The CFH toolbox is a collection of characteristic function transform methods in finance that can be used for example for pricing American/European style options in affine jump diffusion models such as Heston or Pan, risk free bonds or CDS spread pricing in CIR or Vasicek specifications and many other models.
The toolbox is a collection of characteristic function transform methods in finance. It combines the seminal approach of Affine-Jump-Diffusion (AJD) option pricing of Duffie/Pan/Singleton (2000) with the Fast Fourier Transform methods of Carr/Madan (1999) and Chourdakis (2004).
The thoroughly documented CFH Toolbox...
- allows the user to evaluate all possible AJD processes in terms of their resulting characteristic function and extended characteristic function, call option prices and implied densities. The AJD processes may possess any number of jump components.
- can obtain European call option prices from user supplied characteristic functions.
- can obtain American call and put option prices from user supplied characteristic functions of Lévy processes.
- can obtain spread call and put option prices from user supplied characteristic functions.
- can obtain conditional expectations on any linear combination of state variables for any given characteristic function.
- can compute implied densities from any characteristic function.
- contains a (yet small) collection of commonly encountered characteristic functions.
- contains a (yet small) collection of commonly encountered jump distributions in finance.
- contains a function to compute zero bond prices from AJD dynamics or characteristic functions.
- contains a function to compute the extended transform of DPS2000 and is thus applicable to the pricing of CDS contracts and Asian options.
- contains a GUI for easy application of most components of this toolbox.
After copying all files into a folder, you might want to run 'install.m' or at least add the relevant folder to your list of paths.
This toolbox is still a work in progress, any comment is highly appreciated! Thank you.
- Duffie/Pan/Singleton (2000) Transform Analysis and Asset Pricing for Affine Jump-Diffusions, in: Econometrica 68/6.
- Carr/Madan (1999) Option Pricing and the Fast Fourier Transform, in: Journal of Computational Finance 2/4.
- Chourdakis (2004) Option Pricing using the fractional FFT, in: Journal of Computational Finance, 8/2.