This study proposes an N-state Markov-switching general autoregressive conditionally heteroskedastic (MS-GARCH) option model and develops a new lattice algorithm to price derivatives under this framework. The MS-GARCH option model allows volatility dynamics switching between different GARCH processes with a hidden Markov chain, thus exhibiting high flexibility in capturing the dynamics of financial variables. To measure the pricing performance of the MS-GARCH lattice algorithm, we investigate the convergence of European option prices produced on the new lattice to their true values as conducted by the simulation. These results are very satisfactory. The empirical evidence also suggests that the MS-GARCH model performs well in fitting the data in-sample and one-week-ahead out-of-sample prediction.

Novel coumarin–iminophosphorane (IPP) fluorophores that have stable resonance contributions from aza-ylides were formed by using the nonhydrolysis Staudinger reaction. The NP formation reaction kinetics obey the conventional Staudinger reaction. The absorption and emission profiles of the coumarin–IPP derivatives can be fine-tuned: an electron-donating group at PPh3 enhances absorption and fluorescence, whereas an electron-withdrawing group at C-3 drives absorption and emission peaks toward blue-light wavelengths. Two-photon adsorption, accompanied by anti-Stokes fluorescence, is achieved under near-infrared femtosecond laser excitation.

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