CAS Public Access DFA Model

CAS currently have an ongoing working party looking at this issue.

Their current DFA model is called DynaMo3. It is set up to run in an Excel spreadsheet in conjunction with @Risk. Unfortunately, I (ND) don't have @Risk, so will not be able to test it properly, though I will try to review it as far as possible before our next meeting. Perhaps someone with @Risk could have a look too?

Two papers on this model are available from the Pinnacle website:

• Building a Public Access PC-Based DFA Model
• Using the Public Access DFA Model: A Case Study

Brief Summary of DynaMo3

Overview

This model is designed for a US property-casualty insurer. It is based around a balance sheet projection for 5 years. It is currently set up for two lines of business, but as it is based in Excel, more could be added and formulae adjusted as required.

You can set the variables that you are interested in (e.g. statutory surplus at the end of year 5) and, once calibrated, you can run the desired number of simulations. Note this is relatively slow, but there is a counter to show progress. I believe you can graph the outputs, but this functionality did not work for me.

There does not appear to be any explicit assumption between random variables. Instead, the model focuses on the drivers of those correlations. For example, the interest rate modelling will drive correlations between asset classes, liabilities, premium rates. Similarly, claims liabilities between different lines of business will be both affected by the same inflation driver.

Interest Rate Model

The interest rate model influences many of the other aspects of the model, such as assets, claims inflation and the underwriting cycle. The model is based on the Cox-Ingersoll-Ross model of short term interest rates. As this is a mean-reversionary model, spot rates tend to the long term mean as the term increases.

The model is also used to generate claims inflation, via a further stochastic variable.

Investment Assets

These are modelled in detail based upon the stochastic term structure of interest rates modelled above. Bond cashflows are modelled, by type of bond (US Gov, Municipal, etc) and term. Certain structures are allowed for, such as callable bonds. Apparently, default risk is modelled, but this was not apparent.

Equity modelling is also based on short term interest rates. Overall market return is simulated and the insurer’s portfolio is assumed to change in line with the CAPM (i.e. based on the portfolio’s beta).

Underwriting Module

Four phases of the underwriting cycle are considered: (1) Mature Hard; (2) Immature Soft; (3) Mature Soft; (4) Immature Hard, with assumptions regarding the exposure growth and implied rate changes. Phases are modelled as a Markov Chain, though may be affected by catastrophes or extreme interest rates. Actual rates are linked to the stochastic inflation and recent loss ratio experience.

Claims Module

Claims are modelled by accident year. For the prior years (reserving risk), ultimates are set manually. For future years, (non-cat) claim frequency and severity are modelled separately to determine an ultimate.

Claims payment patterns are modelled via a beta distribution and determine the final ultimate claims costs.

Cat Module

Catastrophes for future years are modelled on a market wide basis via a Poisson distribution for frequency and a lognormal distribution for severity. The primary US state hit is sampled and a contagion matrix used to distribute the total loss to other states. This is spread across lines of business via assumptions regarding the insurer’s market share by state.

Reinsurance

Simple QS and XOL RI contracts are modelled. QS takes the relevant percentage ceded to determine recoveries. XOL assumes a lognormal distribution for claim severity, using the mean of the small losses and a larger coefficient of variation, in order to determine the proportion of claims affected by the RI layer.