Overview of Premia's main features

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 :

  • (i) be a powerful testing platform for comparing different numerical methods
  • (ii) build a link between researchers from academic and financial institutions
  • (iii) provide useful teaching material to Master and PhD students in mathematical finance
  • (iv) be a single entry point for accessible overviews and basic implementations of various numerical methods

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.

Equity 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.
Interest rate derivatives

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: CDS, 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)
Hybrid products

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 ar considered.
Premia provides a toolbox for pricing swing options using finite differences, Monte-Carlo Malliavin-based approach and quantization algorithms.


 
 


Research project done with Ecole des Ponts ParisTech (Cermics) and the University of Marne la Vallée bilocalized in Rocquencourt and Marne la Vallée - France
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