Electronic Thesis and Dissertation Repository

Thesis Format



Master of Science


Statistics and Actuarial Sciences


Li, Shu


Insurance and options have been often used by investors to protect themselves from market crashes and significant financial losses. Thanks to its desired features, drawdowns can be a very useful tool in the marketplace, allowing investors to protect against the downside risks which commonly occur in the marketplace. Several insurance products are proposed via including protection against drawdown sizes, speed of market crash and frequency of drawdowns. We also design a knock-in drawdown option with generalized payoffs. In this thesis, we explore the probabilistic approach to drawdowns and use the technique of Laplace transform to find the fair market price of the designed insurances/options. Their connections with the existing models are discussed, and numerical results are then demonstrated as well as the sensitivity tests.

Summary for Lay Audience

The financial market is a place where great gains and losses are created for investors every day. From the risk control’s point view, investors could prevent themselves from the suffering of large losses on the financial products through the purchase of the insurances and options. The insurance provides a guarantee of compensation for specified losses, and an option helps limit the size of loss via its payoff design and in the strategy of hedging. Drawdown is one of the performance measures commonly used in the financial market, which determines the declines in value of the asset over time. With the help of drawdown measure, we could answer the questions like, how much the asset price has been dropped from its previous maximum value, how many days it takes for such a drop, and how many such drops occur in a year. Based on the size, speed and frequency of drawdowns, we design an insurance that provides the protection on the series of drawdown events. And an cheaper option is also proposed, whose strike price depends on the historical maximum given a drawdown event happens. The insurance and option are priced fairly using regular financial standards and advanced mathematical techniques. Finally, these newly proposed insurance and option are tested through various possible market variations, and we are able to connect them with the existing options in the marketplace.