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Section: Software

Keywords : pricing, hedging, calibration, pricer, options.

Development of the software PREMIA for financial option computations

Participants : A. Alfonsi, V. Bally, J-Ph.. Chancelier, B. Jourdain, A. Kolotaev, A. Kohatsu Higa, J. Lelong, B. Lapeyre, V. Lemaire, N. Privault, A. Sulem, P. Tankov, X. Xei, A. Zanette.

The development of Premia software is a joint activity of INRIA and ENPC/CERMICS, undertaken within the MathFi project. Its main goal is to provide C/C++ routines and scientific documentation for the pricing of financial derivative products with a particular emphasis on the implementation of numerical analysis techniques. It is an attempt to keep track of the most recent advances in the field from a numerical point of view in a well-documented manner. The aim of the Premia project is threefold: first, to assist the R&D professional teams in their day-to-day duty, second, to help the academics who wish to perform tests of a new algorithm or pricing method without starting from scratch, and finally, to provide the graduate students in the field of numerical methods for finance with open-source examples of implementation of many of the algorithms found in the literature.

Consortium Premia.

Premia is developed in interaction with a consortium of financial institutions or departments presently composed of: CALYON, the Crédit Industriel et Commercial, EDF, Société générale, Natexis and IXIS CIB (Corporate & Investment Bank) now unified as Natixis. The participants of the consortium finance the development of Premia (by contributing to the salaries of expert engineers hired by the MathFi project every year to develop the software) and help to determine the directions in which the project evolves. Every year, during a ``delivery meeting'', a new version of Premia is presented to the consortium by the members of the MathFi project working on the software. This presentation is followed by the discussion of the features to be incorporated in the next release. In addition, between delivery meetings, MathFi project members meet individual consortium participants to further clarify their needs and interests. After the release of each new version of Premia, the old versions become available on Premia web site http://www.premia.fr and can be downloaded freely for academic and evaluation purposes. At present, this is the case for the first five releases.

Content of Premia.

The development of Premia started in 1999 and 9 are released up to now. Release 1,2 and 4 contain finite difference algorithms, tree methods and Monte Carlo methods for pricing and hedging European and American options in the Black-Scholes model in one and two dimensions.

Release 3 is dedicated to Monte Carlo methods for American options in high dimension (Longstaff-Schwartz, Barraquand-Martineau, Tsitsklis-Van Roy, Broadie-Glassermann) and is interfaced with the Scilab software.

Release 5 and 6 contain more sophisticated algorithms such as quantization methods for American options and methods based on Malliavin calculus for both European and American options. It also contains algorithms for pricing, hedging and calibration in some models with jumps, local volatility and stochastic volatility.

Release 7 implements routines for pricing vanilla interest rate derivatives in HJM and BGM interest rate models (Vasicek,Hull-White, CIR, CIR + + , Black-Karasinsky, Squared-Gaussian, Li-Ritchken-Sankarasubramanian, Bhar-Chiarella and the Libor Market Model). It also contains calibration algorithms for various models (including stochastic volatility and jumps) and numerical methods based on Malliavin calculus for jump processes.

Premia 8 is devoted mainly to Lévy models: Exponential Lévy models (Merton's model and more generally other finite intensity Lévy processes with Brownian component (Kou)), Tempered stable process, Variance gamma, Normal inverse Gaussian). Various numerical methods (Fourier transform, Finite difference methods)are implemented to price and hedge European options and barrier options on stocks in these models. An algorithm for non-parametric calibration of finite-intensity exponential Lévy models to prices of market-traded is also included. Option pricing methods for the following interest rate models were implemented: affine models, jump diffusion Libor Market Model and Markov functional Libor Market Model. Premia 8 also implements reduced-form models for pricing and hedging Credit Default Swap.

Premia 9, the last release of the software developed in 2006 will be presented to the consortium members in February 2007. It contains in particular a calibration toolbox for Libor Market model using a database of swaption and cap implied volatility provided by CDC-IXIS, a participant of Premia consortium.

N. Privault has supervised postdoctoral research engineer and interns at INRIA for the implementation of algorithms in calibration of LIBOR interest rate models, pricing of LIBOR derivatives using Lévy jump models, optimal exercise of Bermudan options. P. Tankov has developed new calibration and hedging modules for Premia. Afef Sellami has implemented an algorithm for the pricing of swing options with a quantization approach. Moreover Anton Kolotaev (expert engineer), P. Tankov, J. Lelong, J-Ph. Chancelier are working on the architecture and interface of Premia (Excel and NSP, the New Scilab project).

Detailed content of Premia Release 9 developped in 2006


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