A Model for Drawdown Insurance

Tim Leung, Ph.D.
3 min readAug 28

Many individual and institutional investors are wary of large market drawdowns as they not only lead to portfolio losses and liquidity shocks but also indicate potential imminent recessions.

As is well known, fund managers are typically compensated based on the fund’s outperformance over the last record maximum, or the high-water mark. As such, drawdown events can directly affect the manager’s income.

Also, a major drawdown may also trigger a surge in fund redemption by investors, and lead to the manager’s job termination. Hence, fund managers have a strong incentive to seek insurance against drawdowns.

These market phenomena have motivated the application of drawdowns as path-dependent risk measures.

On the other hand, existing market-traded contracts, such as vanilla and even lookback puts, are ineffective for insuring market drawdowns. These observations suggest that drawdown protection can be useful for both institutional and individual investors, and there is an interest in synthesizing drawdown insurance.

We consider an insurance contract based on a drawdown event. Specifically, the protection buyer who seeks insurance on a drawdown event of size k will pay a constant premium payment p continuously over time until the drawdown time τ. In return, the protection buyer will receive the insured amount α at time τ.

The fair premium as a function of maturity in a hypothetical drawdown insurance contract.
The fair premium as a function of volatility in a hypothetical drawdown insurance contract.

In this journal article, we have studied the practicality of insuring against market crashes and proposed a number of tractable ways to value drawdown protection.

Under the geometric Brownian motion dynamics, we have derived the formulas for the fair premium for a number of insurance contracts and examined its behavior with respect to key model parameters (see figures above).

We’ve also introduced a cancellable drawdown insurance contract, whereby the protection buyer would monitor the drawdown process and optimally stop the premium payment as the…

Tim Leung, Ph.D.

Boeing Endowed Chair Professor of Applied Math, Director of the Computational Finance & Risk Management (CFRM) Program at University of Washington in Seattle

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