Models and Methods

Equities

All equity models support discrete and continuous dividends, with a term structure in the latter case, and quanto adjustments.

• Black Scholes

  - Support of both constant and deterministic volatility term-structure.
  - Monte Carlo multiple-asset or PDE single/dual-asset model implementation.

• Local volatility

  - Calibration to European call and put quotes using an implied volatility surface fitting.
  - Several forms of implied volatility surface (e.g., Gatheral, polynomial).
  - Monte Carlo multiple-asset or PDE single/dual-asset model implementation.

• Heston (stochastic volatility)

  - Calibration to European call and put quotes using semi-closed formula and numerical integration.
  - Advanced time discretisation scheme (quadratic exponential).
  - Monte Carlo multiple-asset or PDE single asset model implementation.

Interest rates

All interest-rate models are delivered with calibration routines for cap/floor and swaption quotes.

• Hull-White 1 factor

  - Monte-Carlo or PDE model implementation.
  - Exact large steps simulation using the forward-neutral probability.
  - Support of constant, second-degree and step volatility term structure.

• Hull-White 2 factors (G2++)

  - Monte-Carlo or PDE model implementation.
  - Exact large steps simulation using the forward-neutral probability.

• Cheyette (quasi-Gaussian model)

  - Monte-Carlo implementation using QE scheme.
  - Linear local volatility and linear local volatility with CIR stochastic volatility parametrisations.
  - Time-dependent parameters.
  - Captures most shapes of volatility smiles.
  - Optimised calibration: calibrating first a proxy swap rate market model (SMM) on implied volatility, then bootstraping the Cheyette model parameters to fit SMM parameters.

• Lognormal forward-LIBOR model (LFM)

  - Monte Carlo model implementation.
  - Large steps simulation (using Runge-Kutta discretisation).
  - Functional volatility and correlation structures.
  - Dimension reduction using principal component analysis.

Foreign exchange

• Garman-Kohlhagen

• Hull-White 1 factor + Garman-Kohlhagen

  - Interest rates are modelled with a Hull-White 1-factor model.
  - Monte Carlo large steps model implementation.

Commodities

• Schwartz 1 factor

  - Monte-Carlo model implementation.

• Schwartz 2 factors

  - Monte-Carlo model implementation.

• Gabillon

  - Monte-Carlo model implementation.

Inflation

• Jarrow-Yildirim

  - Monte-Carlo large steps model implementation.

Credit

• Deterministic intensity

  - Deterministic.
  - Single risk.

• Intensity with copula

  - Multiple correlated risk factors.
  - Monte Carlo model implementation.

Hybrids

• Hybrid equity / interest rate / exchange rate

  - Equities are modelled with a Black-Scholes model (with a term structure of volatility).
  - Interest rates are modelled with a Hull-White 1-factor model.
  - Exchange rates are modelled with a Garman-Kohlhagen model.
  - Monte-Carlo large steps model implementation.
  

• Hybrid equity / interest rate / inflation index

  - Equities are modelled with a Black-Scholes model (with a term structure of volatility).
  - Interest rates are modelled with a Hull-White 1-factor model.
  - Inflation indices are modelled with a Jarrow-Yildirim model.
  - Monte-Carlo large steps model implementation.