This study adopts the Markov-switching ARCH (hereafter SWARCH) model to examine the volatility nature and volatility linkages of four segmented Chinese stock indices (SHA, SZA, SHB, and SZB). Our empirical findings are consistent with the following notions. First, we find strong evidence of regime shift in the volatility of four segmented markets and SWARCH model appears to outperform standard GARCH family models. Second, although there are some common features of volatility switch in segmented markets, there exist a few difference: (i)compared with the A-share markets, B-share markets are more volatile and shift more frequently between high- and low-volatility states; (ii) B-share markets have longer stays at high volatility state than the A-share markets; (iii) the relative magnitude of the high volatility compared with that of the low volatility is much greater than the case in two A-share markets. Third, B-share markets are found to be more sensitive to international shocks, while the A-share markets seem immune to international spillovers of volatility. Finally, analyses of volatility spillover effect among the four stock markets indicate that the A-share markets play a dominant role in volatility in Chinese stock markets.

Early-stage ?rms usually have a single large Research and Development (R&D) project that requires multi-stage investment. Firms? volatility can dramatically change due to the evolvement of R&D e¤orts and stage clearing. First, the success (failure) of R&D e¤orts within each stage (jump risk) decreases (increases) the un- certainty (i.e. volatility) level of the ?rms?future returns ?"jump e¤ect". Second, at the end of each stage, ?rms decide whether to continue next stage investment upon re-evaluating the project prospect conditional on the resolution of technical uncertainty and other information; as ?rms survive each investment stage and are becoming mature, the uncertainty level of their future returns should eventually decrease in later investment stages that lead to maturity ?"stage-clearing e¤ect". Ignoring these e¤ects results in incorrect estimation of ?rms?future volatility, an important element for early-stage ?rm valuation. In this paper, I develop a gener- alized Markov-Switching EARCH methodology for early-stage ?rms with discrete stage-clearing and jumps. My methodology can identify structural changes in the idiosyncratic volatility and also explore the relation between price changes and future volatility. Using a hand-collected dataset of early-stage biotech ?rms, I con?rmed the existence of the "stage-clearing e¤ect" and the "jump e¤ect". In the second part of my paper, I model early-stage ?rms as sequences of nested call options with jumps that lead to mature ?rms. "Jump e¤ect" arises because the early-stage ?rms are modeled as compound call options with jumps on the underly- ing cash ?ows, the volatility of the early-stage ?rms at each stage is determined by the compound call option elasticity to the underlying cash ?ows. If the downside (upside) jump happens, the value of the underlying cash ?ows decreases (increases), which makes the compound call option elasticity go up (down). As a result, the compound call option becomes riskier (less risky). "Stage-clearing e¤ect" arises because as ?rms exercise their option to continue investment, the new options that ?rms enter into will eventually become a less risky option.