When best to use deterministic vs. Stochastic models
stochastic is best when
- assessing the impact of guarantees
- when variable of interest has stable and predictable pdf.
- indicating the effect of year-on-year volatility, random fluctuations, on risk
- identifying potentially high-risk future scenarios, for example, by tracing the sequence of events that have led to the worst simulated outcomes.
deterministic is best when:
- you need a quick result, which is less computationally expensive.
- model results can be very sensitive to the pdf chosen
- you need a more understandable result for a non-technical audience
- there is a clear indication of which scenarios have been tested (not just all of them as for stochastic)
- for operational risks where quantity cannot be determined stochastically
- when trying to model cause and effect relationships
- stress testing a deterministic model can be used as a check for a stochastic model
Risk-neutral vs. Real-world calibration
Risk neutral, also known as ‘market-consistent’, calibration.
- used for valuation purposes, particularly where there are options and guarantees.
- aim is to replicate the market prices of actual financial instruments as closely as possible, using an adjusted, risk neutral, probability measure.
Real-world calibration.
- used for projecting into the future
- e.g. calculating the appropriate level of capital to hold to ensure solvency under extreme adverse future scenarios at a given confidence level.
- aim is to use assumptions that reflect realistic ‘long-term’ expectations and that consequently also reflect observable ‘real-world’ probabilities and outcomes.
Interaction
Interactions exist when the effect of one factor varies depending on the value of another factor.
Example: age (under 30, above 30), level (1,2,3)
Complete interactions between factors are where a new, single factor, can represent every combination of two other factors.
under301 + under302+…
Marginal interaction is when an interaction term is added to the model to reflect the interaction between two factors in the model.
age*level
Aliasing
- A linear dependency among observed covariates in a model.
- Intrinsic aliasing is when there are inherent dependencies in the definition of the covariates.
- Extrinsic aliasing is when dependencies arise from the nature of the data itself rather than inherent properties of the covariates.
Parameter smoothing
- In a GLM model, there may be a large number of explanatory variables and factors.
- This can result in large variation in the premium rates outputted
- Parameter smoothing aims to retain the granularity in the data but to use patterns in the data to help group and thus smooth the parameters.
- could group data prior to putting it in the model
- could group using modelling package, if multiple relativities of a factor grouped together = custom factor
What are the shortfalls of multiple linear regression and how does GLM solve for it?
- assumes residuals are normally distributed
> not the case, especially with claims which are positively skewed
> solved through exponential family of distributions - assumes the relativities are additive
> link function helps to produce multiplicative or other kinds of relationships
> link function should be differentiable so MLE of relativities can be estimated
> link function should be monotonic so relationship between response and linear predictor is maintained. - the variance is assumed to be constant
> for exponential distributions, the mean increases with the variance of the response
> more in line with claims distributions
Requirements of a good model
- Appropriate inputs to be used
- Adequately reflect the risk profile being modelled
- Parameters must allow for all features to be modelled
- Valid, rigorous, and adequately documented
- Easy to appreciate and communicate
- Capable of independent verification
- Sufficiently detailed but not excessively complex
- Flexible and capable of refinement and development
- Able to facilitate testing of results
- Sensible joint behaviour of variables.
Immunisation
- used when cannot match liabilities with assets perfectly
- immunisation protects against changes in interest rate
- only useful for guaranteed liabiltiies
- liability and asset position will be immunised if:
a) PV (liability outgo) = PV (asset proceeds)
b) DMT (liability outgo) = DMT (asset proceeds)
c) The spread about the mean term of the value of the asset proceeds is greater than the spread of the value of the liability outgo.
Different models to model how asset prices move over time
Different models to model mortality
- Lee-Carter Model - future mortality probability follow a lognormal distribution. Focuses on time-trends.
- Cairns-Blake-Dowd (CBD) model - future age-based mortality probability, follow a bivariate lognormal distribution. Considers both age and time.
- Cohort effect - different cohorts/generations have different mortality experiences
Model process
- Appropriate data
- Appropriate model
- Importance of each explanatory variable
- Model goodness of fit
- Sensitivity test
- Model restrictions
Use of ALM in different scenarios
DB: determine appropriate pension increases, funding level
DC: appropriate investment strategy to achieve target IRR
Insurer: solvency level
