Frequency of Drawdowns in a Brownian Motion Model

While sustaining downside risk can be appropriately characterized using the drawdown process and its first passage time, economic turmoil and volatile market fluctuations are better described by quantities containing more path-wise information, such as the frequency of drawdowns. In Chapter 4, we directly address the problem on the frequency of drawdowns by determining the probability distributions of two sequences of drawdown first passage times, depending on whether the maximum is revisited between these first passage times. These stopping times characterize the fluctuations of the underlying through consecutive drawdowns. We illustrate how our analytical formulas can be used for evaluating options written on the number of drawdowns in a given time-horizon.