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Section: Software
PREMIA
Participants : Antonino Zanette, Mathrisk Research team, Agnès Sulem [correspondant] .
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. https://www-rocq.inria.fr/mathfi/Premia
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 (genuin license for the Consortium Premia)
Type of human computer interaction: Console, interface in Nsp, Web interface
APP: The development of Premia started in 1999 and 14 are released up to now and registered at the APP agency.
Size of the software: 11 Mbyte of code split into 275,000 lines. 93 Mbyte of PDF files of documentation
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.
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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.
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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.
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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, Schönbucher)
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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 design
Anton Kolotaev (ADT engineer), supervised by J. Lelong, has developed a web platform allowing online tests (https://quanto.inria.fr/premia/koPremia ). This online version allow us to supply benchmarks both for professional R&D teams and academics in mathematical finance. This will considerably increase the impact and the visibility of the software. Up to now, to use the opensource version of the software, one has to download from Premia's website and install it on its own computer and this had become a brake on using Premia. Providing an online version of Premia is an original way of keeping up with the new standards of software usability without focusing too much on a dedicated solution per operation system.
To enable easy an advanced usage of Premia without being an advanced C or C++ programmer, we have started to implement Python bindings. The choice of Python has been quite obvious as Python has become over the past few years a standard cross–platform interpreted language for numerical problems.
Premia has managed to grow up over a period of more than a dozen 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 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 will be made to continue and stabilize the development of PNL.
Algorithms implemented in Premia in 2012
Premia 14 was delivered to the consortium members in March 2012. It contains the following new algorithms:
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Forward Variance Dynamics: Bergomi's model revisited. S.M. Ould Aly
Volatility of Volatility Expansion for Bergomi's model. S.M. Ould Aly
Robust Approximations for Pricing Asian Options and Volatility Swaps Under Stochastic Volatility. M. Forde, A.Jacquier Applied Mathematical Finance, Volume 17 Issue 3 2010
Small-time asymptotics for implied volatility under the Heston model, M. Forde, A. Mijatovic, and Jaquier, A. International Journal of Theoretical and Applied Finance, Volume 12, issue 6, 2009
Asymptotic formulae for implied volatility under the Heston model. Forde, F, Jacquier, A, and Mijatovic, A. Proceedings of the Royal Society A, to appear.
A Mean-Reverting SDE on Correlation Matrices. A. Alfonsi, A.Ahdida
Fast and Accurate Long Stepping Simulation of the Heston Stochastic Volatility Model J.H. Chan, M S. Joshi, Preprint
High order discretization schemes for stochastic volatility models. B. Jourdain, M. Sbai. Quantitative Finance, to appear
A Fourier-based Valuation Method for Bermudan and Barrier Options under Heston Model. F.Fang, C. W. Oosterlee. SIAM J. Finan. Math. 2, 2011, 439-463.
Numerical methods and volatility models for valuing cliquet options.
H. Windcliff, P.A. Forsyth, K.R. Vetzal, Applied Mathematical Finance 13 2006.
Pricing Discretely Monitored Asian Options by Maturity Randomization. G.Fusai, D. Marazzina, M. Marena. SIAM Journal on Financial Mathematics, Vol. 2 2011
Wiener-Hopf techniques for Lookback options in Levy models. O. Kudryavtsev
Computing VaR and AVar in Infinitely Divisible Distributions. Y.S. Kim, S. Rachev, M.S. Bianchi, F.J. Fabozzi. Probability and Mathematical Statistics, Vol. 30, Fasc. 2 2010.
Analytical formulas for local volatility model with stochastic rates. E. Benhamou, E. Gobet, M. Miri 2009
Nonparametric Variance Reduction Methods on Malliavin Calculus. B. Lapeyre, A. Turki SIAM Journal on Financial Mathematics, to appear
Stochastic expansion for the pricing of call options with discrete dividends. P. Etore, E. Gobet. Applied Mathematical Finance, to appear
American options in high dimension solving EDSR with penalization C. Labart, J. Lelong
Static Hedging of Standard Options. P. Carr, L. Wu. Preprint.
The software Premia 14 has been deposited at the APP (Agence pour la Protection des Programmes) with the reference IDDN.FR.001.190010.011.S.C.2001.000.31000.