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CFH Toolbox (Characteristic Function Option Pricing)

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05 May 2014 (Updated )

Implementation of Option Pricing Transform Methods

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Description

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.

References:
- 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.

Required Products MATLAB
MATLAB release MATLAB 7.14 (R2012a)
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Comments and Ratings (4)
11 Aug 2014 Matthias Held

Hi Marcel,

the upper range of integration can be specified see, for example,

>> help cf2call

I have embodied a double exponential jump specification, but will update this part some time in the near future as well. Hints are always appreciated.

11 Aug 2014 Luis

Great Toolbox

11 Aug 2014 Marcel  
11 Aug 2014 Marcel

Hi Matthias,

thanks for this very helpful toolbox. I have a few more questions:

Can you manually change numerical accuracy in the evaluation of the characteristic function?

Is it possibel to add a few other jump distributions, e.g. mixture exponential distributions (those can give you more flexibility in modelling the jump densitiy due to more paramters)?

Would it be possible to provide a slightly more detailled explanation of the four examples in the GUI (i.e. BlackScholes, Heston, SVJ, DefaultRisk)?

Thanks

Updates
06 May 2014

- Introduced the extended transform
- Added bond option pricing to the documentation

28 May 2014

- Added FFT capability to the Conditional Expectation function CF2GABY
- Updated the help files
- Changed the upper integration limits to 200.
- Added a readme

04 Jun 2014

Added Kou's model
Added Double exponential jump distribution
Further Debugging

06 Jun 2014

added the extended transform function and its inverse transform, allowing for pricing of Asian options. Updated the jump library. Updated the help files.

09 Jun 2014

updated readmes

13 Jun 2014

added American option for Lévy models;
added spread option pricing for any characteristic function;
various bug fixes;
updated help files

16 Jun 2014

added arbitray payoff function capability to cf2spread

09 Aug 2014

added a GUI

12 Aug 2014

changed description and file title

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