Abstract
A whole host of researchers have modeled volatility as a non-constant stochastic process, based on the principle that volatility follows a stochastic process whose parameters are not directly observable in the market. The objective of this research paper is to empirically investigate the forecasting performance of three most dominant models of this species namely, Hull-White (1988), Heston�s (1993), and Heston-Nandi GARCH (2000) option pricing model. These three models have been collaterally compared and contrasted against Black-Scholes and market for pricing S&P CNX Nifty 50 index option of India.
The Hull-White model not only warrants a range of stochastic volatility specifications but also incorporates correlation of volatility of asset return and its price changes. The closed form Heston�s (1993) model explicitly and elaborately communicates non-lognormal distribution of the assets return, leverage effect, and mean-reverting property of volatility. The model of Heston-Nandi, also in closed form, successfully incorporates variance of asset returns as a range of GARCH process. It strongly permits correlation between returns of the spot asset and variance and also technically accepts multiple lags in the dynamics of the GARCH process.
To decide, determine, and delineate the effectiveness of stochastic models against the Black-Scholes and market, the current paper adopts a structured approach of relative error price, viz., percentage mean error (PME) and mean absolute percentage error (MAPE). The most turbulent period of the Indian economy � January 1, 2008 to December 31, 2008 — was considered appropriate for testiing the suggested model. It was a testing time for the Indian economy as well as a critical period questioning the sustainability of all financial products/models and challenging their fundamental platform depicted as equity market. How to safeguard investors� faith and at least protect their investments if not multiply returns in the face of such financial hardships remained a burning question for all thinkers and experts on the subject. Data pertaining to the specific period of such drastic disturbance was analysed with the help of the proposed models. After rigorous churning of specific data taken across various models, the Heston model was found to outperform and surpass other models.