Premia is a software designed for option pricing, hedging and financial model calibration. It is provided with it's C/C++ source code and an extensive scientific documentation.
Efficient computations of prices and hedges for derivative products are major issues for financial institutions. The development of increasingly complex financial products requires the use of advanced stochastic and numerical analysis techniques. A consortium of banks have been using Premia since it's beginning in 1999 and have brought important contributions to the project.
Premia is developed by the MathRisk team which gathers research scientists from INRIA (the French national institute for research in computer science and control), Ecole des Ponts ParisTech (CERMICS laboratory on applied mathematics and computing), and the Gustave Eiffel University.
Major features of Premia :
The Mathfi team keeps track of the most recent advances in the field of computational finance. It focuses on numerical analysis techniques for both probabilistic and deterministic methods.
An important feature of Premia is its detailed documentation which provides extended references in option pricing.
Also Premia's C/C++ sources are often integrated in the consortium's own financial softwares.
The aim of the Premia project is to :
Premia contains various numerical algorithms (Finite-differences, trees and Monte-Carlo) for pricing vanilla and exotic options on equity, interest rate, credit and energy derivatives.
Black-Scholes model (up to dimension 10), stochastic volatility models (Hull-White, Heston, Fouque-Papanicolaou-Sircar), models with jumps (Merton, Kou, Tempered stable processes, Variance gamma, Normal inverse Gaussian), Bates model.
For high dimensional American options, Premia provides the most recent Monte-Carlo algorithms: Andersen-Broadie, Longstaff-Schwartz, Barraquand-Martineau, Tsitsklis-Van Roy, Broadie-Glassermann, quantization methods Malliavin calculus based methods.
Dynamic Hedging for Black-Scholes and jump models is available.
Calibration algorithms for some models with jumps, local volatility and stochastic volatility are implemented.
HJM and Libor Market Models (LMM): affine models, Hull-White, CIR++, Black-Karasinsky, Squared-Gaussian, Li-Ritchken-Sankarasubramanian, Bhar-Chiarella, Jump diffusion LMM, Markov functional LMM, LMM with stochastic volatility.
Premia provides a calibration toolbox for Libor Market model using a database of swaptions and caps implied volatilities.
Reduced form models and copula models are considered.
Premia provides a toolbox for pricing CDOs using the most recent algorithms (Hull-White, Laurent-Gregory, El Karoui-Jiao, Yang-Zhang)
PDE solver for pricing derivatives on hybrid products like options on inflation and interest or change rates is implemented.
Mean reverting and jump models are considered.
Premia
provides a toolbox for pricing swing options using finite
differences, Monte-Carlo Malliavin-based approach and quantization
algorithms.
Premia is developed in interaction with a consortium of financial institutions presently composed of Crédit Agricole Corporate and Investment Bank, Natixis.
The participants of the consortium finance the development of Premia (by contributing to the salaries of expert engineers hired by the MathRisk project every year to develop the software) and help to determine the directions in which the project evolves.
Financial institutions interested in joining the consortium may contact premia@inria.fr.
Every year, during a "delivery meeting", a new version of Premia is presented to the consortium by the members of the MathRisk project working on the software. This presentation is followed by a discussion on the features to be incorporated in the next release.
In addition, between delivery meetings, MathRisk project members meet individual consortium participants to further clarify their needs and interests.
After the release of each new version of Premia, two year older versions become available on this web site and can be freely downloaded for academic purposes.
The consortium is composed of the following financial institutions :
For any questions about technical aspects of the Premia Software package please contact: premia@inria.fr
For any questions about a presentation of
please contact:
INRIA
Centre de recherche Inria de Paris
2 rue Simone Iff
CS 42112 - 75589 Paris Cedex 12 - France
e-mail: agnes.sulem@inria.fr
Tel: (33) 01 39 63 55 69
CERMICS / Ecole des Ponts
6 et 8 avenue Blaise Pascal
Cité Descartes
77455 Champs-sur-Marne
Marne -la-Vallée cedex 2
email: aurelien.alfonsi@enpc.fr
Tel : (33) 01 64 15 35 29
Research project done with Ecole des Ponts ParisTech (Cermics) and the Gustave Eiffel University bilocalized in Paris and Marne la Vallée - France
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reserved.