**Custom calibrations of economic scenario models are becoming more common, says Matthew Lightwood, and actuaries will have to use considerable forethought at the model selection stage**

Will interest rates fall or turn negative in the next five years? What is the probability of a Eurozone break-up in the next 12 months? What will be the value of the FTSE tomorrow?

Insurance and pension firms are increasingly requiring that their own view of future market dynamics is embedded into their risk modelling environments. To do this effectively, one must have the people, processes and tools in place to implement these views. It is this implementation step that has often proved the most challenging for users of statistical models, such as those found within an 'economic scenario generator' (ESG).

**Views, predictions and uncertainty**

Views as they relate to statistical or stochastic models are often confused with predictions. A prediction is a single-point estimate of the future. A view may encompass a prediction but includes the addition of uncertainty, acknowledging that our best estimate of the future is just one possible outcome in a wider distribution of things that can happen. There are many applications for a custom ESG calibration embedding an own view, including:

**Regulatory risk management -**Some elements of regulatory regimes, such as Article 120 (use test) of the Solvency II directive, require firms to take into account the assumptions of the internal model in making business decisions. Having ownership of the underlying assumptions of the economic models is a key element in satisfying such regulatory requirements.

**Stress testing -**Stress testing is a widely used tool in risk management. Stressing the core assumptions of models represents an alternative view that allows for the impact of extreme and unexpected events to be studied and quantified.

**'Strategic asset allocation' (SAA) -**SAA is commonly based on analysis of expected returns and risk from an ESG over a medium-term time horizon, for example, five years. To be most effective, it should consider the optimal asset allocation, taking into account the risks inherent in the liabilities and the implied cost of capital. The SAA calibration can embed the shorter-term assumptions of the internal model into a multi-year stochastic projection.

Regardless of the intended use of an ESG, we must first consider which variables to take a view on. For practical reasons these will normally be restricted to those variables that are most material. We should also decide whether our best estimate forms the mean or median for the projected distribution, and whether to use standard deviation as the sole measure of risk or to specify the distribution further by also targeting tail measures such as the 0.5th percentile. Data analysis and expert judgment are then the cornerstones for the construction of the final view.

**Practical implementation of own views**

Implementation of an own view usually involves either the manipulation of an existing scenario set or the estimation of the ESG parameters, taking into account the view and/or market data. Depending on the model used, the nature of the view, and the materiality of the risks being modelled, a number of methods and techniques are available:

**Analytical data driven methods -**Many techniques are available for the analytical estimation of model parameters based on market data. These techniques include 'maximum likelihood estimation' (MLE) and the 'generalised method of moments' (GMM). Both of these techniques aim to recover the true or most likely parameters of the data generating process from supplied market data.

**Path filtering and path reweighting -**Path filtering refers to a process of selecting a subset that meets the specified views from a large simulation. Path reweighting (typically employing maximum entropy constraints) changes the relative weights of the simulated stochastic paths, moving the overall distribution of results closer to the desired view.

**Parameter optimisation -**With parameter optimisation, an optimiser is used to find a set of parameters that minimises the difference between the own view and their simulated modelled values. For very tractable ESG models the statistical moments of the distribution may have an explicit mathematical form which permits 'direct moment targeting' (DMT), the application of highly efficient algorithms to locate parameter sets that optimise the fit to the targeted economic view. For less tractable models, a 'brute force optimisation' in which a full re-simulation is required at each optimisation step can be used, but it may take many hours to find a solution, which can often be suboptimal.

Which method is ultimately chosen will be determined by practical considerations. These include the availability of suitably expert internal resources to implement and maintain the process, the types of views deemed necessary, the models used and the capabilities of any recalibration tools packaged within the ESG.

**Case study: UK gilt yields**

How important is the view to the robustness of a model? To answer this question we consider two scenario sets for gilt yields over a one-year time horizon. Leveraging the tractability of an extended multifactor Cox-Ingersoll-Ross model, we implement our views using DMT rather than a brute force approach. Starting from the 31 December 2013 yield curve, we form targets for the means, standard deviations and 0.5th percentiles of the distribution of the one-year, five-year, and 10-year yields for both a 'low yield' scenario set and a 'high volatility' scenario set. The precise values of the expressed views used and the values achieved in the recalibration are shown in

*figure 1*.

_{Figure 1: Recalibration to two alternative views on gilt yields}

The recalibration of the model for both low yield and high volatility was achieved in less than 90 seconds with an average absolute error of 2bps for the former and 2.5bps for the latter. Of course such speed and accuracy are only possible because of the tractability of the chosen model and the efficiency of the DMT technique used.

Figure 2 compares the simulated distributions of each case with the actual values on 31 December 2014. What is interesting to observe is that the different views are equally robust when compared to what actually happened to gilt yields in 2014. There is nothing special about one view over another view, and no correct view. What is important is that the view is arrived at logically and systematically and is appropriate for the use.

_{Figure 2: Simulated distributions from two gilt yield custom calibrations}

Custom calibrations of ESG models are becoming more common, driven by increased demand to have ownership of the economic assumptions underlying models and the calibration process, and a desire to use the same ESG models for multiple applications. Custom calibrations also allow the effect of alternative views on key metrics such as value at risk and the solvency capital requirement to be assessed. Forming views for a given variable may be relatively easy and the precise view may be less important than the fact that they are arrived at in a logical way. Implementation of own views is likely to be a significant technological challenge and a drain on resources. Overcoming these challenges requires considerable forethought at the model selection stage, with tractability and the availability of recalibration tools being key selection criteria. Only then can the right process be put in place and repeated by non-expert users, creating calibrations specific to the intended use**. **

*Dr Matthew Lightwood is vice president, quantitative finance, Conning Asset Management*