Implementing Fourier Transform Pricing methods for the European Call in Python,
with a focus on the Fast Fourier transform method proposed in Carr and Madan 1999.
Comparison of two underlying stock processes: the traditional Geometric Brownian Motion
and the Variance-Gamma process.
See Maths/OptionPricing.pdf for detailed mathematical explanations.
Classes and functions for option pricing are contained in the module optionfft.py.
The script error_analysis.py calculates the absolute and relative errors for the FFT pricing method
and writes the data to the tex file Analysis/err_table.tex. The prices computed by each method are
also written to Analysis/all_prices.csv. The script timing.py computes the average time
over a default of 10 independent runs for each method to yield the call prices in the given range of
strike prices.
Carr, P, Madan, D.B, 1999, "Option Valuation using the Fast Fourier Transform", Journal of Computational Finance, 2, 61-63.
Madan, D.B., Carr, P., and Chang, E.C., 1998, "The variance gamma process and option pricing.", European Finance Review, 2, 79-105.
Matsuda, K, 2004, "Introduction to Option Pricing with Fourier Transform: Option Pricing with Exponential Levy Models", PhD Thesis, The City University of New York.