Calibrating Heston to Variance Swaps - a bad idea?

An interesting idea to calibrate the Heston model in a more stable manner and reduce the calibration time is to make use of variance swap prices. Indeed, there is a simple formula for the theoretical price of a variance swap in the Heston model.&#xA; &#xA; &#xA;&#xA;It is not perfect since it approximates the variance swap price by the expectation of the integrated variance process over time. In…