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Stochastic Modeling and Fair Valuation of Drawdown Insurance

  • Hongzhong Zhang
  • Tim Leung
  • Olympia Hadjiliadis

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.

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File URL: http://arxiv.org/pdf/1310.3860
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Paper provided by arXiv.org in its series Papers with number 1310.3860.

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Date of creation: Oct 2013
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Handle: RePEc:arx:papers:1310.3860
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  1. Libor Pospisil & Jan Vecer, 2010. "Portfolio sensitivity to changes in the maximum and the maximum drawdown," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 617-627.
  2. Manishi Prasad & Peter Wahlqvist & Rich Shikiar & Ya-Chen Tina Shih, 2004. "A," PharmacoEconomics, Springer Healthcare | Adis, vol. 22(4), pages 225-244.
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  4. Pospisil, Libor & Vecer, Jan & Hadjiliadis, Olympia, 2009. "Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2563-2578, August.
  5. Alexei Chekhlov & Stanislav Uryasev & Michael Zabarankin, 2005. "Drawdown Measure In Portfolio Optimization," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 13-58.
  6. Riccardo Rebonato & Valerio Gaspari, 2006. "Analysis of drawdowns and drawups in the US$ interest-rate market," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 297-326.
  7. Moore, Kristen S., 2009. "Optimal surrender strategies for equity-indexed annuity investors," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 1-18, February.
  8. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  9. Olympia Hadjiliadis & Jan Vecer, 2006. "Drawdowns preceding rallies in the Brownian motion model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 403-409.
  10. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276.
  11. Cheung, Ka Chun & Yang, Hailiang, 2005. "Optimal stopping behavior of equity-linked investment products with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 599-614, December.
  12. Vikas Agarwal & Naveen D. Daniel & Narayan Y. Naik, 2009. "Role of Managerial Incentives and Discretion in Hedge Fund Performance," Journal of Finance, American Finance Association, vol. 64(5), pages 2221-2256, October.
  13. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
  14. Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282.
  15. Peter Carr & Hongzhong Zhang & Olympia Hadjiliadis, 2011. "Maximum Drawdown Insurance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1195-1230.
  16. Johansen, Anders, 2003. "Characterization of large price variations in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 157-166.
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