HullWhite & Heston Market Model (July, 2014)
Article Summary:
AXIS has the HullWhite & Heston market model. It can be used to generate realworld and riskneutral stochastic scenarios for Monte Carlo simulation. It can be used to price equity index option using closed form approximation. This market model can be calibrated. The user can do sensitivity testing on the parameters to see the calibration quality.
In the integrated HullWhite & Heston market model, the interest rate is modeled using the HullWhite model while the equity follows the Heston model. In a riskneutral setup, the equity drift equals the interest rate generated by the HullWhite model. In a realworld setup, the user can specify the equity drift.
The Heston model is similar to the Lognormal model, except that the volatility of the equity is stochastic and generated by a separate random Cox Ingersoll Ross process.
The HullWhite model is a model of future interest rates (implemented in AXIS already as a part of the combined HullWhite and Lognormal model). It belongs to the class of noarbitrage models that are able to fit today’s term structure of interest rates.
The integrated HullWhite & Heston market model can currently generate one interest rate curve and up to 15 equities. The user can specify all the parameters for both models as well as correlations between risk drivers for interest rate, equities, and equity variances.
Currently, the HullWhite & Heston market model is under Beta feature code 377. The following features are available for the HullWhite & Heston market model:
 Generate scenarios using “Buildandview”.
 Do Monte Carlo simulation using the HullWhite & Heston model to price equity index options.
 Price equity index options using closed form approximation. This feature is under Beta feature code 431.
 Calibrate the market model interactively. The HullWhite interest rate model is calibrated separately from the calibration of the Heston model for each equity.
 Do sensitivity testing interactively. The sensitivity testing is done separately for HullWhite interest rate model and the Heston model for each equity.
