Abstract
Recently there has been a surge of interest in higher order moment properties of time varying volatility models. Various GARCH-type models have been developed and successfully applied in empirical finance. Moment properties are important because the existence of moments permit verification of how well theoretical models match stylized facts such as fat tails in most financial data. In this paper, we consider various types of random coefficient autoregressive (RCA) models with quadratic generalized autoregressive conditional heteroscedasticity (GARCH) errors and study the moments, mean, variance and kurtosis. We also consider the Black-Scholes model with RCA GARCH volatility and show that these moments can be used to evaluate the call price for European options.
Highlights
It is well-known that many financial time series such as stock returns exhibit leptokurtosis and time-varying volatility [1]
Studies using generalized autoregressive conditional heteroscedasticity (GARCH) models commonly assume that the time series is conditionally normally distributed; the kurtosis implied by the normal GARCH tends to be lower than the sample kurtosis observed in many time series Bollerslev [1]
Thavaneswaran et al [3], Appadoo et al [4] have extended the results to stationary random coefficient autoregressive (RCA) processes with GARCH errors and Paseka et al [5] further extended the results to RCA processes with stochastic volatility (SV) errors
Summary
It is well-known that many financial time series such as stock returns exhibit leptokurtosis and time-varying volatility [1]. Thavaneswaran et al [3], Appadoo et al [4] have extended the results to stationary RCA processes with GARCH errors and Paseka et al [5] further extended the results to RCA processes with stochastic volatility (SV) errors. We introduce various classes of RCA GARCH models and study the moments and discuss applications in option pricing. The moments derived for the RCA GARCH volatility models provide more accurate estimates of market data behaviour and help investors, decision makers, and other market participants develop improved trading strategies. The assumption sensure that the i 1 ut s are uncorrelated with zero mean and finite variance and that the 2 t process is weakly stationary In this case, the autocorrelation function of 2 t will be exactly the same as that for astationary ARMA(R,Q) model. The kurtosis ofthe GARCHprocess is denoted by K when it exists
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