Pricing Excess Layers in Commercial Insurance Use of Simulation

1
Pricing Excess Layers in Commercial Insurance --
Use of Simulation

• Manalur Sandilya
• Max Europe Holdings Ltd

2
Preliminaries

• Quick review of two common methods
• Pure Premium Method
• Loss ratio method
• Output -- Pricing manuals
• Relatively Easy to Use at Point of Sale
• Underwriting Issues

3
Applicability of Standard Methods

• Two Important Considerations --
• Moral Hazard
• Anti Selection
• Question -- how to avoid
• Theory -- underwriting selection
• Practice -- size of the exposure

4
Applicability of Standard Methods

• Homogenous data
• Existence of Valid Mean and Variance
• Credibility of data
• Functioning of the Insurance Principle
• Risk Bearing and Risk Sharing
• Insurance Operation is Expensive
• Value to the Insured

5
Applicability of Standard Methods

• Large market
• Similar Risks
• Measurability
• Insurability
• Motor
• Homeowners

6
Characteristics of Commercial Exposures

• Small Commercial -- Main Street Commercial --
  Standard methods workable
• Middle Commercial -- standardization is becoming
  difficult
• Large Commercial -- standardization is almost
  impossible

7
Characteristics of Excess Layers

• Very low Frequency
• High Severity
• Data will not be credible
• Exposure comparison may be invalid
• Risk bearing or Risk Sharing -- cannot really
  distinguish between the two
• Working Layer and Excess Layer

8
Characteristics of Excess Layers

• Self Insured Retention
• Aggregate Retention
• Attachment
• Drop-down
• Single or multi tower
• Vertical or Horizontal cover

9
Review Pricing Basics

• Expected Loss Cost
• Distribution
• Risk Load
• Cost of Capital
• Market Forces
• Available methods to estimate the different pieces

10
Frequency Severity

• Primary Relationship
• Estimation Strategies
• Theoretical Approaches
• Limitations
• Complexity
• Simple Example
• Simulation

11
Severity

• Distributions
• Extreme Distributions
• Cupolas
• How simulation can be used to simplify the
  various combinations
• Fitting/Selection -- Theory/Art/Practice

12
Frequency

• Dependent or Independent
• Statistical or Practical sense
• Essentially conditional Distributions
• Goodness of Fit issues
• Layers of interest
• Practical consideration -- need a robust
  estimate for the layer under consideration

13
Risk Premium

• Variance Approach
• Cost of Capital Approach
• Other Variable Costs

14
Worked Example

• Problem Statement
• Basic Assumptions
• Simple Situations
• Increased Complexity
• Simulation Exercise

15
Conclusion

• Typical Exposures
• Implementation Issues
• Level of Expertise
• Working with Underwriters
• Questions