Dynamics of Bankrupt Stocks

In this thesis, we study the behavior of bankrupt stocks. Bankrupt stock is a special case of the Hard-to-Borrow stocks. Besides the general nice feature of the Hard-to-borrow feedback for the buy-in demand, the bankrupt stocks could exclude the diffusive effects. This nice property would modify the Marco Avellaneda and Mike Lipkin’s jump-diffusion model for the Hard-to-Borrow stocks into the pure jump systems with stochastic intensity. Under this main assumption, our model is a two-dimensional integrate-and-fire model which is recursively tractable. By investigating the dynamics of the model, we could capture the self-reinforcing aspect of the buy-ins and subsequent crashes of the stock price. Having the recursively explicit dynamics of the stock prices and buy-in rate on hand, we can calibrate the model under the physical measure by error minimization. One way to justify the fit of the calibration results is to compare the sample path and the real prices. On the other hand, we match the option pricing theory against observed behavior of the options to see how the periodic buy-ins would act to cover the the cost of the short position, which gives the mechanism of the essential feedback of the Hard-to-Borrowness.