Stochastic Modeling and Fair Valuation of Drawdown Insurance

25 Pages Posted: 28 Mar 2013 Last revised: 15 Oct 2013

Hongzhong Zhang

Columbia University

Tim Leung

University of Washington - Department of Applied Math

Olympia Hadjiliadis

CUNY - The Graduate Center; City University of New York (CUNY) - Hunter College

Date Written: October 14, 2013

Abstract

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.

Keywords: drawdown insurance, early cancellation, optimal stopping, default risk

JEL Classification: C61, G01, G13, G22

Suggested Citation

Zhang, Hongzhong and Leung, Tim and Hadjiliadis, Olympia, Stochastic Modeling and Fair Valuation of Drawdown Insurance (October 14, 2013). Insurance: Mathematics and Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2240210

Hongzhong Zhang

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States
9253381749 (Phone)

HOME PAGE: http://faculty.washington.edu/timleung/

Olympia Hadjiliadis

CUNY - The Graduate Center ( email )

365 5th Ave
New York, NY 10016
United States

City University of New York (CUNY) - Hunter College ( email )

695 Park ave
New York, NY 10065
United States

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