Dealing with Uncertainty in Catastrophe Modelling
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Catastrophe models are used to understand natural disaster risk exposure and aid in pricing and structuring reinsurance programs. The models simulate hazard events and calculate potential financial losses by considering a building's vulnerability and the costs of damage. Key outputs include loss exceedance probabilities, average annual losses, and probable maximum losses. However, there is uncertainty in catastrophe modeling given limitations in data, science, and sampling. Model results are best interpreted as a range rather than a single value.
Dealing with Uncertainty in Catastrophe Modelling
- 2. H. Katrina (2005) Japan/NZ EQ, Thai Floods (2011) Northridge EQ (1994) Source :Swiss Re Economic Consulting and Research
- 4. • Why perform Cat Modelling? • How do Cat Models work? • Interpreting Cat Model Output • Uncertainty in Cat Modelling
- 5. • Understanding risk exposure • Direct Pricing • Structuring and Pricing Reinsurance Programs • Regulatory Requirements / Dynamic Financial Analysis (DFA) • Pricing of Alternative Risk Transfer (ART) Mechanisms
- 7. Hazard • Science, Simulation of many events Vulnerability • How do buildings respond to events? Financial Loss • What is the cost given the damage?
- 8. Simulated Hurricane Tracks Simulated Earthquake Events (Epicenters) Sources : Franco, G. (2010) “Minimization of Trigger Error in Cat-in-a-Box Parametric Earthquake Catastrophe Bonds with an Application to Costa Rica” Earthquake Spectra, AIR
- 9. Source: Latchman S, Quantifying the Risk of Natural Catastrophes (http://understandinguncertainty.org/node/622)
- 11. Earthquake MDR Peak Ground Acceleration Wood Frame Masonry Cyclone MDR Peak Wind Gust Wood Frame Masonry
- 12. • Combined loss distribution for 2 (or more) buildings in different locations is computed via convolutions, for each event. Where: L = loss of amount L for event P1(Li) = probability distribution for Location 1 P2(Lj) = probability distribution for Location 2 Li (for P1) Li + Lj For e.g. , what is probability of loss of 10m for this event? Lj (for P2) Source : Latchman S., Quantifying the Risk of Natural Catastrophes, 2010 𝑷 𝑳 = 𝑷 𝟏 𝑳𝒊 × 𝑷 𝟐 𝑳𝒋
- 13. • Return Period = 1 / Probability of Exceedance • Hence, the 1 in 10 year Hurricane loss corresponds to 10% EP with a loss of 99m Loss (m) Source: Modelling Fundamentals : What is AAL? By Nan Ma and Greg Sly (AIR CURRENTS , March 2013)
- 14. • AAL = (250*0.1) + (150*0.1) + (0*0.1) + (0*0.1)...... = 40m Average Annual Loss (AAL): What is the expected loss from earthquakes this year for Japan EQ? Source: Modelling Fundamentals : What is AAL? By Nan Ma and Greg Sly (AIR CURRENTS , March 2013)
- 15. Different EP curve shape Identical AAL Source: Modelling Fundamentals : What is AAL? By Nan Ma and Greg Sly (AIR CURRENTS , March 2013)
- 16. ExceedanceProbability Loss XSAAL p RP Loss (PML) TCE (p) = E (L | L >= RPLp) AAL AAL Applications: • Direct Pricing • Understanding key drivers of loss • Underwriting Guidelines PML Applications: • Pricing Cat Reinsurance Treaties • Rating Agency Reporting (APRA) XSAAL & TCE • Help understand drivers of tail risk • Average severity of losses in tail
- 17. • Epistemic vs Aleatory Uncertainty – Epistemic : Imperfect science ; limited historical record; sampling errors – Aleatory: Intrinsic randomness ; irreducible • Primary Uncertainty – Focused more on the hazard generation component – i.e. event occurrence, parameters that govern cyclone path • Secondary Uncertainty – Focused more on vulnerability component – i.e. ground motions/ wind speeds at site, damage given particular ground motion/ wind speed.
- 18. Primary Uncertainty (Hazard) : EQ Ground Motion attenuation Secondary Uncertainty(Vulnerability) : Cyclone Damage Source: RMS
- 19. CV=SD/MDR Mean Damage Ratio, MDR DamageRatio,D Peak Wind Gust, v 𝒇 𝒅 𝒗 = damage ratio distribution, at PWG v Probability Peak Wind Gust, v 𝒇 𝒗 = wind speed distribution, at PWG v Probability Damage Ratio,D f(d) = overall damage ratio distribution = 𝒇 𝒅 𝒗 × 𝒇 𝒗 𝒅𝒗 𝝈 X X The larger the event, MDR ↑ while CV ↓
- 20. 𝑺𝑫𝒊 𝑺𝑫𝒊+𝟏 . . . . If Location losses are perfectly correlated (𝐢. 𝐞. , 𝝆 = 𝟏), 𝑺𝑫 𝒕𝒐𝒕𝒂𝒍,𝒄𝒐𝒓𝒓𝒆𝒍𝒂𝒕𝒆𝒅 = 𝒊 𝑵 𝑺𝑫𝒊 𝑺𝑫𝒊 𝑺𝑫𝒊+𝟏 . . . . If Location losses are perfectly uncorrelated (𝐢. 𝐞. , 𝝆 = 𝟎), 𝑺𝑫 𝒕𝒐𝒕𝒂𝒍,𝒊𝒏𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 = 𝒊 𝑵 𝑺𝑫𝒊 𝟐+ + 𝑺𝑫 𝒑𝒐𝒓𝒕𝒇𝒐𝒍𝒊𝒐 = 𝒘 ∗ 𝑺𝑫 𝒕𝒐𝒕𝒂𝒍,𝒄𝒐𝒓𝒓𝒆𝒍𝒂𝒕𝒆𝒅 + 𝟏 − 𝒘 ∗ 𝑺𝑫 𝒕𝒐𝒕𝒂𝒍,𝒊𝒏𝒅𝒆𝒑𝒆𝒏𝒅𝒆𝒏𝒕 Hence, overall portfolio standard deviation, Where w is correlation weights (i.e. more geo-concentrated portfolio will have larger w than one that is more diverse)
- 21. Source: RMS Example showing how uncertainty is incorporated into return period loss estimates.
- 22. • Repeated resampling of Event List Table (ELT) • Plot new EP curve with each realization, and sort them • Build confidence intervals for desired percentiles
- 23. • Reduce model risk from reliance on single vendor opinion • May diversify away ‘independent imperfections’ • But, may introduce new uncertainties in the process! Model A Model B Blended Model
- 24. Source: Ian Cook, Using Multiple Catastrophe Models, 2011 • If we have good reason to believe that, say at 400 year RP: – Greater chance the ‘true’ 1 in 400 year loss to be below B than above B – Greater chance the ‘true’ 1 in 400 year loss to be above A than below A • Then weighted average of A and B may be ‘less wrong’ than pure A or B alone.
- 25. • Invokes a Bayesian approach, i.e. : • 𝑷 𝑹𝑷𝒍𝒐𝒔𝒔 = 𝑷 𝑹𝑷𝒍𝒐𝒔𝒔 𝑴𝒐𝒅𝒆𝒍 𝑨) ∗ 𝑷 𝑴𝒐𝒅𝒆𝒍 𝑨 + 𝑷 𝑹𝑷𝒍𝒐𝒔𝒔 𝑴𝒐𝒅𝒆𝒍 𝑩) ∗ 𝑷 𝑴𝒐𝒅𝒆𝒍 𝑩 • Preserves event sets for other uses such as being fed into capital models. Source: Ian Cook, Using Multiple Catastrophe Models, 2011
- 26. • Sensitivity testing/ Stress Testing of model assumptions • Historical Event validation • Expert Judgment / Consultation with model vendors • Bias Correction Methods
- 27. Alexander Pui Email: alexpui8@gmail.com Linkedin : https://au.linkedin.com/in/alexander-pui-94a33821