LOCALLY RISK-NEUTRAL VALUATION OF OPTIONS IN GARCH MODELS BASED ON VARIANCE-GAMMA PROCESS

Lie-Jane Kao ()
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Lie-Jane Kao: Department of Banking and Finance, Kainan University, No. 1, Kainan Road, Luzhu Shiang, Taoyuan 33857, Taiwan

International Journal of Theoretical and Applied Finance (IJTAF), 2012, vol. 15, issue 02, 1-21

Abstract: This study develops a GARCH-type model, i.e., the variance-gamma GARCH (VG GARCH) model, based on the two major strands of option pricing literature. The first strand of the literature uses the variance-gamma process, a time-changed Brownian motion, to model the underlying asset price process such that the possible skewness and excess kurtosis on the distributions of asset returns are considered. The second strand of the literature considers the propagation of the previously arrived news by including the feedback and leverage effects on price movement volatility in a GARCH framework. The proposed VG GARCH model is shown to obey a locally risk-neutral valuation relationship (LRNVR) under the sufficient conditions postulated by Duan (1995). This new model provides a unified framework for estimating the historical and risk-neutral distributions, and thus facilitates option pricing calibration using historical underlying asset prices. An empirical study is performed comparing the proposed VG GARCH model with four competing pricing models: benchmark Black–Scholes, ad hoc Black–Scholes, normal NGARCH, and stochastic volatility VG. The performance of the VG GARCH model versus these four competing models is then demonstrated.

Keywords: Variance-gamma process; feedback effect; leverage effect; locally risk-neutral valuation relationship (LRNVR); Black–Scholes model; ad hoc Black–Scholes model; normal NGARCH model; stochastic volatility VG model (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S021902491250015X

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