Abstract: In this study, we propose a pattern matching procedure to seize similar price movements of two stocks. First, the algorithm of searching the longest common subsequence is introduced to sieve out the time periods in which the two stocks have the same integrated volatility levels and price rise/drop trends. Next we transform the price data in the found matching time periods to the Bollinger Percent b data. The low frequency power spectra of the transformed data are used to extract trends. Pearson’s chi square test is used to assess similarity of the price movement patterns in the matching periods. Simulation results show the proposed procedure can effectively detect the co-movement periods of two price sequences. Finally, we apply the proposed procedure to empirical high frequency transaction data of NYSE.
Abstract: An empirical study is employed to investigate the performance of implied GARCH models in option pricing. The implied GARCH models are established by either the Esscher transform or the extended Girsanov principle. The empirical P-martingale simulation is adopted to compute the options efficiently. The empirical results show that: (i) the implied GARCH models obtain accurate standard option prices even the innova tions are conveniently assumed to be normal distributed; (ii) the Esscher transform describes the data better than the extended Girsanov principle; (iii) significant model risk arises when using implied GARCH model with non-proper innovations in exotic option pricing.