financial modeling of extreme events thomas weidman cas spring meeting may 19, 2003
TRANSCRIPT
Financial Modeling of Extreme Events
Thomas Weidman
CAS Spring Meeting
May 19, 2003
Financial Modeling of Extreme Events
defining and modeling extreme events – insured vs. total financial impact
financial event modeling correlated events: insured + financialcase study: capital management
Defining Extreme Events
Miami HurricaneSan Francisco EQSeptember 11, 2001
Defining Extreme Events
0
10
20
30
40
50
60
70
80
San Fran EQ Miami 11-Sep
Insured Damage ($B)
Defining Extreme Events
SARSWest Nile VirusSpanish Flu
Defining Extreme Events
SARS virus – first outbreak, China Nov 2002
West Nile Virus – first cases in western world 1999
Influenza – first description from 412 B.C. 0
5000
10000
15000
20000
25000
30000
35000
40000
Sar wn Flu
cases
deaths
3-DColumn 3
Defining Extreme Events
AsbestosTobaccoShareholders’ Class Actions
Defining Extreme Events
Asbestos: $200 billion cost/$100 billion insured
Tobacco: $246 billion settlement with state governments
Tort Costs: $205 billion/$146 billion insured in 2001, a 14% increase over 2000
[source: US Tort Costs-2002 Update, Tillinghast]
Defining Extreme Events
Stock Market Credit Markets
Defining Extreme Events
Stock Market Returns: (65)% in 1929-33 (37)% in 1973-4 (38)% in 2000-3
Bond Market Returns: (8)% in 1999 (7)% in 19942 worst annual returns
in past 100 years
Defining Extreme Events
Pricing InadequacyReserving Inadequacy
Defining Extreme Events
Pricing Inadequacy
AY loss ratios 10 points higher than CY loss ratios from 1997 through 2000
Reserving Inadequacy
$48 to $92 billion at December 2001 excl asbestos and environmental (ISO)
Defining Extreme Events
Rogue TraderRogue UnderwriterRogue Agent/Broker
Defining Extreme Events
Operational Risk:
Risk of direct and indirect loss resulting from failed or inadequate process, systems, or people and from external events
Difficult to quantify, see Basel accords for treatment by banks
Summary of Risk Types and Models
Risk Type:Risk Type:CatastropheNon-catastropheReservesMarketCreditOperational
Risk Model:Risk Model:AIR, RMS, EQEExposure x freq x sevReserve rangesVaR modelsDefault models ?? Basel II?
Quantifying Extreme Events
Historical dataEmpirical distributionsRealistic Disaster ScenariosModelsFitted probability distributionsExtreme value theory
Extreme Value Theory
Based on work describing the extreme behavior of random processes
Extrapolate the tail of a distribution from underlying data
Distributions to fit tails:– Generalized Pareto Distribution (GPD)– Generalized Extreme Value (GEV) Extrapolate the tail
of a distribution from underlying dataProvides a rigorous framework to make
judgments on the possible tail
Extreme Value Theory
GEV family of distributions:
Mn = Max{x1,x2,x3,….xn} for n sufficiently large
“What is the maximum loss to be expected in one year?”
Extreme Value Theory
Generalized Pareto Distribution (GPD) fits tails of distributions above a threshold
Pr (Y>y+u|y>u) for large u
“What is the expected loss to an excess layer?”
Extreme Value Theory
Resources:
The Management of Losses Arising from Extreme Events, GIRO 2002
Kotz and Nadarajah, Extreme Value Distributions
Coles, An Introduction to Statistical Modeling of Extreme Events
Embrechts, etal., Modeling Extremal Events
Modeling Financial Events: VAR
VAR is a method of assessing market risk that uses standard statistical techniques routinely used in other technical fields.
VAR is the maximum loss over a target horizon such that there is a low, prespecified probability that the actual loss will be larger.
A bank might have a daily VAR of its trading portfolio of $35 million at the 99% confidence level.
Modeling Financial Events: Credit Risk
Credit Risk ModelsDefault ratesLoss Given Default (LGD)Migration matrices
Modeling Financial Events: Credit Risk
Default Rates = Frequency of loss = MortalityQuantitative Models for Credit Assessment1. Identify characteristics that differentiate
defaulting firms (e.g., Altman 1968); credit scoring models
2. Use credit market prices to estimate default rates
3. Structural models – use equity option pricing techniques (both equity and debt are options on the value of a firm’s assets)
Modeling Financial Events: Credit Risk
Loss Given Default = SeverityMany models assume a constant loss given
default Dependent on both exposure volatility and
recovery rate volatilityCorrelated with default rates?
Modeling Financial Events: Credit Risk
Credit Migration MatricesHistorical changes in credit rating of obligors ‘loss triangles’ for credit ratingsUse S&P or Moody’s dataUseful for portfolio risk assessment, pricing
credit derivatives, capital requirementsDependent on current and future economic
conditions ( recession vs. expansion)
Summary of Risk Types and Models
Risk Type:Risk Type:CatastropheNon-catastropheReservesMarketCreditOperational
Risk Model:Risk Model:AIR, RMS, EQEExposure x freq x sevReserve rangesVaR modelsDefault models ?? Basel II?
Capital Management
Market Share of Industry LossProbable Maximum Loss
(PML)/Aggregate ExposureRisk of Ruin Approach:
Pr (insolvency) < p over time period t
where p is small, e.g., .01 or .001
Capital Management - Issues
Consistent definition across all risk typesCorrelations across risksAllocation/attribution of capital to productAccounting framework: GAAP vs. Fair
Value Matching capital to management
responsibilities, e.g., assets vs. liabilities
Correlated (Extreme) Events
Global warming – storms – virusesLawyers’ fees from tobacco/asbestos winsStock markets – D&O/E&O claimsCredit - Equity pricesPricing – Reserving (e.g., B-F methods)Catastrophes – Demand Surge –
Reinsurance Recoverable
Correlated (Extreme) Events
Exposure: cat Non-cat
reserves market credit Ops
risk
Property X X x x x ?
Casualty x X X x X ?
Surety x X x x X ?
Inv Assets x x x X X ?
Correlated (Extreme) Events
Cas
cat
Cas
Non-cat
Cas
reserves
Cas
market
Cas
credit
Cas
ops
Prop-cat Low Low Low Low Low ?Prop-non-cat
Low Med Low Low Low ?
Prop reserves
Low Low Med Low Low ?
Prop market
Low Low Low High Med ?
Prop- credit
Low Low Low Med High ?
Correlated (Extreme) Events
Generally impossible to model joint distributions of risks (unless multivariate normal)
Therefore:Estimate distributions for each risk typeCombine distributions into a joint
distribution using ‘copulas’
Correlated (Extreme) Events
Copulas:Multivariate functions that combine marginal
distributions into a joint distributionUsing a normal copula leads to a simpler
approach for Monte Carlo simulation of correlated variables
CAS papers by Wang (1998) and Meyers (1999)
Financial Modeling of Extreme Events
Past experience lacks credibility
Current state of the art:Sophisticated risk models across all types of risk Integration/Correlation of risk models important
to management, rating agencies and regulatorsMajor role for actuaries