ABSTRACT
In this chapter I discuss the use and some of the challenges associated with economic scenario generation within an insurance context. In Europe, the Solvency 2 directive came into force in January 2016 and this has put an onerous requirement on insurers to model the risks on their balance sheets by stochastic methods. Under Pillar 1 of the directive, insurers who choose to build an internal model will need to produce scenario sets to drive the market and non-risk components of their asset and liability modelling systems. Furthermore, they must be able to create scenario sets under both real world and market-consistent/risk-neutral measures for forecasting and pricing, respectively.
In this chapter I cover the main asset classes for modelling market risk and discuss scenario generation to cover non-market risks such as policy holder lapse and surrender risk, and operational risk. This extends the notion of an economic scenario generator to a risk scenario generator. Non-market risks must also be considered under both Pillars 1 and 2 of Solvency 2. I introduce the flexible copula co-dependency structure as a flexible way to correlate these variables.
To illustrate the degree of complexity in modelling market and non-market risks in scenario generation, I go into some detail with two examples. Firstly, a method to represent the distribution function of composite non-market operational risk variables with finite elements is given. Secondly, a method using orthogonal polynomials is applied to solve the problem of correlation between stochastic volatility jump and diffusion models of equities and any other assets. Both these methods are new and permit the variables to be easily correlated through a copula and marginal factorization.
Finally, I conclude with a discussion on the challenges I consider as important and some others that I have omitted. Any views held are, of course, entirely my own and are not necessarily representative of the views of Moody's Analytics.
