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Ultimate Reserve Decoded

8/3/2022

A head to head comparison of loss development triangle and frequency-severity approach

Team 18

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CONTENTS

01. Background and Aim

02. Method

03. Comparison

04. Conclusion

05. Discussion

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· Background

Company

  • Insurance company for concert and event
  • A catastrophic event happened

Data - Latest 13 years’

  • loss/severity/claim counts development triangles by accident year and development month
  • indemnity/medical

​

​

​

Discussion

Conclusion

Method

Background & Aim

Comparison

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· Aim

  • Calculate ultimate reserve estimates using two methods
    • Chain Ladder Method (Method 1)
    • Frequency-Severity Analysis (Method 2)
  • Compare ultimate reserve estimates difference and the reason for it
  • Find out the reflection of catastrophic event

​

​

​

Discussion

Conclusion

Method

Background & Aim

Comparison

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now

all cases closed

already paid/reported

how much we still need until all cases closed

·Same aim for two methods

Background & Aim

Method

​

Comparison

Conclusion

Discussion

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·Method 1 - Chain Ladder

2014

2015

​

2016

+

+

+

CDF =

CDF =

CDF =

=

Ultimate reserve estimate

All Cases

Classification by year

Regard as a whole

Ultimate

reserve for cases happened in 2014

Ultimate

reserve for cases happened in 2015

Ultimate

reserve for cases happened in 2016

+

+

*CDF: Cumulative Development Factor

Background & Aim

Method

​

Comparison

Conclusion

Discussion

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·Method 2 - Frequency-Severity

2014

2015

​

2016

Ultimate reserve estimate

All Cases

Classification by year

Take average

counts(C)

severity(S)

C*CDF

S*CDF

+

Ultimate

reserve for cases happened in 2014

C*CDF

S*CDF

+

Ultimate

reserve for cases happened in 2015

C*CDF

S*CDF

+

Ultimate

reserve for cases happened in 2016

counts(C)

severity(S)

counts(C)

severity(S)

+

+

=

*CDF: Cumulative Development Factor

Background & Aim

Method

​

Comparison

Conclusion

Discussion

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·Cumulative Development Factor

72 months

Ultimate

df = 1

60 months

24 months

12 months

df = 1.002

CDF

df = 1.426

Counts by year

Severity by year

Paid/Reported Amount by year

CDF

by year

Counts at Ultimate by year

Severity at Ultimate by year

Paid/Reported Amount at Ultimate by year

Background & Aim

Method

​

Comparison

Conclusion

Discussion

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Direct Accident Year Case Reported Loss Development Factors

INDEMNITY in $Thousands

Accident

Year

12

24

36

48

60

72

2016

47,025

62,026

68,849

71,259

70,974

71,116

2017

46,781

63,996

71,227

73,222

73,881

​

2018

46,352

68,446

78,366

81,043

​

​

2019

42,577

57,266

65,798

​

​

​

2020

38,744

58,387

​

​

​

​

2021

43,013

​

​

​

​

​

Target - Direct Accident Year Case Reported Loss Development Factors

INDEMNITY

Accident

Year

12 to 24

24 to 36

36 to 48

48 to 60

60 to 72

72 to Ultimate

2016

1.319

1.110

1.035

0.996

1.002

​

2017

1.368

1.113

1.028

1.009

​

​

2018

1.477

1.145

1.034

​

​

​

2019

1.345

1.149

​

​

​

​

2020

1.507

​

​

​

​

​

2021

​

​

​

​

​

​

·Age-to-Age Factor

Background & Aim

Method

​

Comparison

Conclusion

Discussion

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72 months

Ultimate

df = 1

60 months

24 months

12 months

df = 1.002

CDF

df = 1.426

Direct Accident Year Case Reported Loss Development Factors

INDEMNITY in $Thousands

Accident

Year

12

24

36

48

60

72

2016

47,025

62,026

68,849

71,259

70,974

71,116

2017

46,781

63,996

71,227

73,222

73,881

​

2018

46,352

68,446

78,366

81,043

​

​

2019

42,577

57,266

65,798

​

​

​

2020

38,744

58,387

​

​

​

​

2021

43,013

​

​

​

​

​

Target - Direct Accident Year Case Reported Loss Development Factors

INDEMNITY

Accident

Year

12 to 24

24 to 36

36 to 48

48 to 60

60 to 72

72 to

Ultimate

2016

1.319

1.110

1.035

0.996

1.002

​

2017

1.368

1.113

1.028

1.009

​

​

2018

1.477

1.145

1.034

​

​

​

2019

1.345

1.149

​

​

​

​

2020

1.507

​

​

​

​

​

2021

​

​

​

​

​

​

set tail factor = 1

take avg of last two years

·Development Factor

Background & Aim

Method

​

Comparison

Conclusion

Discussion

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Select tail factor

Select development factor

  • Cases that have been processed for a time we considered long enough have the development factor of around 1
  • Precise preparation for cases

·Decision making

  • Check outlier(catastrophic event)
  • Check latest years pattern

Background & Aim

Method

​

Comparison

Conclusion

Discussion

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· Result Comparison

Background & Aim

Method

Comparison

Conclusion

Discussion

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· Abnormal Case Methods Comparison

What happened

Case Description

Reflection on Method 1

Reflection on Method 2

One extremely heavy case happened

Counts grows a little, but severity grows a lot

Reserve ++

Count +

Severity ++

Many small cases happened

Counts grows a lot, but severity grows a little

Reserve ++

Count +++

Severity ~

A tragic event that caused many heavy cases

Counts grows a lot, and severity grows a lot

Reserve ++++

Count ++

Severity ++

Company regulation changed or government policy changed

Depends

Depends

Depends

Background & Aim

Method

Comparison

Conclusion

Discussion

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· Result Comparison

Background & Aim

Method

Comparison

Conclusion

Discussion

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· Method Comparison Conclusion

  • Difference in reflection of features
  • Method 1 is more sensitive to macro changes
  • Method 2 can show more details

Background & Aim

Method

Conclusion

Discussion

Comparison

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· Limitation

  • Loss of credibility (Method 1)
  • Can’t explain data from 2018

Background & Aim

Method

Conclusion

Discussion

Comparison

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· Suggestions for CUO

  • Check latest regulation change
  • Check if the case for 2018 will happen again
  • Seasonality

Background & Aim

Method

Conclusion

Discussion

Comparison

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Thank you!

2023.1.14