In this research paper, Dr. Serguei Mechkov examines the Heston model in the limit of infinitely fast mean-reversion for the stochastic volatility process (CIR). The paper shows 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 at all horizons.
Author: Serguei Mechkov, Senior VP Quantitative Research, Quantitative Research and Development, Numerix
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