1 / 38

Hedging Catastrophe Risk Using Index-Based Reinsurance Instruments Lixin Zeng

Hedging Catastrophe Risk Using Index-Based Reinsurance Instruments Lixin Zeng 2003 CAS Seminar on Reinsurance June 1-3, 2003 Philadelphia, Pennsylvania. Presentation Highlights Index-based instruments can play a key role in managing catastrophe risk and reducing earnings volatility

Download Presentation

Hedging Catastrophe Risk Using Index-Based Reinsurance Instruments Lixin Zeng

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Hedging Catastrophe Risk Using Index-Based Reinsurance Instruments Lixin Zeng 2003 CAS Seminar on Reinsurance June 1-3, 2003 Philadelphia, Pennsylvania

  2. Presentation Highlights • Index-based instruments can play a key role in managing catastrophe risk and reducing earnings volatility • The issue of basis risk • Possible solutions

  3. Fixed premium Variable payout Index-based instruments: general concept Buyer Seller Index

  4. General concept(continued) • Instrument types • Index-based catastrophe options • Industry loss warranty (ILW) a.k.a. original loss warranty (OLW) • Index-linked cat bonds • Index types • Weather and/or seismic parameters • Modeled losses • Industry losses

  5. limit Industry loss trigger Payoff* Industry loss Industry loss warranty (ILW) * Payoff XI might not exceed actual loss, depending on accounting treatment

  6. Industry loss warranty (ILW) • Simple • Can be combined to replicate other payoff patterns • Different regional industry loss indices • Different triggers • Used as examples in this presentation

  7. Some advantages of index-based instruments • Simplified disclosure and underwriting • Practically free from moral hazard • Opens additional sources of possible capacity (e.g. capital market) • Potentially lower margin and cost • Attractive asset class for capital market investors • Selected background references: Litzenberger et. al. (1996), Doherty and Richter (2002), Cummings, et. al. (2003)

  8. Potential drawbacks of index-based instruments • Form (reinsurance or derivative) may affect accounting • Basis risk – the random difference between actual loss and index-based payout • The term “basis risk” came from hedging using futures contracts

  9. An illustration of basis risk Index-based recovery Indemnity-based recovery Reinsured’s loss recovery Reinsured’s incurred loss

  10. Our tasks • Quantify/measure basis risk • Reduce basis risk • Optimize an index-based hedging program

  11. Measures of basis risk • Rarely are 100% of incurred losses are hedged; instead, we usually hedge large losses only • Index-based payoff vs. a benchmark payoff • Benchmark • Indemnity-based reinsurance contract, e.g., a catastrophe treaty • Other types of risk management tools

  12. XI= Index-based payoff L*I= L -XI = loss net of index-based payoff XR = Benchmark payoff L*R= L - XR = loss net of benchmark payoff Measures of basis risk (cont.) L = Incurred loss L*I vs. L*R Basis risk

  13. Measures of basis risk (cont.) ComparingL*I and L*R Calculate risk measures of L, L*I and L*R(denoted yg, yi andyr) Compare the differences among yg, yi andyr Define DL = L*R - L*I = XI - XR Analyze the conditional probability distribution of DL Type-I basis risk(a) Related to hedging effectiveness Type-II basis risk(b) Related to payoff shortfall

  14. Type-I basis risk (a) • Hedging effectiveness • Basis risk a • Related references: Major (1999), Harrington and Niehaus (1999), Cummins, et. al. (2003), and Zeng (2000)

  15. Type-II basis risk (b) • Based on the payoff shortfall DL • DL is a problem only when a large loss occurs • We are primarily concerned about negative DL • Calculate the conditional cumulative distribution function (CDF) of DL:

  16. Type-II basis risk (b, cont.) • Basis risk bis measured by • The quantile (sq) of the conditional CDF • Scaled by the limit of the benchmark reinsurance contract (lr)

  17. Example 1 • Regional property insurance company wishes to reduce probability of default (POD)* from 1% to 0.4% at the lowest possible cost • Benchmark strategy: catastrophe reinsurance Retention = 99th percentile probable maximum loss (PML) Limit = 99.6th percentile PML – 99th percentile PML * Default is simply defined as loss exceeding surplus

  18. Example 1 (cont.) • Alternative strategy: ILW Index = industry loss for the region where the company conducts business Trigger = 99th percentile industry loss Limit = 99.6th percentile company PML – 99th percentile company PML (same as the benchmark) • Next: show the two measures of basis risk (a and b) for this example

  19. Type-I basis risk (a) • Hedging effectiveness • Basis risk a

  20. Example 1 (cont.)

  21. Type-II basis risk (b) • Based on the payoff shortfall DL • DL is a problem only when a large loss occurs • We are primarily concerned about negative DL • The conditional cumulative distribution function (CDF) of DL: • Basis risk bis measured by the quantile (sq) of the conditional CDF scaled by the limit of the benchmark reinsurance contract (lr)

  22. Example 1 (cont.) conditional CDF DL

  23. Which basis risk measure to use? • They view basis risk from different angles • Which one to use as the primary measure depends on the objective • to structure a reinsurance program with optimal hedging effectiveness, a should be the primary measure • to address the bias toward traditional indemnity-based reinsurance, b should be the primary measure

  24. Ways to reduce basis risk (Example 1, cont.) Cost=95M* Cost=70M* POD=0.2% Cost=45M* Limit ($M) POD=0.4% Cost=20M* POD=0.6% POD=0.8% * technical estimates Trigger ($M)

  25. Ways to reduce basis risk (Example 1, cont.) Cost=95M* Cost=70M* POD=0.2% Cost=45M* Limit ($M) POD=0.4% Cost=20M* POD=0.6% POD=0.8% * technical estimates Trigger ($M)

  26. Keys to reducing basis risk • Cost/benefit analysis • Should be an integral part of the process of building an optimal hedging program • Accomplish specific risk management objectives at the lowest possible cost • Maximize risk reduction given a budget • Objective: building an optimal hedging program using index-based instruments

  27. Building an optimal hedging program • Specify constraints For Example 1: POD≤ 0.4% • Define an objective function For Example 1: cost of ILW = f( ILW trigger, limit, …) • Search for the hedging structure such that • The objective function is minimized or maximized • The constraints are satisfied For Example 1: find the ILW that costs the least such that POD≤ 0.4% • References: Cummins, et. al. (2003) and Zeng (2000)

  28. Improvement to a (Example 1, cont.)

  29. Improvement to b (Example 1, cont.) conditional CDF DL

  30. Building an optimal hedging program (cont.) • Real-world problem • Exposures to various perils in several regions • Multiple ILWs and other index-based instruments are available • Same optimization principle but requires a robust implementation • Challenges to traditional optimization approach • Non-linear and non-smooth objective function and constraints • Local vs. global optimal solutions

  31. Building an optimal hedging program (cont.) • A viable solution based on the genetic algorithm (GA) • Less prone to being trapped in a local solution • Satisfactory numerical efficiency • More robust in handling non-linear and non-smooth constraints and objective function • GA reference: Goldberg (1989)

  32. Example 2 • Objective: maximize r = expected profit / 99%VaR • Constraints: 99%VaR < $30M

  33. Example 2 (cont.) • Available ILWs

  34. Example 2 (cont.) • GA-based vs. exhaustive search (ES) solutions

  35. Example 2 (cont.) • Results of optimization

  36. Summary: basis risk may not be a problem… • If the buyer is willing to accept some uncertainty in payouts in exchange for the advantages of an index based structure. • If basis risk does not pose an impediment to achieving the buyer’s objectives. • If the effects of basis risk can be minimized at the optimal cost (our topic today).

  37. Areas for ongoing and future research • Appropriate constraints and objective functions for optimal hedging • The choice of risk measure • Bias toward using traditional reinsurance • Parameter uncertainty • The sensitivity of the loss model results to parameter uncertainty (e.g., cat model to assumption of earthquake recurrence rate) • The sensitivity of the optimal solution to the choice of risk measures and objective function

  38. References • Artzner, P., F. Delbaen, J.-M. Eber and D. Heath, 1999, Coherent Measures of Risk, Journal of Mathematical Finance, 9(3), pp. 203-28. • Cummins, J. D., D. Lalonde, and R. D. Phillips, 2003: The basis risk of catastrophic-loss index securities, to appear in the Journal of Financial Economics. • Doherty, N.A. and A. Richter, 2002: Moral hazard, basis risk, and gap insurance. The Journal of Risk and Insurance, 69(1), 9-24. • Goldberg, D.E., 1989: Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Pub Co, 412pp. • Harrington S. and G. Niehaus, 1999: Basis risk with PCS catastrophe insurance derivative contracts. Journal of Risk and Insurance, 66(1), 49-82. • Litzenberger, R.H., D.R. Beaglehole, and C.E. Reynolds, 1996: Assessing catastrophe reinsurance-linked securities as a new asset class. Journal of Portfolio Management, Special Issue Dec. 1996, 76-86. • Major, J.A., 1999: Index Hedge Performance: Insurer Market Penetration and Basis Risk, in Kenneth A. Froot, ed., The Financing of Catastrophe Risk (Chicago: University of Chicago Press). • Meyers, G.G., 1996: A buyer's guide for options and futures on a catastrophe index, Casualty Actuarial Society Discussion Paper Program, May, 273-296. • Zeng, L., 2000: On the basis risk of industry loss warranties, The Journal of Risk Finance, 1(4) 27-32.

More Related