### EXECUTIVE SUMMARY

Using stochastic calculus, modern project management tools and open source software, we moved the Cost of Guarantee calculations for a Life Insurer from an error-prone spreadsheet process into a reproducible document containing all the relevant information and assumptions.

### OUTLINE

A small life-insurer had a closed With Profits (WP) fund for which they had provided maturity guarantees to the policy holder upon retirement. They had old software that calculated the Cost of Guarantees on these policies but documentation was sparse and a number of assumptions underlying the calculations were not readily apparent. As a result, questions were asked over the accuracy of their calculations as they were not easy to audit or verify.

### SOLUTION

Using reproducible research techniques and stochastic calculus with Monte Carlo simulation, we were able to reproduce the calculations in the model in a much more discoverable and transparent way. A major benefit of the approach was the self-documenting nature of the software, allowing us to mix text, code and visualisation into a single document. Our Monte Carlo simulation enabled us to easily extend the simulation beyond the simple Black-Scholes option formula, facilitating a more direct calculation of the option characteristics of fund.

### BUSINESS OUTCOMES

- The Cost of Guarantee calculations were much easier to verify and audit.
- Material reductions in time spent on data cleaning and verification
- Ease of change of distributional, yield curves and volatility asumptions
- Subsequent work on the calculations were simpler to do

### PROJECT OUTCOMES

- Monte Carlo simulation enabled risk assessment previously unavailable
- Risk assessed on ‘full fund’ basis rather than individual policies
- Alternative distributional assumptions straightforward to apply
- Stress testing easy to set up and run

### IMPLICATIONS

- Existing calculations verified for BEL but missed correlation risks
- Future iterations of the model simple to implement
- Tail risk of the liabilities significantly underestimated

### KEY CLIENT BENEFITS

- Future iterations of the model simple to implement
- Full pipeline of data manipulation to CoG calculation
- Underlying assumptions and stressed readily discoverable

### TOOLS AND TECHNIQUES

- R
- Excel
- Stochastic Calculus
- Monte Carlo Simulation
- Reproducible Research

### CONTACT DETAILS

Michael Crawford

M: +353 (0)87 996 7437

E: mcrawford@agrippadataconsulting.com

Mick Cooney

M: +353 (0)87 819 5992

E: mcooney@agrippadataconsulting.com