New Software and Platforms
Antonino Zanette, Mathrisk Research Team, Agnès Sulem [correspondant] .
Premia: general description
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.
The Premia project keeps track of the most recent advances in the field of
computational finance in a well-documented way. It focuses on the
implementation of numerical analysis techniques for both probabilistic
and deterministic numerical methods. An important feature of the
platform Premia is the detailed documentation which provides extended
references in option pricing.
Premia is thus a powerful tool to assist Research & Development professional teams in their day-to-day duty. It is also a useful support for academics who wish to perform tests on new algorithms or pricing methods without starting from scratch.
Besides being a single entry point for accessible overviews and basic implementations of various numerical methods, the aim of the Premia project is:
to be a powerful testing platform for comparing different numerical methods between each other;
to build a link between professional financial teams and academic researchers;
to provide a useful teaching support for Master and PhD students
in mathematical finance.
License: Licence Propriétaire (genuine license for the Consortium Premia)
Type of human computer interaction: Console, interface in Nsp, Web interface
OS/Middelware: Linux, Mac OS X, Windows
APP: The development of Premia started in 1999 and 15 are released up to now and registered at the APP agency.
Premia 15 has been registered on 18/03/2013 and has the number IDDN.FR.001.190010.012.S.C.2001.000.31000
Programming language: C/C++ librairie Gtk
Documentation: the PNL library is interfaced via doxygen
Size of the software: 280580 lines for the Src part only, that is 11 Mbyte of code, 130400
lines for PNL, 105 Mbyte of PDF files of documentation.
Nsp for Windows/Linux/Mac, Excel, binding Python, and a Web interface.
Publications:  ,  ,  ,  ,  ,  ,  .
Content of Premia
Premia contains various numerical algorithms (Finite-differences, trees and Monte-Carlo) for
pricing vanilla and exotic options on equities, interest rate, credit and energy derivatives.
The following models are considered:
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: Longstaff-Schwartz, Barraquand-Martineau, Tsitsklis-Van Roy, Broadie-Glassermann, quantization methods and 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.
Interest rate derivatives
The following models are considered:
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.
Credit derivatives: Credit default swaps (CDS), Collateralized debt obligations (CDO)
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,
A PDE solver for pricing derivatives on hybrid products like options on inflation and interest or change rates is implemented.
Energy derivatives: swing options
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 has managed to grow up over a period of fifteen years; this
has been possible only because contributing an algorithm to Premia is subject
to strict rules, which have become too stringent. To facilitate contributions,
a standardized numerical library (PNL) has been developed by J. Lelong under the LGPL since
2009, which offers a wide variety of high level numerical methods for dealing
with linear algebra, numerical integration, optimization, random number
generators, Fourier and Laplace transforms, and much more. Everyone who
wishes to contribute is encouraged to base its code on PNL and providing such a
unified numerical library has considerably eased the development of new
algorithms which have become over the releases more and more sophisticated. An
effort is made to continue and stabilize the development of PNL.
J. Ph Chancelier, B. Lapeyre and J. Lelong are using Premia and Nsp for Constructing a Risk Management Benchmark for Testing Parallel Architecture
Development of the PNL in 2014 (J. Lelong) -
Release 1.70. and 1.7.1 of the PNL library (http://pnl.gforge.inria.fr/ ).
Sampling from new distributions: non central Chi squared, Poisson,
When using quasi Monte Carlo sequences, sampling from any
distribution resorts to using the inverse of the cumulative distribution
A CMake module is provided to automatically detect the library when
used by third party codes.
Add a sparse matrix object with advanced functionalities provided
by Blas & Lapack. This new object is handled by the MPI binding.
Complete refactoring of the Basis object to considerably speedup the
evaluation functions. Multivariate polynomials are represented as tensor
products of one variate polynomials. The matrix holding the tensor
product now uses a sparse storage which avoids many operations leading to a
zero value thus leading to an impressive reduction the computational
All random number generators are thread–safe.
Algorithms implemented in Premia in 2014
Premia 16 has been delivered to the Consortium Premia in March 2014.
In this release we have developed the Haar Wavelets-based approach for quantifying
credit portfolio losses, Monte Carlo simulations of Credit Value Adjustment (CVA) using Malliavin
techniques, asymptotic and exact pricing options on variance and
importance sampling, and multilevel methods for jump models.
It contains the following new algorithms:
Commodities, Forex (FX), Insurance, Credit Risk
Pricing and hedging gap risk. P. Tankov.
Journal of Computational Finance. Volume 13 Number 3, Spring 2010.
An Optimal Stochastic Control Framework for Determining the Cost of Hedging of Variable Annuities. P. A. Forsyth K.Vetzal
Haar Wavelets-Based Approach for Quantifying Credit Portfolio
J. J. Masdemont, L. O. Gracia. Quantitative Finance, to appear
Cutting CVA’s complexity. P. Henry-Labordère. Risk Magazine 04 Jul 2012
Towards a coherent Monte Carlo simulation of CVA. L. Abbas Turki,
A.Bouselmi, M.Mikou, hal-00873200
Stochastic local intensity loss models with interacting particle
A. Alfonsi, C. Labart, J. Lelong Mathematical Finance,
Repricing the Cross Smile: An Analytic Joint Density. P. Austing.
On the Fourier cosine series expansion (COS) method for
stochastic control problems. R.F.T. Aalber, C.W. Oosterlee and
A multifactor volatility Heston model. J.Da Fonseca
M. Grasselli C. Tebaldi.
Quant. Finance 8 (2008), no. 6,
General approximation schemes for option prices in
stochastic volatility models. K.Larsson, Quantitative Finance
Volume 12, Issue 6, 2012
A robust tree method for pricing American options with the Cox-Ingersoll-Ross
interest rate model.
E. Appolloni, L. Caramellino and A. Zanette
IMA Journal of Management Mathematics 2014, to appear.
A hybrid tree-finite difference approach for the Heston and
Bates model model. M. Briani, L. Caramellino and A. Zanette Preprint
A Closed-Form Exact Solution for Pricing Variance Swaps with
Stochastic Volatility. S. Zhu and G. Lian, Mathematical Finance, Volume 21, Issue 2, April 2011
Asymptotic and exact pricing options on variance. M.Keller-Ressel
Finance & Stochastics, Volume 17 (2013), issue 1
Importance sampling and Statistical Romberg Method for jump
M.B. Alaya, A. Kebaier and K. Hajji
Smart expansion and fast calibration for jump diffusions
E. Benhamou, E. Gobet and M. Miri, Finance Stochastics
Volume 13, Number 4, September, 2009
Scaling and multiscaling in financial series: a simple
Andreoli, A., Caravenna, F, Dai Pra, P. Posta, G., Advances in Applied Probability. (2012), 44(4), 1018-1051.
Smooth convergence in the binomial model.
L.B. Chang, K. Palmer.Finance Stochastics Volume 11, Number 1,2007.