Seasonal volatility models with applications in option pricing

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Date
2011-03
Authors
Doshi, Ankit
Journal Title
Journal ISSN
Volume Title
Publisher
Gowas Publishing House
Abstract
GARCH models have been widely used in finance to model volatility ever since the introduction of the ARCH model and its extension to the generalized ARCH (GARCH) model. Lately, there has been growing interest in modelling seasonal volatility, most recently with the introduction of the multiplicative seasonal GARCH models. As an application of the multiplicative seasonal GARCH model with real data, call prices from the major stock market index of India are calculated using estimated parameter values. It is shown that a multiplicative seasonal GARCH option pricing model outperforms the Black-Scholes formula and a GARCH(1,1) option pricing formula. A parametric bootstrap procedure is also employed to obtain an interval approximation of the call price. Narrower confidence intervals are obtained using the multiplicative seasonal GARCH model than the intervals provided by the GARCH(1,1) model for data that exhibits multiplicative seasonal GARCH volatility.
Description
Keywords
Option pricing, Seasonality, Volatility, GARCH, Kurtosis, Bootstrap, Brownian motion, Black-Scholes
Citation
Doshi, A., Frank, J. and Thavaneswaran, A. (2011). Seasonal volatility models. Journal of Statistical Theory and Applications, 10, 1-10.