Catastrophe Risk Modeling and Application- Risk Assessment for Taiwan Residential Earthquake Insurance Pool

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1 5.00% 4.50% 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% 0.00% Return Period (yr) OEP Catastrophe Risk Modeling and Application Risk Assessment for Taiwan Residential Earthquake Insurance Pool WenKo Hsu 1, DungMou Hung 1,, W.L. Chiang 1, C.P. Tseng 1,, C.H. Tsai 2 1 Department of Civil Engineering, National Central University, Chungli, Taiwan 320, R.O.C. 2 Department of Information Management, Taiwan Hospitality & Tourism College, Hualien, Taiwan, R.O.C. 3 Department of Logistics Management, ShuTe University, 59 Hun Shan Rd., Yen Chau, Kaohsiung, Taiwan 82445, R.O.C. Corresponding author: s @cc.ncu.edu.tw ABSTRACT Taiwan lies at earthquakeprone area. More than 200 sensible earthquakes occurred every year in Taiwan. Average annual loss due to 83 disastrous earthquakes since 1900 is about NT$19 billion dollars which equals to 0.7% GDP. Therefore, the Taiwan Residential Earthquake Insurance Pool (TREIP) was created by the Taiwan Ministry of Finance (MOF) to facilitate a risk sharing mechanism between private insurance companies and the Government covering insured residential earthquake losses. In this paper, we have built up an eventbased seismic hazard assessment and financial analysis model for earthquake disasters. As we know, low occurrence rate, tremendous loss and high uncertainty are characteristics of earthquake disasters. For the above issues, the model we built integrates knowledge from many fields including earth science, seismology, geology, risk management, structural engineering, the insurance profession, financial engineering and facility management. The model use the Monte Carlo simulation technology can construct an annual exceeding probability curve, which relates probability to size of loss, the specific event loss and allows for the evaluation of different insurance and reinsurance programs KEY WORDS Earthquake, Risk assessment, Insurance, Monte Carlo simulation 1. Introduction Earthquake risk, a longtime concern in Taiwan, is increasingly being recognized as a concern in insurance industry and government. The Taiwan Residential Earthquake Insurance Pool (TREIP) was created by at April, 2002 the Taiwan Ministry of Finance (MOF) to facilitate a risk sharing partnership between private insurance companies and the Government covering insured residential earthquake losses. TREIP collects for the earthquake risk from the insurance companies and redistributes the to the various risk sharing entities (including itself). If losses occur, TREIP collects the appropriate funds from the risk sharing entities and reimburses the direct insurers for their payments to the policyholders. This paper established the eventbased earthquake loss model to analysis the TREIP insurance scheme to find out the loss exceeding probability curve, both the annual aggregate loss and standard deviation of loss for each layer. Based on the analysis result, we can provide the TREIP how to modify the insurance scheme. The framework of catastrophe model can be described by figure1. It would be introduced how the primary components work in the following sections. Event Loss / Total Sum Insured % Stochastic Earthquake Event Hazard Analysis Procedure Vulnerability Analysis Procedure Financial Analysis Procedure Figure1 Framework of Earthquake Loss Model 2. Catastrophe model for earthquake risk There are four primary components within earthquake loss assessment and management model. 1. Stochastic earthquake event generator, which uses a collection of relevant inventory and analysis parameters for the development of seismic damage assessment and loss estimation. 2. Hazard analysis procedure, can assess the intensity of ground shaking, maximum surface 1

2 acceleration with the attenuation function in Taiwan and soil condition. 3. Vulnerability analysis procedure, can calculate the probability of different damage state to structural and content. 4. Financial analysis procedure, can assess loss include the direct and indirect economic losses. It also can provide the loss exceeding probability curve and dynamic financial analysis result. 2.1 Stochastic Earthquake Event An representative earthquake event set is important to an event based earthquake model.for this reason, we collect the historical distribution of the epicenters of earthquakes in Taiwan during 1900 to 2004 from the Taiwan Central Weather Bureau. It includes 43 seismic zones, 21 shallow seismic sources, 7 deep seismic sources, and 15 subduction zone seismic sources [1]. There are also 42 active faults in the event generator [2]. The rate of occurrence of different magnitude events is estimated based on a GutenbergRichter [3] frequencymagnitude relationship. The earthquake occurrence rate is modeled by the Poisson model. There are 17,710 hypothetical earthquake events distributed across all sources in the generator and each event includes the parameters which the other analysis procedure need such as location, depth, magnitude, direction etc. 2.2 Hazard Analysis Procedure To asses the intensity of ground shaking for each simulated earthquake event is the purpose of the hazard analysis procedure. As described in the following diagram, we can calculate the Peak Ground Acceleration (PGA) for the location of the building. In analysis procedure, all crustal sources use the attenuation developed by Loh [4] while the subduction sources use Young et al.[5]. For the site effect, we also consider soil classifications are rock, weak rock / dense soil, stiff soil, and soft soil. Soil map inferred from the analysis of records of Freefield StrongMotion Stations of Taiwan Central Weather Bureau and Geologic Map from Taiwan Central Geological Survey, MOEA. Geotechnical data is derived from geologic maps published by the Taiwan Ministry of Economic Affairs at 1:50,000 and 1:250,000 resolutions. 2.3 Vulnerability Analysis Procedure According to the result of the hazard analysis procedure, we can obtain the capacity curve of building. Then, using the response spectral method described in the right diagram, a specific group of (Sd, Sa) can be determined. Finally, we can get the probability of each damage state of building. To Calculates the mean damage ratio and coefficient of variation to buildings, contents, and the resulting loss of use, the earthquake loss model includes four major elements: construction classes; occupancy classes; additional building classifications such as year built, number of stories, and seismic code zones. Based on the seismic resistance of buildings, vulnerability analysis procedure can assess the probability of each damage state to structure and content. Spectral Acceleration Spectral Displacement Damage State Spectral Displacement Figure 2 Assessment for the probability of each damage state 2.4 Financial Analysis Procedure Before the beginning of the financial analysis, we must build the event loss table by the procedures we described above. As the described the following diagram, we can create the event loss table in the form include event id, annual mean rate and mean loss for each event. Stochastic Earthquake Event Event Table 18,852 hypothetical earthquake events ID #0001 #0002 #0003 Hazard Analysis Procedure Magnitude & Hypocenter Annual Mean Rate Vulnerability Analysis Procedure Loss$ 0.65 Billion Figure 3 Building the event loss table CV 2.00 Portfolio Policy conditions Deductible, Limit 2

3 The direct and indirect economic losses caused by the simulated earthquakes can be estimated using the financial analysis procedure. Damage to assets is converted to monetary losses by ratio of repair/rebuilt cost. However, depending on the terms of the policy, the loss is shared by more than one party. This part of the modeling reflects the workings of a policy or treaty; it is included as an integral part of the overall modeling approach because of the intimate interaction between the insurance structure and damage to the physical buildings or assets. After the event loss table was created, we can use the Monte Carlo simulation to establish aggregate or occurrence loss exceeding probability curve. First, we use the Poisson distribution to describe the earthquake occurrence times. According to the occurrence rate of each event, we can get the occurrence times N in every simulation and simulate the accumulative probability of severity distribution randomly. Therefore, we can generate the loss exceeding probability curve like the following diagram. Event Loss Table Second, this approach utilizes advances in computer technology and modeling techniques to provide almost instantaneous feedback to decision makers, allowing for the evaluation of numerous operating alternatives. The specific innovations to the planning process that are incorporated in DFA modeling are: 1. DFA provides a probability distribution of likely outcomes, rather than a single expected value forecast. 2. DFA incorporates the correlations among lines of business, between loss reserve adequacy and rate adequacy, and between the investment and underwriting sides of insurance operations. 3. By utilizing the technology of personal computers and common software, DFA models can be run by the users many times with different assumptions and different parameters, in order to see the effect that changes in the model or in operations can have on the results. Investment Interest(CIR) Catastrophe Occurrence Rate λ Simulate M times Severity distribution 100% 0% Loss $ Investment Cash Flow Underwriting Underwriting Cash Flow Simulate Occurrence? (Poisson Model ) N times Simulate Loss? L 1, L 2,, L N Occurrence N times AEP k = L 1 + L L N OEP k = Max (L 1, L 2,, L N ) Balance sheet Provider AEP 1, AEP 2,, AEP M OEP 1, OEP 2,, OEP M Figure 4 Flowchart for building the loss exceeding probability curve After the losses for all locations in a portfolio are calculated, the financial analysis procedure allocates the losses to different participants, i.e., insured, insurer, and reinsurer through various insurance and treaty structures. Because there are many sources of uncertainty in modeling (from attenuation, vulnerability and incompleteness of data), the loss at the location level is treated as a random variable. In financial analysis procedure, we also create dynamic financial analysis model (DFA).It represents an enhanced approach to the traditional planning function. It provides a far more effective tool for forecasting future financial and operating conditions of a risk manager than prior methods for two primary reasons. First, the interactions between the underwriting and investment sides of the insurance business are formally integrated. Figure 5 Framework of Dynamic Financial Analysis 2.5 Example of TREIP Analysis TREIP have 1,383,731 policies until September 31, The aggregate liabilities are NT$ 1.8 trillions and take up rate are 18.19%. TREIP collects for the earthquake risk from the insurance companies and redistributes the to the various risk sharing entities (including itself). If losses occur, TREIP collects the appropriate funds from the risk sharing entities and reimburses the direct insurers for their payments to the policyholders. The insurance scheme includes six layers is like the figure 6. TREIP has four tiers totally NT$50 billion as its capacity. The coinsurance in Taiwan retain the first NT$ 2 Billions. Second layer is foundation layer. TREIP commissions the Central Re to be an administrator for the management of funds from the government to the private insurance and ultimately to policyholders. The third layer is reinsurance layer and the third layer had a Cat Bond for the first US$ 100 million. The government then provides additional resources of NT$ 10 billion in excess of NT$ 40 billion. The scheme sets a cap limit of 3

4 NT$50 billion. In the event that losses exceed the capped amount, the losses paid to policyholders will be scaled down. 4th Tier Government 10 billion Table 1 Exhaustion probabilities in different layer Layer Attachment Point (NT$ Billion) Layer Amount (NT$ Billion) Penetration (%) Return Period (year) 2 nd Layer Reinsurance 20% Domestic 80% overseas 10 billion % rd Tier 1st Layer Reinsurance Cat Bond 6.6 billion US$ 100 million Government % Second layer reinsurance % nd Tier 1st Tier Taiwan Residential Earthquake Insurance Fund Domestic Insurers Coinsurance 18 billion 2 billion Figure 6 The TREIP insurance scheme For each policy, we can obtain the zipcode level location and characteristics of building such as building type, building height and built year. The for each policy are NT$1459. Otherwise, the claim of TREIP policy will be paid in an amount equal to the policy limit (NT$1.2 millions) if the building is no longer habitable or the damage ratio exceeds 50%. In addition, a further NT$180,000 of reimbursement is provided per household for Contingent Living Expenses. So we need to have a threshold trigger in the vulnerability analysis procedure. With the parameters described above and TREIP portfolio, we can use the earthquake loss assessment and management model to simulate the loss exceeding probability curve and penetration probabilities for each layer like the charts below. In figure 7,it shows that the loss ratio is about 3.75% based on 500 year return period. It means that it will occur once event of the loss ratio are greater than 3.75% in 500 year. In Table 1, it shows the current scheme can grantee the event loss in years return period. Event Loss / Total Sum Insured % 5.00% 4.50% 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% OEP First layer reinsurance % Cat Bond % Found % 22.6 Coinsurance The TREIP and expense flow diagram shows how the policy is collected from the insured and ultimately received by TREIP and how expenses are distributed. According to the figure 8 and our assumptions, the surplus of foundation layer can be simulated by using Dynamic Financial Analysis (DFA) model of the economic analysis procedure. The assumptions details are as followed: 1. Premium rate will not change as the result of a earthquake event percent of policy is paid to the primary insurers as commission percent of policy (20 percent of 85 percent net ) is paid to the primary insurers as compensation for retaining the first claims layer percent of policy is paid to CRC to cover administration expenses percent of policy is paid to Foundation to cover the claims for the second claims layer percent of policy is allocated to cover fluctuating reinsurance costs in the future. 7. The interest of Cat Bond is 4.5% of the capacity. The issue cost are NT$ 67 million. 8. TREIP is a taxexempt entity % 0.00% Return Period (yr) Figure 7 Loss exceeding probability curve 4

5 Direct Insurers Policyholders 100 % (8.0 % commissions % percent % to cover to manage insurance exposure) 100 % Surplus of CRC (TREIP asset manager) Foundation (18bnX2bn) 4.5% Capacit y 1.8% Capacity 1.4% Capacity 2.5 % Reserve for fluctuating reinsurance costs Cat Bond (3.4bnX20bn) Reinsurance Layer I (6.6bnX23.4bn) Reinsurance Layer II (10bnX30bn) Government (10bnX40bn) Figure 8 TREIP Premiums and Expense Flow Diagram After 100,000 times simulation, we can obtain the net cash flow of the foundation layer like the chart below. 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% An eventbased probabilistic seismic risk assessment model was established for TREIP. Based on the request of TREIP, the risk assessment analysis results were provided to TREIP as reference for capacity adjustment, reinsurance arrangement, exercise plan of claim process. To TREIP portfolio, current insurance scheme only can grantee the event loss occurs once in years return period. TREIP should increase the earthquake protection capacity, but it also means the cost of insurance will increase. It can design several schemes and use the model we built to see how much the cost increase. Finally, the optimal solution will balance between the earthquake protection capacity and cost of insurance. In this paper, Poisson model was used to simulate the occurrence rate of the stochastic earthquake event. As we know, Poisson model is a timeindependent model. Nevertheless, the behaviour which earthquake event occurs is timedependent in fact. In the future, we should have a further research. The model of optimal reinsurance and retention arrangement strategy for TREIP is under development based on the results of the risk assessment model. Acknowledgements These materials are provided by Taiwan Residential Earthquake Insurance Pool. References [1] Lin B. S, Lee C.T., Cheng C.T,Strong Ground Motion Attenuation Relationship for Subduction Zone Earthquakes in Taiwan, 9 th Conf. on Geophysical Society, China, 2002, [2] An introduction to active faults in Taiwan.( Taiwan Central Geological Survey, MOEA, 2000) [3] Gutenberg, B., Richter, C. F., Frequency of Earthquake in California, Bull. Seism. Soc. Amer. 1991, Vol. 34, p185~188. [4] Loh, C.H. Z.K. Lee etc. Ground Motion Characteristics of the ChiChi earthquake of September 21, 1999,Journal of Earthquake Engineering and Structural Dynamics, 2000,p [5] Young, Subduction Slabs in Taiwan Region, Jour. Geol. China, 40, 1997, Figure 9 of Adjusted Cash Flow in each projection year. 3. Conclusion Because of the concern for uncertainty and engineering model, the earthquake loss assessment model can provide more information than the traditional method. For example, the loss exceeding probability curve can offer the policymaker to determine the earthquake protection capacity according to their tolerance of risk. On the other hand, the traditional method only can give us the single value for the possible maximum loss due to earthquake disaster. 5