Inria / Raweb 2004
Team: Mathfi

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Team : mathfi

Section: Software


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

Development of the software PREMIA for financial option computations

Participants: V. Bally, Adel Ben Haj Yedder, L. Caramellino, J. Da Fonseca, B. Jourdain, A. Kohatsu Higa, B. Lapeyre, M. Messaoud, N. Privault (University of La Rochelle, A. Sulem, E. Temam, A. Zanette.

We develop a software called PREMIA designed for pricing and hedging options on assets and interest rates and for calibration of financial models.

This software [74] contains the most recent algorithms published in the mathematical finance literature with their detailed description and comments of the numerical methods in this field. The target is to reach on the first hand the market makers who want to be informed on this field, and on the other hand the PHD students in finance or mathematical finance.

Premia is thus concentrated on derivatives with rigorous numerical treatment and didactic inclination.

Premia is developed in collaboration with a consortium of financial institutions or departments: It is presently composed of: IXIS CIB (Corporate & Investment Bank), CALYON, the Crédit Industriel et Commercial, EDF, GDF, Société générale and Summit.

History of PREMIA:

The development of Premia started in 1999. There exists now 6 releases.

Premia1, 2 and 4 contain finite difference algorithms, tree methods and Monte Carlo methods for pricing and hedging European and American options on stocks in the Black-Scholes model in one and two dimension.

Premia3 is dedicated to Monte Carlo methods for American options in large dimension. Moreover, it has an interface with the software Scilab [57].

Premia5 and 6 contain more sophisticated algorithms such as quantization methods for American options [2], [52] and methods based on Malliavin calculus both for European and American options [61][60]. Pricing and hedging algorithms for some models with jumps, local volatility and stochastic volatility are implemented. These versions contains also some calibration algorithms.

In 2004, the main development in the release Premia7 has consisted in implementing routines for pricing derivatives in interest rate models: (Vasicek, Hull-White, CIR, CIR++, Black-Karasinsky, Squared-Gaussian, Li, Ritchken, Sankarasubramanian HJM, Bhar Chiarella HJM, BGM). Moreover new algorithms for calibrating in various models (stochastic volatility, jumps, ..) have been implemented and numerical methods based on Malliavin calculus for jump processes have been further explored.

Premia1, 2, 3, 4, 5, 6 have been delivered to the members of the bank consortium in May 1999, December 1999, February 2001, February 2002, February 2003, February 2004 respectively. Premia7 will be delivered in February 2005.

The next release, Premia8, under development in 2005, will be dedicated to the pricing of credit risk derivatives and pricing and calibration for interest rate derivatives.

Premia3 and Premia4 can be downloaded from the web site:

http://www-rocq.inria.fr/mathfi/Premia/index.html.


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