Some of the shortcomings experienced with the Black-Scholes model were strike-price bias and return skewness. Consequently, the development of the Heston model came in as the best alternative tool for the purposes of advanced investments (Gilli, Maringer & Schumann 2011, p.257).
As any other stochastic volatility model, the Heston model utilizes statistical methods when making calculations or forecasts of the various pricing options in consideration. As such, it also bases on the assumption that the underlying security or trading option has an arbitrary volatility. Therefore, the Heston model falls among the various different models of stochastic volatility such as the GARCH model, the Chen model, as well as the SABR model. Consequently, the Heston Model also falls under the standard smile model category, with “smile” in this concept referring to the volatility smile. A volatility smile is a graphical representation of various options that have identical expiration date expressing an increasing volatility. This increase in volatility arises often arises when the options become more out of the money or in the money. The concave shape generated by the graph is what gives rise to the name, the smiles model, as it appears like a smile (Wang 2007, p.3).
The Heston Model applies mathematical calculations in describing the process of evolution in volatility that an underlying asset undergoes under the stochastic volatility options. As such, just as other statistical models mentioned above, the Heston Model equally has a number of assumptions, such as the volatility of an asset not being constant, or deterministic, but rather following a random process. Some the of the basic assumptions of the Heston Model is that the stochastic process determines the asset price, St
In addition, forms part of the Wiener Process as experienced under the GBM (Geometric Brownian Motion) also considered ...