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
- 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
- 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
- Credit derivatives: CDS, CDO
- Reduced form models and copula models are
- Premia provides a toolbox for pricing CDOs
using the most recent algorithms (Hull-White, Laurent-Gregory, El
- Hybrid products
- PDE solver for pricing derivatives on hybrid
products like options on inflation and interest or change rates is
- 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