  This paper studies the stochastic modeling of market drawdown events and the
fair valuation of insurance contracts based on drawdowns. We model the asset
drawdown process as the current relative distance from the historical maximum
of the asset value. We first consider a vanilla insurance contract whereby the
protection buyer pays a constant premium over time to insure against a drawdown
of a pre-specified level. This leads to the analysis of the conditional Laplace
transform of the drawdown time, which will serve as the building block for
drawdown insurance with early cancellation or drawup contingency. For the
cancellable drawdown insurance, we derive the investor's optimal cancellation
timing in terms of a two-sided first passage time of the underlying drawdown
process. Our model can also be applied to insure against a drawdown by a
defaultable stock. We provide analytic formulas for the fair premium and
illustrate the impact of default risk.
