Aniketh Pittea Spoke at a Finance and Insurance Conference in Greece

PhD Student in Actuarial Science, Aniketh Pittea, from the School of Mathematics, Statistics and Actuarial Science (SMSAS) at the University of Kent, spoke at the ‘Recent Developments in Dependence Modelling with Applications in Finance and Insurance – Fifth Edition’ Conference in September.

Aniketh delivered a talk titled, ‘Simulating variables using graphical models’ at the Conference held in Aegina, Greece.

Abstract:

Actuaries and financial risk managers use an Economic Scenario Generator (ESG) to identify, manage and mitigate risks at a range of horizons. In particular, pension schemes and other long term businesses require ESGs to simulate projections of assets and liabilities in order to devise adequate risk mitigation mechanisms. This requires ESGs to provide reasonable simulations of the joint distribution of several variables that enter the calculation of assets and liabilities. In this paper, we discuss how a graphical model approach is used to develop an ESG, and also provide a specific application.
A wide range of ESGs are currently in use in industry. These models have varying levels of complexity and are often proprietary. They are periodically recalibrated, and tend to incorporate a forecasting dimension. For instance, they may incorporate a Vector Auto Regression model. Alternatively, many rely on a cascading structure, where the forecast of one or more variables is then used to generate values for other variables, and so on. In each case, these models balance the difficult trade-off between accurately capturing both short and long term dynamics and interdependences. We argue that, for the purpose of risk calculations over very long periods, it may be easier and more transparent to use a simpler approach that captures the underlying correlations between the variables in the model. Graphical models achieve this in a parsimonious manner, making them useful for simulating data in larger dimensions. In graphical models, dependence between variables is represented by “edges” in a graph connecting the variables or “nodes”. This approach allows us to assume conditional independence between variables and to set their partial correlations to zero. The two variables could then be connected via one or more intermediate variables, so that they could still be weakly correlated.
We compare different algorithms to select a graphical model, based on p-values, AIC, BIC, and deviance using R (and provide the relevant packages). We find them to yield reasonable results and relatively stable structures in our example. The graphical approach is fairly easy to implement, is flexible and transparent when incorporating new variables, and thus easier to apply across different datasets (e.g. countries). Similar to other reduced form approaches, it may require some constraints to avoid violation of theoretical rules. It is also easy to use this model to introduce arbitrary economic shocks.
We provide an example in which we identify a suitable ESG for a pension fund in United Kingdom that invests in equities and bonds, and pays defined benefits. While more complex modelling of the short term dynamics of processes is certainly feasible, our focus is on the joint distribution of innovations over the long term. To this end, we simply fit an autoregressive process to each of the series in our model and then estimate the graphical structure of the contemporaneous residuals. We find that simulations from this simple structure provide plausible distributions that are comparable to existing models. We also discuss how these models can be used to introduce nonlinear dependence through regime shifts in a simple way.
Overall, we argue that this approach to developing ESGs is a useful tool for actuaries and financial risk managers concerned about long term portfolios.