Global Best Practices in ERM for Insurers and Reinsurers Webcast

December 1, 2009

Session 3E: Economic Capital Models: Design, Calibration, Validation and Updating

(Advanced Level)

John Brunello John Hibbert

Moderator

Alessandra Gambini

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Session 3E: Economic Capital Models: Design, Calibration,

Validation and Updating(Advanced Level)

Moderator: Alessandra GambiniPresenters: John Brunello

John Hibbert

Global Best Practices in ERM for Insurers and Reinsurers WebcastGlobal Best Practices in ERM for Insurers and Reinsurers Webcast

From ERM to Solvency II: EurizonVita Case Study2009 Global Best Practices in ERM for Insurers and Reinsurers Webcast

1st December 2009 – Session E3

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Financial Analysis Program

Models and Technologies Development Office

Financial Analysis Program

The FAP System

Model life-cycle

Coverage of Solvency II risk drivers

Processes

Extra-process tasks

Strengths

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Models and Technologies Development office

EurizonVita’s Models and Technologies Development office (SMT - Sviluppo Modelli e Tecnologie) was originally created within the Finance and Actuarial department (and since reassigned to the Administration, Finance and Control department) with the following mission:

Act as a coordinator between various functions across the company (Actuarial, Investments, Control, Risk Management...) for quantitative model development, guaranteeing consistencybetween methodological approaches and processes adopted for different needs

Guarantee that a complete, relevant and updated documentation is available for all models

Adopt (and, if need be, adapt) technologies specific to financial modelling and simulation applications, maximising the benefit to cost ratio and return on investments

Supervise the design, implementation and maintenance of the Enterprise Risk Management system

The specific functional skills required for financial and actuarial modelling is the rationale for locating SMT in the same organisational framework as the functions in charge of the various value and risk evaluation processes.

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Financial Analysis Program

Ensure that projects in the quantitative modelling arena are properly coordinated and prioritised, taking advantage of possible synergies

Develop an effective Enterprise Risk Management system to support various processes requiring dynamic asset/liability financial analysis, guaranteeing that applied methodologies are consistent

Ensure that data and assumptions used for all evaluations are automatically traced, supporting internal (audit) and external (regulatory) reviews of both models and results

Ensure model transparency: each model’s inner workings shall be easily accessible and auditable down to the maximum level of detail

Provide timely stochastic results both for regulatory evaluations and for extra-process ad-hoc analyses (e.g. product development, portfolio spin-off and mergers, updates to investment policy, etc.)

Develop internal know-how, avoid operational dependency on external consulting and limit recurring costs

In September 2005 SMT was tasked to design and implement a long-term development programme, named Financial Analysis Program (FAP), with the following goals:

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FAP system

Data collection at the maximum detail level and with explicit validation steps

Full traceability of the information workflow through all evaluation processes, certification and audit support and guaranteed repeatability of every result

Reduced execution times for stochastic simulation cycles (a few hours max.) without excessive reliance on simplifications and aggregations affecting statistical quality and calibration testing

Business decision support (what-if analysis) and capability to feed simulations with third-party economic scenarios

Modularity, ease of evolution, specific high performance parallel computing architecture and state-of-the-art security

Within the scope of the FAP program, EurizonVita developed internally a bespoke Enterprise Risk Management system (the “FAP system”) designed to provide full end-to-end support(from data collection to final reporting) to value and risk evaluation processes. The fundamental principles followed across all development phases are:

Right from inception, functional specification and certification for ALM models are under the responsibility of end-users (albeit under the supervision of and with assistance from SMT).

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Unit-linked static projection engine

(MoSes)

Traditional (with-profit) static

projection engine (MoSes)

Liability operations system

(Universo + Host FV)

Asset operations system(Sofia)

Asset data validation and enrichment

Economic Scenario Generator

Index Scenario Generator

Traditional (with-profit) ALM stochastic

projection engine

Unit-linked ALM stochastic projection

engine

Policies

Positions Positions

Intranet user interface (FAPweb)

Common FAP database

SLiM (Static Liability Model)

DALiA (Dynamic Asset/Liability Analisys)

LiSA (Linked-products Stochastic Analisys)

ARiM (Asset Risk Measurement)

Pre-existing

FAP program

Legenda

Liability data validation and enrichment

Cash-flow

Cash-flow

Model point

Model point

FAP system: overall architecture

ESG

(Economic Scenario G

enerator)

N.B.: the Guaranteed Pension Fund module is not shown for ease of representation

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FAP system: economic scenario generator

5 volatility drivers (interest rates, inflation, credit spreads, foreign exchange rates and equity returns) with linear correlations, 5 economies (EUR, USD, JPY, CHF, GBP), risk-neutral and real-world modes, high frequency scenarios (monthly time steps) and highly detailed term structures (30+ nodes)

Modular plug-in structure: easy addition of new alternative modules to the model base (e.g. for interest rates: CIR, CIR++, Longstaff-Schwartz) and easy assembly into new econometric models

Complete traceability of parameters used for generation of each scenario (including volatilities, seeds and correlations used for pseudo-random series generation)

Advanced diagnostic tools enabling timely testing of the financial consistency and statistical quality of stochastic scenarios

The FAP system features an embedded proprietary Economic Scenario Generator (ESG) feeding all the value and risk evaluation processes within EurizonVita:

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FAP system: asset risk measurement

Market data

Asset registry

Positions

Asset Data Set

Internal pricing

and rating

VaR, CredRisk

Provider

Asset back office (Sofia)

Providers + manual

completion

ModelliALM

Financial risk

reporting

Internal pricing tool, independent form the pricing modules embedded into ALM models (cross-validation)

Guaranteed data consistency between risk management, performance attribution and ALM simulations

Asset data available on back-office systems is complete and accurate from an accounting pointof view, but is generally not directly suitable for pricing and financial risk measurement purposes (especially for derivative and structured products with complex indexation rules, credit-risk related information - such as issuer and guarantor group hierarchy for concentration risk - and market data - such as volatility surfaces and issuer-specific spreads).

The ARiM (Asset Risk Measurement) module ensures asset data validation and enrichment and provides tools to monitor and manage the Company’s financial risk exposure.

Perfor-mance

reporting

ModelliALM

ALM models

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FAP system: static liability modelling

Assum-ptions

Products registry

Policies

Liability Data Set

Static liability projection

engine (MoSes)

Manual input

Liability back-office (Universo)

Manual completion

ModelliALM

Actuarial reporting

ModelliALM

ALM models

Output

Liability data available from portfolio back-office systems is also generally incomplete for actuarial projections (e.g. assumptions); the SLiM (Static Liability Model) module ensures liability data validation and completion, management and tracing of assumptions and automatic archival of results for actuarial “static” projections (i.e. non-ALM).

The “calculation engine” used for actuarial static is an off-the-shelf modelling environment (MoSes, marketed by Towers-Perrin Software Solutions) and therefore cannot properly be considered part of the FAP system; however, the data flows to and from the static liability models have been fully interfaced.

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FAP system: dynamic ALM models

At the heart of the FAP system, a suite of dynamic ALM (Asset/Liability Management) models, one for each line of business, can simulate at each monthly time step the reciprocal interaction of assets and liabilities based on future economic scenarios.

For maximum consistency, the same ALM models are used both for deterministic projections(what-if analysis, stress scenario analysis, budget projections, etc.) and for stochastic Monte Carlo simulations (EEV, MCEV, Economic Risk Capital, Solvency II SCR) including the pricing of the time value of embedded options and guarantees taking into full account risk mitigation factors and management actions (investment strategy, hedging, risk and profit sharing with policyholders, etc.).

Dynamic cash-flow Financial

income

Fund return

Asset

ManagementLiability

• Investments / divestments

• UCGL management

The “key-words” of FAP’s ALM models are:

dynamic cash-flow based: based on dynamic cash-flow projections

bottom-up: data are fed to the models at a high level of detail, thus enabling value and risk allocation to lines of business, product families, distribution channels, etc.

full balance-sheet: measures the balance-sheet impact of market volatility

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Lapses -50% 405 model points226'287 policies

-14.08%+11.76%

FAP system: linear aggregation limits

Linear aggregation techniques applied to policies (so-called “model points”) incur in well known pricing errors when applied to non-linear payoffs. ALM dynamics amplify such pricing errors to the same order of magnitude as the effects of shocks we are required to measure.

Aggregation can be “calibrated” to minimize errors in a few known deterministic scenarios, but ensuring that calibration itself does not introduce artifacts is a “hard” problem. Experience shows that average aggregation ratios above 50:1 are well in the “danger zone”

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FAP system: replicating portfolios

Dynamic cash-flow

Financial income

Fund return

Asset

StrategyLiability

• Re-balancing

• UCG/L management

Calibration

Replicating portfolio

NPV

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FAP system: replicating portfolios

Pros:

• Instantaneous re-valuation of the mark-to-market value of a life portfolio in different market conditions

• 'Insight' brought by interpreting the options in the replica

• Aggregation across different portfolios

Cons:

• A stochastic ALM model is still needed to generate the cash-flows used for calibration; stable calibration may require lots of scenarios

• The replicating portfolio depends on the asset allocation and the investment strategy used for cash-flow generation

• Calibration cannot add information about the queues of the distribution (but can add artifacts)

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FAP system: pro-ALM liability aggregation

Despite recent advances in technology, policy aggregation techniques are still needed to keep the duration of stochastic ALM simulations within reasonable limits; to avoid non-linear pay-offs distortions becoming material, FAP uses a proprietary methodology based on the aggregation of deterministic cash-flow:

automatic consistency between static and ALM projectionsfor a given aggregation ratio, cash-flow aggregation results in much lower distortions than “traditional” linear policy aggregation methods (i.e. model-points) simpler ALM model: the liability module must discern “only” different accrual methods, not all actuarial and contractual characteristicsThe ALM models can be fed with exogenous cash-flows for non-modelled products

Dynamic cash-flow

Financial income

Dynamic fund return

Asset

ManagementLiability

Dynamic ALM model

Determ

inistic projection

Aggregation

Static liability modelPolicies Static

cash-flow

Aggregated static cash-

flow

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Model life-cycle

Prototypes are typically created to set up models for new products without binding technological constraints: they are useful to clarify as early as possible the details (and expose possible criticalities) in the application of modelling methodologies

Functional specifications, written before model development, double as a constantly up-to-date documentation (passing, by definition, the Solvency II “implementation test”)

Model development, testing and production of “official”results are run on three separate environments; model deployment from one environment to the next is regulated by a strict change management policy.

The “model base” (econometric, actuarial, financial and ALM models) is far from static: constant evolution is driven by new product and business lines, laws and regulations, enhancements in modelling techniques, operational requirements and, not least, by a healthy and ever-increasing “information appetite” created by information availability itself.

To ensure continued availability and relevance for the overall system, model development is governed by a formalized “life-cycle”:

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Testing: stochastic economic scenarios

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Testing: stochastic results

L

A

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Solvency II risk driver coverage

Operational Non-life Market Life Health Default

Premium / reserve

Property

Currency

InterestRate

Spread

Non-life Cat

Equity

Concentration

Mortality

Longevity

Lapse

Expense

Disability

Revision

Life Cat

Expense

Claim

Epidemic

Modelling approachRequired Solvency II

Correlation-based

Factor-based

Scenario-based

Covered by FAP models

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Processes supported by FAP

Market Consistent Embedded Value (MCEV), including fair value pricing of the time value of embedded options and guarantees, sensitivity analysis and analysis of movements; six-monthly with yearly external review

Economic Risk-Based Capital (RBC): capital absorption for each risk-driver (interest rates, equity returns, credit spreads, mortality/longevity, lapses/deferments and expenses) with diversification benefit applied through linear correlations; six-monthly

Budget: yearly impact evaluation of new business and quarterly forecasts

Add-on reserves (ISVAP 1801 and expenses) with formalized investment strategies (demonstrably avoiding “cherry-picking” benefits); six-monthly

Target returns optimising balance-sheet profits; yearly

IFRS3 and IAS accounting with fair value evaluation ; six-monthly

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Extra-process tasks

Examples of ad-hoc tasks performed with direct support form the FAP systems include:

Stress-testing required by the regulator (ISVAP)

Solvency II QIS (Quantitative Impact Study) 3 and 4

What-if analysis for with-profit new business impact in segregated funds

What-if analysis for strategic asset allocation revisions

Hedging strategy effectiveness tests

Investment policy revisions

Portfolio spin-offs

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Strengths

A true company-wide Enterprise Risk Management system, used by four different functions (Investments, Planning and Control, Risk Management and Actuarial), ensuring consistency both in terms of methodologies and of input data for all value and risk evaluations

Compliant to current regulations (new ISVAP regulations, CFO Forum principles) and ready, so far, for Solvency II internal model compliance

Internal skill development and complete control over result quality

Automatic traceability and auditability of every evaluation

The system was successfully presented to the Italian regulator (ISVAP) and is considered “state of the art” on the Italian market

Modular, efficient and timely development phases:

– Phase 1 + phase 2 (MCEV, RBC): 9 months, 1 month late– Phase 3 (add-on reserves, hedging derivatives): 7 months, on time– Phase 4 (yield enhancement derivatives, reporting, user profiling, auditing): 6 months, on time– Phase 5 (guaranteed pensions funds): 6 months, on time– Phase 6 (financial risks monitoring): 9 months, on track

High performance: a stochastic ALM run (5000 scenarios, 40 years, monthly time step) on the full Eurizon Vita group perimeter (including ELL unit-linked business) in less than 2 hours

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Strengths: focus on technology

The unified database is based on state-of-the-art Oracle 11g R2 RAC (Real Applications Cluster) technology, ensuring true “enterprise” level security, robustness, scalability and support in the management of information (the true strategic asset for the company)

Excluding the database management system (Oracle), the application architecture maximises usage of open source components for effective cost cutting

The development language is Java, offering an optimal mix of performance, reduced development and testing time, modularity and ease of maintenance and evolution

ALM models are developed and maintained by a team of “pure” IT professionals– Reduced development and testing time– Optimized computing performance– Industry-standard development methodologies (centralised source code repository, formalized change

management procedure, issue management, etc.)– Substantial cost reductions compared to “developers” with specific actuarial/financial skills

Stochastic simulations run on a parallel computing cluster based on a HPC (High Performance Computing) architecture: low-cost Linux servers, InfiniBand network (20 Gb/s), Lustre high performance distributed file system, …

Over 250 functions available through an intranet portal with user profiling, single-sign-on,advanced security and centralized deployment of software updates

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Thank you for your attention

Questions?

john.brunello@eurizonvita.it

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Liquidity premium: Existence, measurement & application

John Hibbert john.hibbert@barrhibb.com

December 2009Society of Actuaries: Global Best Practices in ERM

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Agenda

+ What is the (il)liquidity premium & why does it matter?+ The questions asked by insurance regulators.+ Recent research:

– Literature review

– Updated estimates

+ Measuring liability illiquidity.+ CEIOPS consultation feedback.

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What is the (il)liquidity premium & why does it matter?

What is the liquidity premium?The basic idea

+ The basic idea is that financial instruments which offer identical cash flows can sell at different prices as a result of their trading liquidity.

+ Hard-to-trade instruments will sell at a price discount (or yield premium) compared to otherwise equivalent assets as a result of demand from ‘mark-to-market’ investors.

+ Liquidity premia have implications for the fair valuation of illiquid liability cash flows.– If markets price liquidity then market-consistent valuation techniques would be

expected to value illiquid (i.e. predictable) insurance cash flows in a consistent way.

– The illiquid replicating asset portfolio reveals the ‘correct’ liability value.

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4

The questions asked by European regulators (CEIOPS)

Solvency II Consultation Paper #40 July 2009

“The great majority of CEIOPS believes the relevant risk-free interest rate term structure should not include an illiquidity premium. Some CEIOPS Members do not fully share this view and believe that this issue requires further investigation.”+The rationale for their position appears to be “to date there is no generally acknowledged method which will derive the illiquidity premium in a prudent, reliable and objective way.”+“Should the discount rate include an illiquidity premium? If so, which (re)insurance liabilities should be considered sufficiently illiquid and how should the illiquidity premium be quantified?” (D.16)+“How can the method used to calculate the risk discount rate be extended to derive a figure consistent across different currencies, including those without government bond and swap markets?” (D.18)

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CEIOPS consultation feedback

Response to CEIOPS CP 40A virtually unanimous response among (c45) respondents in favour of using LP in valuation.

ABI: We fundamentally disagree with the majority view .. which dismisses the liquidity premium without any proper consideration of the issue.. To reject this would be entirely counter to the requirement in Article 76(2) .. would introduce a substantial layer of additional prudence.. and would be very damaging to the interests of millions of consumers in the UK and in other EU countries.

CEA: The CEA believes that the “illiquidity premium” exists and should be taken into account for insurance liabilities and that its amount should be calibrated according to the degree of illiquidity of the term structure and the characteristics of the cash flows.

CFOF: The CFO Forum disagrees with the view that no allowance should be made for illiquidity premia.. The illiquidity premium has become more relevant as it has markedly increased since the widening of spreads during the financial crisis. Solvency II proposals are inconsistent with IFRS Phase II proposals..

CROF: ..an illiquidity premium adjustment to [swap] rates should be taken into account.. The risk that this illiquidity spread widens does not necessarily mean that policyholders are put at increasing risk due to the often illiquid nature of the liabilities..

FEE: .the observed interest rates on AAA-government bonds need to be adjusted for illiquidity to match the cash flows to be discounted.

GDV: We would strongly request further investigation into this issue as the GDV believes that the “illiquidity premium” should be taken into account.

Grp C’tif ..the premium .. is normally modest but can become very substantial..

PwC: .. In certain markets, the exclusion of an illiquidity premium is likely to result in significant policyholder detriment through additional unnecessary cost in purchasing certain contracts, for example, UK annuity contracts. 7

CFO Forum’s evolving thinking+ MCEV principles (June 2008)Principle 7: All projected cash flows should be valued using economic assumptions

such that they are valued in line with the price of similar cash flows that are traded in the capital markets.

G14.4 No adjustments should be made to the swap yield curve to allow for liquidity premiums or credit risk premiums.

+ December 19th 2008: “..the MCEV Principles were designed during a period of relatively stable market conditions .. The CFO Forum has .. decided to conduct a review of the impact of turbulent market conditions .. the result of which may lead to changes to the .. Principles or the issuance of guidance. The particular areas under review include …… the effect of liquidity premia.”

+ May 22nd 2009:The current financial crisis has revealed significant challenges for MCEV, such as adjustments for liquidity premia, which have ultimately harmed comparability. The CFO Forum has agreed to do further work to seek to improve the consistency in the adjustments made for liquidity premium and volatilities. This should also allow due consideration to be given to Solvency II developments where liquidity premium is an equally important issue.

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CFO Forum’s evolving thinking

9

+ October 2009: Revised MCEV Principle 14

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Literature review

Liquidity and asset prices - theory + In a ‘frictionless’ market two assets with identical cash flows will

have the same price. + Where investors face frictional costs, prices must be adjusted

downwards (and returns adjusted upwards) to compensate investors. + ‘Clientele effects’ whereby different groups of investors have

different expected holding periods i.e. they face different probabilities of suffering a ‘liquidity shock’ which requires them to sell an asset. – Investors are characterised as buy-and-hold (with no immediate needs for liquidity)

and mark-to-market with a need to trade specified by a simple trading intensity orliquidity policy.

– The equilibrium that emerges shows that investors with the shortest holding periods hold the assets with the lowest trading costs and investors with the longest holding periods hold assets with the highest trading costs.

+ We can think of a family of spreads (or price discounts) for different asset pools exhibiting varying degrees of illiquidity. – Measures of liquidity premia will therefore be required to reference some

benchmark asset pool.11

Measures of trading liquidity

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The microstructure of a market is reflected in three main characteristics

1.Tightness: measured by the size of bid-ask-spreads;

2.Depth: measured by the volume of trades possible without affecting current prices;

3.Resilience: measured by the speed at which the price impact of trade dissipates.

Liquidity premium literature review

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Corporate bondsThe consensus from the academic literature is clear: liquidity premia do exist in corporate bond markets. They can be substantial, but vary significantly through time. A number of different approaches have been adopted to quantify the impact of liquidity on corporate bond prices. – Microstructure approaches provide worthwhile insights into why liquidity premia could

and should exist in markets with trading frictions, although they tend not to lend themselves well to empirical estimation.

– ‘Direct’ approaches (including the CDS approach) involve choosing a pair of assets or asset portfolios which – other than liquidity – are assumed to be equivalent and then comparing prices, expected returns or yields.

– Structural model approaches using the Merton model. These are closely related to the direct method in that a corporate bond is compared to the cost of manufacturing an approximately equivalent synthetic position from a risk-free (liquid bond) and an option on the issuing firm’s total assets.

– Regression-based approaches which typically regress one or more measures of asset liquidity and trading costs (whose choice is inspired by the microstructure literature) on observed asset prices or yields. Statistically significant regression coefficients are interpreted as providing an estimate for the ‘pure’ price of liquidity.

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Liquidity premium literature review:Corporate bond markets

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16

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Updated estimates

A reminder:Decomposition of market spreads

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+ Default-related credit risks are defined as the expected default loss on bonds plus the risk premium that investors demand for the possibility that corporate defaults will be higher than expected. The LP is the additional part of the spread which is not explained by default-related credit risks.

5 year swap spreads relative to government bonds

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0

50

100

150

Dec-2005 Dec-2006 Dec-2007 Dec-2008

bps

EUR 5 year Swap Spread

USD 5 year Swap Spread

GBP 5 year Swap Spread

Methods

1. CDS basis: Credit default swaps provide a mechanism for insuringagainst the default of a bond issuer. The spread on an insured portfolio (which has relatively low liquidity and is free of credit risk) relative to a liquid risk-free bond is a widely-used method for estimating LP.

2. Structural model: This method compares the yield on an illiquid corporate bond portfolio with the cost/yield on a liquid position with otherwise equivalent risk characteristics constructed from risk-free bonds and notional options, using the Merton model.

3. Covered bond spreads: If (illiquid) covered bonds are viewed as being essentially free of credit risk, the spread over the risk-free reference rate (in the analysis shown here this is assumed to bethe swap rate) can be considered as an estimate for LP.

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LP estimates derived using the model free negative CDS basis approach vs swaps

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-100

-50

0

50

100

150

200

250

300

350

400

450

Dec-2005 Dec-2006 Dec-2007 Dec-2008

bps

Synthetic index - Swap spread - iTraxx

iboxx-Swap Spread - iTraxx

Merrill Lynch - Swap spread - CDX

Weighted averages of liquidity premium by currency (1970 & 1920 calibration) for investment grade bonds vs swaps

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-100

-50

0

50

100

150

200

250D

ec-2

005

Mar

-200

6

Jun-

2006

Sep-

2006

Dec

-200

6

Mar

-200

7

Jun-

2007

Sep-

2007

Dec

-200

7

Mar

-200

8

Jun-

2008

Sep-

2008

Dec

-200

8

Mar

-200

9

Jun-

2009

bps

GBP (1920)USD (1920)EUR (1985)GBP (1970)USD (1970)

EUR covered bond index proxy vs.EUR swaps at different maturities

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-40

-20

0

20

40

60

80

100

120

140

Dec 05 Jun 06 Dec 06 Jun 07 Dec 07 Jun 08 Dec 08 Jun 09

bps

1 Year5 Years10 Years15 Years

How might we make an objective comparison of methods?

+ CredibilityGeneral Economic / theoretical justification

Consistency with financial markets, optimal use market information

Compatibility with accounting standards

Process design Explainable

Objective / minimise use of expert judgment

Reliable, robust to model & parameter errors

Process execution Prudence

Verifiable

Availability of estimation errors

+ PracticalityClarity of process

Timeliness

Frequency

Cost of calculation

+ CoverageAsset types

Maturities

Territory / currency

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Measuring liability illiquidity

Solvency II CP #40 July 2009

“The great majority of CEIOPS believes the relevant risk-free interest rate term structure should not include an illiquidity premium. Some CEIOPS Members do not fully share this view and believe that this issue requires further investigation.” The rationale for their position appears to be “to date there is no generally acknowledged method which will derive the illiquidity premium in a prudent, reliable and objective way.”+Should the discount rate include an illiquidity premium? If so, which (re)insurance liabilities should be considered sufficiently illiquid and how should the illiquidity premium be quantified? (D.16)+How can the method used to calculate the risk discount rate be extended to derive a figure consistent across different currencies, including those without government bond and swap markets? (D.18)

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What liabilities might be viewed as illiquid?+ Insurance & pensions liabilities are long-term in nature.+ But there are significant differences in liquidity offered to

policyholders/savers and predictability of cash flows:– Unit-linked assets which are usually assumed to have comparable liquidity to the

underlying asset portfolio.

– With-profits style contracts offer limited liquidity but subject to policyholder contract.

– Annuity contracts are highly illiquid (although there is some second order mortality risk so cash flows are not exactly predictable)

+ Do policyholders expect rewards for giving up liquidity?+ Conclusion: It may be appropriate to apply an additional LP to a

limited class of liabilities.

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Remember - economic, market-consistent valuation breaks the link between liability value and backing assets.

Fixed Annuity Example

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0

100

200

300

400

500

600

700

800

900

1000

1 6 11 16 21 26 31 36 41 46 51

Initial Expected Cashflow

Projection year

Model point A:  Imm Annuity

Model point B: Def Annuity

Assessing Liquidity

Fixed cash flows:1. Project liabilities on best estimate basis

2. Match best estimate liabilities with risk-free ZCBs (matching portfolio)

3. Project A + L allowing for any uncertainties

+ Mortality / Lapses

4. Cash flow management:

+ Reinvest surplus in, say, cash+ Disinvest any shortfall from cash first then the matching portfolio

5. Calculate the t0 value of the amount disinvested in each simulation as a proportion of the t0 value of assets

6. 1 – the above number, call the Liquidity Ratio (LR)

+ 1 = very illiquid => use all of appropriate LP+ 0 = very liquid => don’t use LP

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Mortality Uncertainty

30

0

100

200

300

400

500

600

700

800

900

1000

1 6 11 16 21 26 31 36 41 46 51

Ann

uity Cash flow

Projection Year

Model Point A 95% to 99%75% to 95%50% to 75%25% to 50%5% to 25%1% to 5%

0

100

200

300

400

500

600

700

800

900

1000

1 6 11 16 21 26 31 36 41 46 51 56 61 66

Ann

uity Cash flow

Projection Year

Model Point B 95% to 99%75% to 95%50% to 75%25% to 50%5% to 25%1% to 5%

Fixed Annuity Example: The LR

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0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

88% 90% 92% 94% 96% 98% 100%

Cumulative Freq

uency (%

)

Liquidity Ratio, LR (%)

Model point A

Model point B

Lump-Sum Endowment Assurance:Results

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Statistic St Dev = 1% St Dev = 2% St Dev = 3% St Dev = 5%Mean 98.5% 97.3% 96.1% 93.6%Std Dev 1.4% 2.9% 4.5% 8.1%50th percentile 98.7% 98.1% 97.4% 96.3%25th percentile 97.7% 95.7% 93.9% 90.7%10th percentile 96.5% 93.3% 90.0% 82.8%5th percentile 95.8% 91.3% 87.1% 77.1%1st percentile 94.3% 88.0% 80.9% 65.1%0.5th percentile 93.8% 86.9% 78.6% 59.7%Minimum 91.5% 82.7% 68.9% 28.1%

Liquidity Ratio, LR, with Lapses Dist'd LN with Mean = 5%

Further Work

+ Extend to more products lines and multiple product lines– Impact of renewal premiums

– Allowing for new business

– Impact of aggregating multiple business lines

– Modelling products where the liabilities are in some way dependent on the underlying assets (e.g. with-profit business)

– Impact of dynamic lapses

+ Standardize the approach and metric– Investigate how surplus / deficit be dealt with in the projections

– What metric / percentile should be used (i.e. 99.5th case, 90th etc)?

+ Incorporating statutory solvency requirements+ The mapping of liquidity ratios to a proportion of liquidity premium

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Conclusions

Conclusions+ Unsurprisingly, given the extraordinary behaviour of markets in

2008, there has been re-appraisal by insurers of the importance of liquidity in asset pricing in bond markets.

+ There is a rich academic literature which supports the existence of liquidity premia.

+ Insurance firms and accountants have been forced to re-think their positions but appear to have accepted the addition of LPs to reference rates for certain classes of business.

+ European regulators are sceptical (given the diversity of firms’assumptions) and have posed a difficult set of questions.

+ Estimation and application of liquidity premia turns out to be achallenging task.

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Some references

1. CFO Forum: Market Consistent Embedded Value Principles, June 2008 & October 2009

2. Consultation Paper No. 40: Draft CEIOPS’ Advice for Level 2 Implementing Measures on Solvency II: Technical Provisions -Article 85 b - Risk-free interest rate term structure, 2 July 2009

3. Liquidity Premium: Literature review of theoretical and empirical evidence, Barrie + Hibbert, September 2009

4. Comments on Consultation Paper No. 40http://www.ceiops.eu/index.php?option=content&task=view&id=591

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