A Parsimonious Multi-Asset Heston Model: Calibration and Derivative Pricing

Abstract

We present a parsimonious multi-asset Heston model. All single-asset sub-models follow the well-known Heston dynamics and their parameters are typically calibrated on implied market volatilities. We focus on the calibration of the correlation structure between the single-asset marginals in the absence of sufficient liquid cross-asset option price data. The presented model is parsimonious in the sense that d(d - 1)/2 asset-asset cross-correlations are required for a d-asset Heston model. In order to calibrate the model, we present two general setups corresponding to relevant practical situations: (1) when the empirical cross-asset correlations in the risk neutral world are given by the user and we need to calibrate the correlations between the driving Brownian motions or (2) when they have to be estimated from the historical time series. The theoretical background, including the ergodicity of the multidimensional CIR process, for the proposed estimators is also studied.