Fast-Reversion Limit of the Heston Model

In this paper we examine the Heston model in the limit of infinitely fast mean-reversion for the stochastic volatility process (CIR). We show that, under an appropriate scaling of the model parameters, the two-factor stochastic volatility Heston model can be exactly mapped to a one-factor pure-jump model that is related to the normal inverse Gaussian (NIG) process. The "fast-reversion Heston" model thus obtained has only three parameters, which are directly connected to the key properties of the implied volatility surface. The model is expected to provide a reasonable fit to the market for all maturities