This README is intended to guide the user in how to use HW-07.
The assignment is hosted on github here:
https://github.com/DavisVaughan/uncc-math-6204/tree/master/assignments/hw-07
The purpose of this module is to calculate the value of European call and put options using fourier transforms. The theory is developed in presentation 07, and the pricing integral is calculated through the FFT. The benefit of this method is that it prices a range of options at once, varied by the strike. The documentation of each function presents the closed form solutions of the pricing integrals and the pieces involved to evaluate them.
The values of alpha all converge on the correct prices. However, alpha = -10 does produce an error. When evaluating the option price, the calculation exp(-alpha * k_n) produces infinity values for large k_n. I think this is just a numerical accuracy problem, but it may be a small error on my part somewhere. I looked but couldn’t find anything.
For the theoretical work, the fourier transform and inverse fourier transform were used to find the solution to the option price. To implement them, the inverse fft was used to approximate the integral after picking an upper bound on the frequency domain.
main.py - (DRIVER) Price the option over a number of different values of alpha and K.
price_option_fft.py - Contains functions that price the European option.
Because the main.py file includes the code:
if __name__ == "__main__":
print(main())the easiest way to run the example is from the terminal.
Within your command line / terminal, navigate to the folder containing the main.py script, and just run:
python2 main.pyA pandas data frame should output:
alpha option_price
0 2.5 31.811887
1 -2.5 7.910241
2 5.0 31.811887
3 -5.0 7.910241
4 10.0 31.811887
5 -10.0 7.910241