Actuarial Notes

Heavy Models, Light Models and Proxy Models: A Working Paper

By The Proxy Model Working Party: Christopher Hursey, Matthew Cocke, Cassandra Hannibal, Parit Jakhria, Iain MacIntyre and Matthew Modisett · Institute and Faculty of Actuaries · 2014 · CP312-102-25

Study guide: Exam CP-312

A working paper of the Proxy Model Working Party, presented to the Institute and Faculty of Actuaries in London on 24 February 2014. It looks at the types of proxy model available to practitioners and suggests a basic framework for "replicating formula" proxies, within which the options in design and implementation are discussed. It closes with four specific proxy models in greater detail, two of which are the subject of a case study, leading to a result on the distinction between risk scenario accuracy and risk distribution accuracy.

On the syllabus

  • Exam CP-312 — CP312-102-25: Chapters 1-5, for outcomes 1d (Topic 1) and 2c (Topic 2).

1 Introduction

2 Background

  • 2.1 A Brief History of Modelling Techniques
  • 2.2 Why are Proxy Models Needed?
  • 2.3 What is a Proxy Model?

3 Designing and Choosing a Model

  • 3.1 Types of Model
  • 3.2 Use of the Model
  • 3.3 Complexity versus Accuracy
  • 3.4 Intuition

4 Methods for Evaluating a Proxy Model

  • 4.1 Introduction
  • 4.2 Quality of Fit
  • 4.3 Ease of Implementation & Cost
  • 4.4 Model Stability and Factors that Influence it
  • 4.5 Complexity – Management Acceptance

5 Calibration

  • 5.1 Introduction
  • 5.2 Determining Formula Structure
  • 5.3 Determining Formula Coefficients
  • 5.4 A Special Case – Least Squares Monte-Carlo

6 Specific Models Discussed in Detail

  • 6.1 Methodology
  • 6.2 Replicating Polynomials
  • 6.3 Radial Basis Functions
  • 6.4 Replicating Portfolios
  • 6.5 Commutation Functions

7 Summary

  • 7.1 Final Thoughts
  • 7.2 Next Steps

References

Appendix 1 Convergence of Least Squares Monte Carlo

Appendix 2 Optimised Components vs Optimised Whole, An Example

Appendix 3 Weighted Least Squares Fit, Sample Proof

Sources