/
│ └─ datos.xlsx
├─ docs/
│ └─ Procesos_Estocasticos_II_Proyecto.pdf
├─ .github/
│ └─ workflows/ # (optional CI, empty by default)
├─ .gitignore
├─ LICENSE
├─ CITATION.cff
└─ README.md

Goals

• Validate GBM assumptions on DUK closing prices.
• Implement and compare numerical methods for European call pricing:
  • Black–Scholes (closed form)
  • Monte Carlo simulation
  • Binomial tree
  • Explicit finite‑difference scheme
• Provide a clear, reproducible pipeline in MATLAB Live Script (.mlx).

Data

• Source: Yahoo Finance
• Range: 2023‑05‑15 to 2025‑05‑09 (daily).
• data/raw/datos.xlsx: input dataset with closing prices of several companies.

If you later fetch data via APIs, keep raw dumps in data/raw/ and document the source here.

Requirements

• MATLAB R2024b (Live Script .mlx).
  • Typical toolboxes: Statistics and others, Financial Toolbox (if available).
• Optional: Python/R for auxiliary checks.

How to Run (MATLAB)

1. Open code/matlab/optionprice.mlx.
2. Ensure data/raw/datos.xlsx is available.
3. Run the Live Script sections from top to bottom.

Methodology (high‑level)

1. Exploratory analysis of prices/returns; highlight outliers and news events.
2. Assumption checks for GBM on returns:
   • Partial autocorrelation (PACF) — no significant autocorrelation. Hurst exponent and fractal dimension indicating trend‑like behavior.
   • Normality tests (Jarque–Bera, KS, Anderson–Darling, Lilliefors).
   • Homoskedasticity checks (ARCH and White tests).
   • Cumulative volatility profile.
3. Parameter estimation for GBM; in‑sample forecasting with 1,000 simulated paths and MAPE as accuracy criterion.
4. Risk‑neutral valuation:
   • Price European calls using Black–Scholes, Monte Carlo, Binomial, Explicit Finite Differences.
   • Risk‑free rate: r = 0.05. Initial spot: last observed price.
   • Maturities T ∈ {1, 1/2, 1/3, 1/4} (years).
   • Strikes K1…K5 derived from simulated projections (see docs).

Results (summary)

• Model fit: in‑sample MAPE ≈ 1.2% (good forecast accuracy).
• Pricing: methods broadly agree according to Black-Scholes equation.
• Efficiency: explicit finite differences is the most computationally expensive, especially for larger T and K (grid grows with domain size).
• Caveat: when the option’s reference price is extremely small (deep OTM), tiny absolute errors translate into large relative errors.

See tables and figures in docs/article.pdf for detailed numbers.

Reproducibility notes

• MATLAB R2024b; some statistical tests used native functions.
• Hurst and fractal dimension are estimated with MATLAB self-implementations (documented briefly in the paper).
• Original experiments leveraged CPU parallelization; GPU not required.

Documentation

• docs/article.pdf — full paper (Spanish), journal style. An English summary may be added in future updates.

Contributing

Personal academic repo. Forks welcome; issues/PRs are optional.