Neglecting parameter changes in GARCH option pricing models and VAR

Abstract

In GARCH models, neglecting parameter changes in the conditional volatility process results in biased estimation. The estimated sum of the autoregressive parameters of the conditional volatility converges to one. In Chapter 2, I analyze the effect of changes in the parameters of conditional volatility on European call option prices when these parameters are estimated ignoring the change-points. Simulation studies show that ignoring parameter changes in the conditional variance process of GARCH(1,1) models leads to biased estimates of option prices. The bias, measured in percentages, is most pronounced for out-of-the-money options, substantial for at-the-money options, and vanishes as options move deep-in-the-money. The empirical study in Chapter 2 shows that the bias in option prices decreases when NGARCH model is used. NGARCH model captures the negative correlation between the stock price and volatility. To analyze this issue further, in Chapter 3, I analyze the effect of changes in the parameters of conditional volatility on European call option prices using Heston's and Nandi's (2000) closed-form GARCH option pricing model. Simulation studies show that option prices obtained by the closed-form expression are biased when parameter changes are ignored, but due to asymmetry effects the bias is less pronounced compared to the results in Chapter 2. In Chapter 4, I analyze the effect of parameter changes in the conditional volatility process on Value-at-Risk (VaR) based on a GARCH model. Ignoring parameter changes results in biased VaR estimates. The bias is more pronounced when parameter changes imply a greater change in unconditional volatility. In addition, the sign of the bias is negatively related to the sign of the change in unconditional volatility.