RBC Easy as 1,2,3. David Menezes 8 October 2014

Transcription

1 RBC Easy as 1,2,3 David Menezes 8 October 2014

2 Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: "There are three kinds of lies: lies, damned lies and statistics." - Mark Twain's Own Autobiography: The Chapters from the North American Review 2

3 Agenda 1. Introductions 2. What this is, what this is not 3. Context 4. The eagle-eye view 5. The detail 6. Example outputs 7. Your questions 3

4 Introductions David Menezes UK trained actuary with 14 years experience across consulting and industry Head of Capital at Atrium Underwriters (Lloyd s of London) 5 Yrs Co-author of 2012 GIRO paper, Practical Issues in Solvency II Internal Model Approval Process (IMAP) 2 years stochastic ALM for global corporate pension fund clients at Mercer Investment Consulting Member of ASHK RBC Taskforce 4

5 What this is, what this is not This is not a discussion about the new RBC framework proposal ASHK Taskforce is collectively forming a view on the proposals and a separate session will be set-up to discuss initial observations and to canvass opinions and views So what is this talk about? Discussion around context and approaches used internationally Exploration of the internal model method in particular 5

6 Context: What is capital? Put simply, capital refers to assets held in excess of a firm s liabilities There are several types of capital: Regulatory capital: the amount of money required to operate within a market, based on the regulator s requirements Economic capital: the amount of money needed to operate ain a manner consistent with a firm s strategic goals (aka an amount consistent with a firm s risk appetite ) Rating agency capital: the amount of money required to maintain a specific credit rating 6

7 Context: Factor-based or Internal models? Factor-based Deterministic / stress test Typically stochastic Simple Typically rely on financial statements to calculate No allowance for risk management profile Complex Requires expertise Internal Model Requires software; black box? May require development of systems to produce data Allows for risk management approach Regulatory default, always worth calculating Usually only available in more mature markets (Exposure is an ) Objective (measure of risk) Subjective Easy to communicate to decision makers and third parties Communication is more difficult, but Generates greater internal understanding/dialogue with management Approval assured Significant effort to get regulatory approval Applying a probabilistic interpretation to the quantum is arbitrary Probabilistic statistics are a natural extension interpretation is still arbitrary! Probabilistic interpretation of quantum is arbitrary Probabilistic statistics are a natural extension interpretation may still be arbitrary though... Application is primarily regulatory focussed Variety of business applications, i.e. wider than regulatory capital 7

8 Context: And now, the regulatory roundup.? Emerging Development stage Mature And the future? Financial Times - October 9, 2013 Large insurers reserve judgment over global capital standards 8

9 The eagle eye view: Conceptual goals Regulatory capital calibrated with reference to projected financial loss under a specified level of stress. Projected financial loss? P&L loss Specified level of stress? A probabilistic measure. Usually the 99.5% percentile (aka Value at Risk or VaR). Some regimes are considering 99% Tail Value at Risk (TVaR). TVaR? Average loss beyond a certain percentile. Standard approach for capital allocation calculation. For non life: TVaR 98-99% ~ VaR 99.5%. Economic Capital >> Regulatory capital. VaR 99.9% often used. Roughly A- credit rating. The goal therefore is a model that produces a dynamic view of the P&L. We will simulate entity s financial results many times. Each time we vary different P&L inputs and collect results. Capital is 99.5% downside result 9

10 The eagle eye view: GI P&L motivation # Quantity Notes 1 Gross Premiums Earned 2 Reinsurance Premiums Includes reinstatements 3 Net Premiums Earned (1) less (2) 4 Gross Claims Incurred Includes IBNR (i.e. accountants incurred) 5 RI Recoveries Incurred Includes defaults 6 Net Claims Incurred (4) less (5) 7 Underwriting Result (3) less (6) 8 Investment Income Total rate of return 9 Insurance Result (7) plus (8) 10 Other Taxes, dividends, etc 11 Profit (Loss) (9) Plus (10) 10

11 The eagle eye view: Structural Blueprint P&L Profit / Loss Simulate ESG Insurance Result UW Result Other Market Risk Premium Risk Reserve Risk Credit Risk Att Lrg Cat Motor Att Cat Binary EC Other... Cat Data 11

12 The detail: Loss Generation - Marginals Risk Type Approach to generation Underwriting Risk Loss ratio Frequency / Severity Event Loss Table (Cats) Scenario-based Reserving Risk Bootstrap Calibrated parametric Scenario based Credit Risk Bernoulli (Reinsurer) ESG (market) Market Risk ESG Parametric investment return Operational Risk Flat add-on Stochastic risk regsiter Scenario based Liquidity Risk Scenario based 12

13 The detail: Dependencies - Approach Premise: Cause and effect Situations where you ll see this? Mathematical approach Drivers Also referred to as ripple effects Where event sets are used i.e. ESG or proprietary catastrophe models Insurance cycle Various, but simple as an if statement typically the triggers for a (re)action. Correlations Multiple drivers may cause different quantities to behave in tandem. An implicit approach is needed in this case Intra-class correlations Variance Covariance correlation matrix to aggregate simpler point estimate models Copula is used for more advanced applications Pros/Cons Easy to e/xplain Too blunt Potentially hard to explain Arbitrary selections leading to material levels of expert judgement 13

14 The detail: Dependencies Copulas Typical approach used in non-life models. Most practitioners favour the simplest model, which is a Gaussian copula To allow for more tail dependence use a t Copula, as only one more degree of freedom and parameterisation is arbitrary Theoretically the t Copula will converge with the Gaussian copula as the number of degrees of freedom tends to infinity 14

15 Example Outputs 15

16 Questions? 16

17 So are internal models black boxes? To some extent, yes. However, I prefer the words of another statistician: All models are wrong, some are useful." - George Box 17