Most traders are intimately familiar the implied volatilities of equity options. These implied volatilities are often smoothed to avoid the temporary spikes in the strike/maturity surface that can lead to butterfly and calendar arbitrage. Many trading desks and market makers use the Heston stochastic volatility model for smoothing.

To understand the genesis behind Heston model, and why it is so important, we must revisit an event that shook financial markets around the world: the stock market crash of October 1987. The consequence on the options market was an exacerbation of smiles and skews in the implied volatility surface which has persisted to this day. This brought into question the restrictive assumptions behind the Black-Scholes option pricing model, the most tenuous of which is that continuously compounded stock returns be normally distributed with constant volatility. A number of researchers since then have sought to eliminate the constant volatility assumption in their models, by allowing volatility to be time-varying.

One popular time-varying approach is to allow volatility to be stochastic. The Heston model, developed in 1993, was not the first stochastic volatility model for pricing equity options, but for mathematical and practical reasons it is by far the most popular and the most successful. It is used throughout the world by option trading desks and market makers, banks, hedge funds, and academics. It forms a crucial part of the options curriculum of financial engineering programs offered by universities across the world. The model has been refined and extended in many ways, to overcome some of the shortcomings of its original formulation. The top option valuation software companies, such as Numerix, SuperDerivatives, and Fincad, all incorporate the model into their pricing routines. My forthcoming book is devoted entirely to the model.

In short, the Heston model is one of the great success stories of mathematical finance, yet most financial professionals have never heard of it. The next time someone mentions the Heston model, you won't be wondering whether it refers to Charlton Heston, the late American actor, or Heston Blumenthal, the quirky British chef, but to Steve Heston, one of the most influential financial engineers of the modern era.

Fabrice Rouah is the author of the forthcoming book "The Heston Model in Matlab
and C#" from John Wiley & Sons.and a consultant on option pricing models.


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