1 / 65

Hedging catastrophe risks using index-based instruments CAS reinsurance seminar New York

Hedging catastrophe risks using index-based instruments CAS reinsurance seminar New York Feb. 28, 2002 Lixin Zeng, Ph.D. Willis Re. Outline Introduction / background Defining basis risk Calculating basis risk Optimal hedging strategies. Index-based risk management instrument

jessej
Download Presentation

Hedging catastrophe risks using index-based instruments CAS reinsurance seminar New York

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 risks using index-based instruments CAS reinsurance seminar New York Feb. 28, 2002 Lixin Zeng, Ph.D. Willis Re

  2. Outline • Introduction / background • Defining basis risk • Calculating basis risk • Optimal hedging strategies

  3. Index-based risk management instrument • Index types • Industry losses • Geophysical parameters • Instruments • Cat options • Industry loss warranty (ILW) • Index-linked cat bonds • Other index-linked instruments (yield guarantee, index-based WC products, etc.)

  4. Fixed premium Actual loss Variable payout General concept Buyer Seller Agree on an index

  5. Examples • Call option on an industry loss index • Call spread on an industry loss index W: index; S: strike; L: limit; P: payout; k: payout ratio

  6. Examples (continued) • Industry loss warranty (ILW) Sometimes subject to an actual loss • Index-linked cat bond • P = Principal payment • I = Interest payments • X = Parameters related to natural disaster event(s)

  7. Compared to traditional indemnity instruments • Advantages • Simpler underwriting • Lower moral hazard • Potentially lower cost • Challenges • Tax/reporting implications • Basis risk: mismatch between payout and actual loss

  8. Outline • Introduction / background • Defining basis risk • Calculating basis risk • Optimal hedging strategies

  9. Example: Mismatching of a cat option payout and the actual excess loss

  10. Example: Mismatching of a cat option payout and the actual excess loss 300 Strike (K*S) 200 Payout factor * Index (K*W) 100 retention 0 50 100 150 200 250 300 Actual loss

  11. Basis “gain” Basis risk 300 strike (K*S) 200 Payout factor * index (K*W) 100 retention 0 50 100 150 200 250 300 Actual loss

  12. What is “basis risk”? Actual excess loss Basis risk a Basis risk g Payout of an “comparable” reinsurance policy Payout of an index-based instrument Basis risk b

  13. Why do we care about basis risk? • Type a • How effective is the index-based instrument in reducing the risk of the underlying portfolio • Type b • How does the index-based instrument compare to the traditional reinsurance policy • Type g • Probability of exhausting the limit, counter-party credit risk, contract dispute, etc.

  14. Definitions • Symbols • Lg = actual gross loss • rt = retention • L = max(0, Lg - rt) (excess loss) • Pi = payout of the index-based instrument A • Pr = payout of a “comparable” traditional reinsurance policy B

  15. Definitions (continued) • An index-based instrument A and a traditional reinsurance policy B are comparable if • The strike of A and the attachment of B have similar probabilities of attaching • A and B have similar payout limit • The costs of A and B are similar

  16. Quantification of basis risk • Measures based on covariance and/or linear correlation between excess loss and payout • Easy to calculate • Commonly used • Actuarial meaning not clear • Can be misleading

  17. Example 1: payout vs. actual excess loss Payout ($100M) Actual excess loss ($100M)

  18. Example 2: payout vs. actual excess loss Payout ($100M) Actual excess loss ($100M)

  19. How to differentiate the two structures?

  20. How to differentiate the two structures?

  21. Better quantification of basis risk • Conditional probability-based measures • Probability distribution of payout shortfall given an excess loss • Explicit actuarial implications

  22. Basis risk for reinsurance instruments • Basis risk type a: the mismatch between actual excess loss and payout when L > 0 • Focus on how the net loss probability will change with different reinsurance strategies • Basis risk type b: the mismatch between index and indemnity instruments when L > 0 • Probability distribution of b = Pr - Pi • Focus on probability of “regret”

  23. Basis risk for reinsurance instruments • Which measure to focus on? • To develop an optimal reinsurance program, a should be used • To address existing bias towards traditional reinsurance, b should be used

  24. Example 3 • Reinsurer in a natural disaster area • 15% market share • Geographically diversified within the region • Goal: • Reduce probability of default from 1% to 0.4% • Enhance risk/return profile • Reduce earning volatility

  25. Example 3 (continued) • Measure of risk • Probability of default • Probable maximum loss or Value at Risk with a 0.4% exceeding probability: a proxy of risk capital • Tail Value at Risk (TVaR): a coherent risk measure • Semi-deviation of underwriting profit (i.e. standard deviation of negative underwriting profit): related to earning volatility

  26. Example 3 (continued) • Measure of success • Return on equity (ROE) expected profit / company equity • Return on Risk Capital (RORC) expected profit / PML • Modified Sharpe ratio expected profit / semi-deviation

  27. Example 3 (continued) • Evaluate competing strategies • Traditional retro policy • retention: 100-year PML • limit: 250-year PML - 100-year PML • ILW (i.e. a binary call option) • trigger: 100-year industry loss • limit: same as above • Industry loss index call option (ICO) • strike: 90% of 100-year industry loss • limit: same as above

  28. Probability of non exceedance

  29. Probability of non exceedance Gross loss Net after retro • Attached at 100-year loss • Cover up to 250-year loss

  30. Gross loss Net after retro Net after ILW • Attached at industry 100-year loss • Same limit as the indemnity contract above Probability of non exceedance

  31. Gross loss Net after retro Net after ILW Net after Index Call Option • Attached at 90% of industry 100-year loss • Same limit as the indemnity contract above Probability of non exceedance

  32. Probability density of b (ILW - retro payout) given L > 0 Basis “gain” Basis risk

  33. Cumulative probability distribution of b (ILW - retro payout) given L > 0 “worst case” b ~ 50% of cover limit Probability of non exceedance b

  34. Example 4 • Reinsurer in a natural disaster area • 10% market share • Not geographically diversified within the region • Goal: • same as Example 3 • Evaluate competing strategies • same as Example 3

  35. Probability density of b given L > 0 Basis risk Basis “gain” b

  36. Probability distribution of b given L > 0 worst case b = 100% of cover limit Probability of non exceedance b

  37. Evaluating pros and cons of using index-based instruments: Factors to consider • Lower margin than a comparable retro • At the same premium, it offers greater reduction of expected loss • Basis risk • Reasonably small for geographically diversified exposures • Potential for negative surprise for concentrated portfolio • Don’t count on the “basis gain”

  38. Index-based or indemnity: which one to use? • No universally applicable answer • Depends on financial objective and risk tolerance • A combination of subjective judgment and objective analysis • Quantitative analyses facilitate consistent decision making • Consistent objective • Optimal position at the risk/return curve • Explicit monitoring of portfolio risk

  39. Outline • Introduction / background • Defining basis risk • Calculating basis risk • Optimal hedging strategies

  40. How to calculate conditional loss distributions • Representation of probability distributions in cat models • Cat model provides loss distributions of gross and net losses • For basis risk type a: calculate probability distribution of annual aggregate loss • For basis risk type b: derive Fbbased on cat model output

  41. Event-based representation of loss probability in a cat model • Cat model output Loss due to simulated event #k Rate of event #k (average number per year)

  42. Event-based representation of loss probability in a cat model • Assumptions • n is large enough for the set to contain nearly all possible natural disaster events • NkNumber of occurrences of event #k ~ Poisson Process with • ? • Events are independent

  43. For basis risk type a • Probability distribution of annual aggregate loss after reinsurance or index-based instrument • Available approaches • Simulation based on per event losses • FFT (e.g. Wang, 1998)

  44. For basis risk type b • Probability distribution of per event loss X • may be any losses e.g. Pr, Pi, b, L, etc.

  45. Number of times event k occurs CDF of Xk

  46. Event-based representation of loss probability in a cat model • Loss probability distribution Xk Frequency for event k Probability that the loss exceeds x given event k occurs

  47. Event-based representation of loss probability in a cat model • Probability distribution of X

  48. Event-based representation of loss probability in a cat model • A frequently used simplification • Assuming Xkis deterministic, i.e. • Then

More Related