Sequential Investments

  • 详情 Volatility of Early-Stage Firms with Jump Risk:Evidence and Theory
    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.