Solvency II SCR Internal Models

Solvency II allows insurers to determine their own solvency capital requirements (SCR) under 1-year VaR. To do this, the insurers must use an internal model that has been accepted by their regulator. The computational demands of a nested stochastic solution are too high for market contingent liabilities, so firms are now investigating various variance reduction and approximation techniques. At Barrie & Hibbert, we categorise these techniques into three groups:

Stress and correlate: Producing stressed time-zero values and combine them under correlation assumptions. Note that Solvency II’s standard formula uses this approach.
Replicating function: Finding a function that fits through a number of different valuations and use this function directly to value under new different starting conditions. This covers techniques such as Least Squares Monte-Carlo and other Curve Fitting approaches.
Replicating portfolio: Finding a portfolio of assets that matches the cashflows of the liabilities under extreme conditions and use this portfolio to value the liabilities.

Using internal models for capital calculation will raise a number of questions, such as:

Which methods provide good estimates for different liability portfolios?
How do these different methods work and how can these techniques be improved?
How much error is associated with each estimate?
How to use an internal model for better risk management?
What should a 1-year distribution look like and how should it be calculated?

Barrie & Hibbert are actively engaged in research and consultancy to help you answer these questions, and have made their latest research available here for you to download.

In addition to the articles linked below, Barrie & Hibbert have also authored a series of articles at Insurance ERM, entitled Calculating the solvency capital requirement. Read Part 1, Part 2, and Part 3 at the Insurance ERM website.

Read our Research:

A comparison between curve fitting and least squares Monte Carlo techniques

This note discusses the similarities and differences between least squares Monte Carlo and ‘curve- fitting’ procedures for 1 year VaR calculation. We look at how both techniques approximate a nested stochastic calculation. Further, we show that ‘curve fitting’ is a special but inefficient case of a least squares Monte Carlo technique.
Solving the “nested stochastic problem”: a Least Squares Monte Carlo approach to liability proxy modelling and capital calculation

This note outlines a method which can be used for solving the nested stochastic problem, creating a function which approximates a multi-dimensional insurance liability through the use of Monte Carlo Simulation and Regression. The process, model choices, automation and validation are discussed in detail.

Although a liability proxy function has many applications within insurance risk management this note will discuss use of proxy modelling in the context of a Solvency II 1 year VaR capital calculation.
A primer in replicating portfolios

New to the idea of replicating portfolios? Adam Koursaris will help you to appreciate and understand what they can do for you
Improving capital approximation using the curve-fitting approach

The second article in the SCR calculation series from Adam Koursaris looks at using a curve -fitting approach to improve capital approximation.
The advantages of Least Squares Monte Carlo

The third article in our SCR calculation series look at the least-squares Monte Carlo (LSMC) approach and some of its advantages over curve fitting.
Calculating the Solvency Capital Requirement

In the first of his series of articles on SCR calculation, originally published in InsuranceERM, Adam Koursaris highlights some of the issues of covariance matrix methodology as a basis of the Solvency II standard formula.
Risk aggregation: generalising dependency in the Barrie & Hibbert ESG

In the first of our Global insurance risk management reports, we describe a relatively straightforward way of changing dependency in Barrie & Hibbert’s ESG. This report looks at how dependency arises in the ESG, in particular how we can change dependency through changing the distribution of the random shocks used to drive the ESG models.
Where is that Elusive 1-Year Tail?

Estimates of the location of the ‘tails’ of the equity returns distribution are now a key part of economic capital assessment work for life insurers. In this note we take a very brief look at some possible approaches to estimation of the 99th percentile tail position and highlight one approach we just donÂ’t like: ‘bootstrapping’ (i.e. sampling) daily price changes or returns from the past empirical distribution to manufacture a distribution of possible 1-year returns.
‘Smart’ Nested Simulation: Learning from Option Traders

Having developed models for market-consistent valuation of their balance sheets, actuaries are now looking to take these models a stage further, asking the question: how will my balance sheet change as I project forward during the course of a best-estimate stochastic projection?
1-year VaR assessment and dynamic management actions

In this note, an illustrative case study is used to demonstrate the materiality of this effect in the context of dynamic management actions in with-profit business.
Quantifying and minimizing the uncertainty in tail estimates

An estimate of capital requirements which is simply based on a single 'best guess' number e.g. "my 99.5% 1-year VaR is £1,000m" provides limited information as it says nothing about the statistical error around this estimate. What if the ESG is run under a different seed and the number changes to £1,100m or £900m? Furthermore, it is an estimate of a single point on the distribution (the 99.5th percentile). What about the 99.9th? Or the 99.5th CVaR? This note outlines a methodology (extreme value theory) for answering these questions.
One year calibration and choice of equity model

This Insight note provides guidance on how to make the correct choice of equity model for Solvency II. It illustrates the differences between a constant volatility and SVJD model with a back testing example against actual returns in 2009.
Nested Simulation for Economic Capital

A common definition of an insurer‟s economic capital requirements is based around a 1-year Value at Risk (VaR) metric. This defines capital requirements in terms of some tail percentile (typically the 99.5th percentile) of the market-consistent value of the insurer‟s balance sheet in 1 year‟s time. The problem of estimating such a metric naturally leads to the concept of nested simulation.
Solvency II: Preparing your ESG for Internal Model Approval
Model Insights - Replicating portfolios for economic capital

In this note we demonstrate the use of Replicating Portfolios for calculation of economic capital requirements using a simple illustrative example. This analysis indicates that an apparently good RP (based on a standard goodness-of-fit metric) can result in significant errors in estimated capital requirements. We also indicate how the RP technique can be supplemented with Monte Carlo valuation techniques in order to minimise the approximation errors introduced by the use of RPs alone.

Barrie & Hibbert