Abstract
Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.
Highlights
The Heston Model Heston (1993) is one of the most widely used stochastic volatility models
In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation
It is well known that the OU process is a mean-reverting process, i.e., whilst we initialize the stochastic correlation process so that it can rapidly reach its mean value μρ, the option price computed in the extended Heston model should be the same as the original Heston price with the constant correlation ρ = μρ
Summary
The Heston Model Heston (1993) is one of the most widely used stochastic volatility models. A couple of papers on the numerically stable and efficient computation of European-style option prices were published, e.g., (Andersen 2008; Carr and Madan 1999; Kahl and Jäckel 2005; Lee 2004; Lewis 2001; Lipton 2002). It has been pointed out, in many works (see, e.g., (Christoffersen et al 2009; Grzelak and Oosterlee 2011)) that the Heston model is unable to provide enough skew in the implied volatility as market required, especially for a short maturity.
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