‘Hot-start’ initialisation of the Heston model

Multi-factor models usually have hidden variables – for example, stochastic volatility – with unknown spot values. This suggests the initial value of such variables is actually random, with a distribution generated through stochastic evolution before formal modelling starts. Serguei Mechkov applies this approach to the Heston model and demonstrates its significant effect on the implied volatility smile

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A logical way of making a model more closely fit observed behaviour is to augment its dimensions by adding a hidden process that somehow affects the evolution of the principal observable value. The complete model specification then acquires the parameters of the hidden process and its possible correlation with the principal process. This also requires a description of how the hidden process starts, which is the main subject of this paper.

The very fact the