This project compares option pricing using Geometric Brownian Motion (GBM) and Fractional Geometric Brownian Motion (fGBM) under different Hurst parameters.
compare_fgbm_gbm_H_0_95.py: Compares option pricing between GBM and fGBM for Hurst parameter ( H = 0.95 ).compare_fgbm_gbm_H_0_5.py: Demonstrates that fGBM with ( H = 0.5 ) is equivalent to GBM.
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Run the comparison for ( H = 0.95 ):
python compare_fgbm_gbm_H_0_95.py
This will generate a CSV file (
option_pricing_comparison_H_0_95.csv) and a plot (option_prices_comparison_H_0_95.png). -
Run the comparison for ( H = 0.5 ):
python compare_fgbm_gbm_H_0_5.py
This will generate a CSV file (
option_pricing_comparison_H_0_5.csv) and a plot (option_prices_comparison_H_0_5.png).
The results demonstrate the following:
- For ( H = 0.95 ), fGBM captures long-term dependencies and yields different option prices compared to GBM.
- For ( H = 0.5 ), fGBM reduces to GBM, resulting in identical option prices.
option_prices_comparison_H_0_95.png: Comparison of GBM and fGBM Call Option Prices (H=0.95)option_prices_comparison_H_0_5.png: Comparison of GBM and fGBM Call Option Prices (H=0.5)
- Python 3.x
- numpy
- scipy
- pandas
- matplotlib