danielhstahl / fftoptionpricing

Option pricing using FFT

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FFT Option Pricing

This repository does Carr Madan, Fourier Space Time Stepping Algorithms, and Fang Oosterlee pricing from Carr and Madan, Sukov Vladimir, and Fang Oosterlee. Requires my Functional Utilities, my Characteristic Functions, my Fang Oosterlee , and my Runge Kutta library.

Benefits to FSTS: It only requires a CF and a payoff. No further manipulations necessary. Can also price American options. Disadvantages: slower. Roughly twice as slow as Carr and Madan for Europeans. Prices in log asset instead of log strike; so not as easy to price all strikes for a given stock price.

Benefits to Carr Madan: Ubiquitous. Prices in log strike. Disadvantages: requires algebraic manipulations for each payoff. Does not converge quickly.

Benefits to Fang Oosterlee: Fast convergence in u. U and X are separate and so can price only the options available in the market without interpolation. Prices in either asset or strike. Disadvantages: requires algebraic manipulations for each payoff. For a given size of "X", tends to be slower than Carr Madan. Benefit is that "X" can be whatever the market provides.

Examples

See the tests for examples on how to use each of these algorithms.

Generate charts and calibration documentation

For the calibration aspect, run make generateCharts and then run ./generateCharts. Then open OptionCalibration.Rnw in RStudio and compile as PDF.

fftoptionpricing's Issues

Make a mathematically optimal choice for .95 threshold

We need to choose a cutoff such that the log spline kicks in prior to the pointy part of the CF. Currently the cutoff is arbitrarily at .95. See line 103 of https://github.com/phillyfan1138/FFTOptionPricing/blob/ff3d3cd6f92949368a02495cc3cd4dd30be2e26f/OptionCalibration.h.

Make Delta, Gamma, and Theta

Allow for Delta, Gamma, and Theta for option pricing