Homepage Inria website

Section: New Software and Platforms


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.

  • Equity 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, Schönbucher)

  • Hybrid products

    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.