Based on the findings in this paper, portfolio managers, traders and other financial professionals and others interested in calculating options prices can use this new non-affine stochastic volatility model to price options relatively easily in a more realistic context.
Option pricing is affected by volatility, a phenomenon for which many researchers have developed models to understand. However, because these models are exogenous (they rely on dynamics specified by the researcher), they do not always fully explain the root cause of asset price volatility. A new model has been developed that, its authors say, pinpoints a possible cause: the volatility of the underlying asset is caused by a fraction of irrational traders in the market.
Most stochastic volatility models (in which volatility fluctuates randomly over time, rather than remaining constant as in the classical Black-Scholes framework) are affine, a concept of linearity. Although this is a rather technical issue, an affine structure is chosen in order to facilitate option pricing. However, imposing this restriction may cause a model to be less realistic.
Walter Farkas, Ciprian Necula, and Boris Waelchli of the University of Zurich developed a stochastic volatility model that has a more realistic, non-affine structure. In this model, volatility is amplified by the irrational behavior of traders while also making it relatively easy to price options.
To create the model, the authors used S&P 500 index options data from OptionMetrics that spanned January 1996 to August 2013. ?Testing this kind of model requires reliable, historical data on option prices,? explained Ciprian Necula. ??OptionMetrics has long been used as a data source in academic research on option pricing, which is why we used it.?
In their paper, ?Herding and Stochastic Volatility,? the authors start with a simple trading model in which volatility caused by the fraction of irrational traders emerges. Since there is only one variable (the fraction of irrational traders) that influences the dynamics, this type of model is referred to as a one-factor model.
Subsequently, the authors come up with a controllable method of pricing options using an expansion-based pricing methodology. Finally, they calibrate the model for a long period of time (1996 ? 2013) and compare its performance to that of affine models.
The authors found that their non-affine one-factor stochastic volatility option pricing model produced better results than an affine one-factor model, and similar results to an affine two-factor model. In general, adding more factors to a model makes it more flexible and more likely to fit the market data. Encouraged by the results of the one-factor model, the authors are now investigating how to incorporate more factors into their non-affine framework while trying to keep the pricing of options controllable.
Based on the findings in this paper, portfolio managers, traders and other financial professionals and others interested in calculating options prices can use this new non-affine stochastic volatility model to price options relatively easily in a more realistic context.