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In this study, we introduce an asymmetric Generalized Autoregressive Conditional Heteroscedastic (GARCH) model, Glosten, Jagannathan and Runkle-GARCH (GJR-GARCH), in Value-at-Risk (VaR) to examine whether or not GJR-GARCH is a good method to evaluate the market risk of financial holdings. Because of lacking the actual daily Profit and Loss (P&L) data, portfolios A and B, representing FuBon and Cathay financial holdings are simulated. We take 400 observations as sample group to do the backward test and use the rest of the observations to forecast the change of VaR. We find GJR-GARCH works very well in VaR forecasting. Nonetheless, it also performs very well under the symmetric GARCH-in-Mean (GARCH-M) model, suggesting no leverage effect exists. Further, a 5-day moving window is opened to update parameter estimates. Comparing the results under different models, we find that the model is more accurate by updating parameter estimates. It is a trade-off between violations and capital charges.

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Many researches indicate that the Black-Scholes (BS) option-pricing model demonstrates systematic biases due to some unreasonable assumptions. In practice, implied volatilities tend to differ across exercise prices and time to maturities. To solve the problem, Heston and Nandi (HN) (2000) develop closed-form Generalized Autoregressive Conditional Heteroscedasticity (HN-GARCH) model. In this study, we apply their model on Financial Time Stock Exchange (FTSE) 100 index option. As a benchmark, we employ the ad hoc BS model which uses a separate implied volatility for each option to fit the smirk/smile in implied volatilities. The test finds that the HN GARCH has smaller valuation errors than the ad hoc BS model.

This study explores dynamic conditional and unconditional causality relations between intraday return and order imbalance on extraordinary events. We examine intraday behaviour of NASDAQ speculative top gainers. In this study, we employ a regression model to examine intraday return-order imbalance behaviours. Moreover, we introduce a multiple-hypotheses testing method, namely a nested causality, to identify the dynamic relationship between intraday returns and order imbalances. We find order imbalance convey more information than trading volume does. While examining three intraday time regimes, we find the contemporaneous order imbalance-return effect is significant in the third sub-period, which implies that informed trading will take place in the afternoon. The size-stratified results show there is a negative relation between firm size and the order imbalance-return effect. The impact of the trading volume on the order imbalance-return effect is weaker than that of the firm size. Moreover, the volume-stratified results suggest that order imbalance be a better return predictor in small trading volume quartile and the order imbalance-based trading strategies are useful in the afternoon regime.