CAD/HUF Currency Option Pricing Project

Quantitative Finance & Time-Series Modeling Study This project investigates FX option pricing using both classical financial models and modern machine learning approaches. It combines GARCH volatility estimation, Monte Carlo simulation, and a hybrid LSTM-GARCH forecasting framework to analyze pricing sensitivity under realistic market dynamics.

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📚 Overview

This project focuses on the analysis and option pricing for the CAD/HUF (Canadian Dollar / Hungarian Forint) currency pair using financial time series modeling techniques.
The study aims to:

• Analyze historical exchange rate data.
• Evaluate the statistical properties of log-returns.
• Estimate volatility (both historical and GARCH-based).
• Price At-The-Money (ATM) European Call and Put options.
• Compare multiple option pricing methods, including a novel Hybrid LSTM-GARCH Monte Carlo model.

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🛠️ Tools and Libraries Used

• Python 3.10+
• pandas
• numpy
• matplotlib
• seaborn
• scipy
• statsmodels
• arch
• scikit-learn
• tensorflow / keras
• yfinance (for future improvements)

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📈 Methodology

1. Data Preparation

• Imported CAD/HUF historical exchange rate data.
• Reconstructed closing prices using Price and Change %.
• Cleaned, sorted, and prepared the dataset for analysis.

2. Log-Returns Calculation

• Computed daily log-returns from the reconstructed prices.

3. Statistical Analysis

• Conducted visual normality checks (QQ Plot, Histogram).
• Applied formal statistical tests (Jarque-Bera, Kolmogorov-Smirnov, Anderson-Darling).
• Tested independence of log-returns using the Ljung-Box Test.

4. Volatility Estimation

• Calculated historical volatility (annualized).
• Modeled advanced volatility dynamics using a GARCH(1,1) model.

5. Option Pricing Models

• Black-Scholes Model (adjusted for FX options)
• CRR Binomial Model
• Monte Carlo Simulation
• Hybrid LSTM-GARCH Monte Carlo:
  • Simulated price paths using LSTM-GARCH volatility estimates.
  • Estimated expected payoff under risk-neutral framework.

6. Comparison

• Compared Call and Put option prices from all three methods.

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📊 Key Results

Method	Call Price	Put Price
Black-Scholes	3.948767	4.227695
CRR Binomial	3.946723	4.225651
Monte Carlo	3.947293	4.246676
Hybrid Model	2.4938	5.0619

• The LSTM-GARCH Monte Carlo model demonstrated greater responsiveness to market volatility structure and non-linear dynamics.

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🚀 Advanced Extensions (Optional)

• Add support for real-time dynamic option pricing using APIs.
• Implement Reinforcement Learning for optimal hedging strategies.
• Extend the LSTM-GARCH framework to multivariate FX modeling.

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📂 Project Structure

CAD_HUF_Project/
├── CAD_HUF_Historical_Data.csv
├── CAD_HUF_Analysis.ipynb
├── LSTM_GARCH_Model.ipynb
├── README.md
└── requirements.txt