Extreme Events:
Extreme Events David SandersAgenda:
Agenda Geophysical Events
Reserving Pricing Management
Extreme Geophysical Events
Financial EventsLisbon Earthquake 1755:
Lisbon Earthquake 1755 Rousseau
The price mankind paid for civilizationPricing/Reserving/Managing:
Pricing/Reserving/Managing Collect Data
Look at pricing/ reserving models
EVT
Cat Modelling
Others
Look at Management Issues
Measure RiskActuarial/Mathematical Modelling:
Actuarial/Mathematical Modelling Edmund Halley
Worlds first meteorological map (1686)
d’Alembert
creation of partial derivatives to determine law of governing winds (1746)
A reflection:
A reflection Tectonic Plate theory is less than 40 years old
Catastrophe theory and Morphogenesis (Rene Thom) is just over 30 years old
Chaos Theory is less than 30 years old
Extreme Value Theory is about 20 years old
Computer modelling is less than 10 years old
Data:
Data Understand the issues - what are likely losses
Try and understand sources/limitations of data
Are certain geophysical events connected Connections:
Connections Hurricanes spawn tornadoes
Earthquakes sometimes occur after cyclones
Kanto/Hugo
Earthquakes and volcanoes are connected
Earthquakes can trigger consecutive earthquakes (Lomnitz 1996 statistical study)
Volcanoes can trigger volcanoes
1902 Mount Pelee/la Soufriere of St VincentCatastrophe Models:
Catastrophe Models These are essentially ground up models
The results are as good as the models
need for calibration
The results differ for different models
Still learning
Not good at predicting events in time
gives probability and cost
Integrate to give priceCatastrophe Models:
Catastrophe Models Predictive Models are not very good
Meteorological models
Fine grids
Difficulty in predicting long into future
Blamed on Chaos Theory/Butterfly effect
BUT Prediction error grows linearly
suggests model errorCatastrophe Models:
Catastrophe Models Rapid growth in models
Complex/black box
Data in paper you can build your own hurricane model (hints see Karen Clarke’s original CAS paper)
They will get better - but need more events
Likely to be VERY wrong at Extreme EventsExtreme Value Theory:
Extreme Value Theory Top down approach
Not used for fitting the whole distribution
Generalised Extreme Value Distribution
Gumbell
Frechet
Weibull
depends on shapeExtreme Value FunctionExamples:
Extreme Value Function Examples In mortality, the population a time age x is half that at age x-1
The log return period of an earthquake is proportional to the size
and so onGeneralised EV Distribution:
Generalised EV Distribution P(Y < y) =GEV(y; ξ, μ, σ)
= exp (-[1+ξ(y- μ)/σ]+ -1/ξ)
Estimate yp where GEV(yp ) =1-p
yp is return level associated with return period 1/p
μ is location parameter
σ is the scale parameter
ξ is the shape parameter
Compare with Craighead Curve!Generalised Pareto:
Generalised Pareto Pr(Y< y) ~ 1- λu [1+ ξ (y-u)/ σ ]+ -1/ξ
Relationship between Pareto family and GEV Distribution
Threshold Distribution
high exceedence
mean residual life plotsExample:
Example How big is a San Franciscan Earthquake
Data exhibits linearity at lower ends to support the log period /intensity ratio
BUT
at top end of scale this doesn’t apply
EVT suggested maximum of 8.6-8.7
Geophysical evidence supports that numberManagement - Theory:
Management - Theory Pre event
Loss scenarios
Underwriting control
Good internal Management
Post event
Claims estimation
Claims managementManagement Theory:
Management Theory Clarity of roles and responsibilities
Underwriting issues should go beyond the technical underwriter
some of the issues they face require additional skill sets that can be more readily be brought to bear by others
Management in Practice:
Management in Practice There is no check and balance within the underwriting group
in a number of cases, individuals have proved to apply insufficient professionalism.
Others are more concerned with tactical issues than strategies issues - which a broader group should bring to bear.
Management - Practice:
Management - Practice Cynical view
Gross loss = top of reinsurance protection
Net loss is fixed
Difficulty in estimating exposure
Need to PML total exposure
Difficulty from computer records in finding where you are in the layer (retro)PML:
PML PML is a somewhat arbitrary measure
Post Sept 11, it was common for PMLs to be factored up by an arbitrary amount i.e. x 1.25 to x 2.0
The value of PML as a proxy for exposure is limited for coverages that have limits or attachment points
Computer Records:
Computer Records Rarely have quantitative data regarding the underlying portfolios.
Actuarial discussions with underwriters are to understand
who is reinsured
what they write
the levels they write, backups, deductibles etc
BUT we only tend to build up an approximate pictureManagement Practice:
Management Practice Estimates on the low side
Increase as required
Hope can hide away when there is a good year!
BUT
Property claims are settled faster than in 1990!Mangement Practice:
Mangement Practice Newer underwriters have “forgotten” disciplines af early 1990’s
WHY
No mega loss seriously impacting book
September 11 has changed all thatReally Extreme Events:
Really Extreme EventsHow Extreme ?:
How Extreme ? Meteorite Collisions
65 million years ago a meteor hit
The NORTH SEA
About the same size as the famous Arizona impact site
Once every 100k years`Meteorite Strikes:
Meteorite Strikes Meteor Clusters
Taurid Shower (mid summer)
Tunguska Event
Destroyed an area equivalent to that enclosed by M25
Average 3,000 plus deaths per annumHurricanes:
HurricanesHurricanes:
Hurricanes Expectations of $80 billion plus
Potential for stronger hurricanes as water heat increases above 28 degrees
2 or more extreme hurricanes in one year
Short memory in rating - Puerto RicoHurricane from Space:
Hurricane from SpaceHurricanes:
Hurricanes 1986 Airic Publication
What if two $7 billion hurricanes hit
Todays study
$50bn? $80 bn?
Largest portion paid by reinsurance industryTornadoes:
Tornadoes The First Ever Tornado PhotographTornadoes:
Tornadoes Solve Navier Stokes equation for axisymmetric flow in a rotating cylinder!
Cities are NOT immune
Local extreme events
Earthquake:
Earthquake Still little understood and not really managed
Tsunami after earthquake
Eventually there will be a big one and loss will depend on
location
design of building
fire after - See 1986 Airmic Study on Fire after EarthquakeKobe:
KobeEarthquake:
Earthquake UK has one on scale 4.5 every 10 years
Paris is vulnerable to a one in 10,000 year quake - buildings not designed to withstand such a shock
Concern over European quakeTsunami:
TsunamiTsunami:
Tsunami Earthquake - height in meters
Meteorite Hit- depends on size
Land slide
very devastating
heights in 100’s m
Canary Islands could devastate East Coast of USVolcanoes:
Volcanoes Mt St Helens with Mt Rainier Volcanoes:
Volcanoes Man builds on volcanoes due to fertile soil
Most volcanic explosions are local - but have a global impact
Tambora (1815)
year without summer (1816)
Frankenstein
Mega eruptionsMega Scale:
Mega ScaleVolcano:
VolcanoMega Eruptions:
Mega Eruptions Once every 50,000 years
Last one 72,000 years ago
Mankind reduced to 10k individuals
Not from typical volcanoes - but from large caldera
Example is Yellowstone Park
Estimates are 1 billion deaths Other IssuesOil Spills:
Other Issues Oil SpillsOther IssuesChemical Explosion:
Other Issues Chemical ExplosionWhere do we stand?:
Where do we stand? Mega events are not insurable - so why pretend they are
Concentration of risks making extreme losses more likely
Mega cities built in tectonic or storm areas
Miami, Los Angeles, Mexico City, Tokyo, New York, Naples, and so onInsurance not being diversified:
Insurance not being diversified Concentration in a diminishing number of major players
Increasing relaince on A graded reinsurance
Remember insurance needs diversification and not concentration.Newer Capital:
Newer Capital Needed to cover most extreme risks
Build up reserves
Question over where invested?
Need for diversificationComments:
Comments There are some extreme events that cannot be insured
How much are they?
What do we do with the larger risks?
Are running such risks really the price of civilisation?Financial Extremes:
Financial Extremes
Concentrate on Financial Extremes
Fundamentally differs from geophysical extremes
Postulate they are fundamentally the result of human irrational behaviour
If this is the case we need a new approach to understanding the issues
Some Examples :
Some Examples
Alchemy
Tulips
South Sea Bubble
Internet Bubble
Enron
Fundamental Drivers :
Fundamental Drivers
Greed
Fraud
Stupidity
Irrational behaviour
Madness of Crowds
Early Schemes:
Early Schemes
Alchemy
Turn Lead into Gold – a super investment if it worked
Elixir of Life
Tulipmania
Not just Dutch
International to seek arbitrage opportunities
Price completely irrational
South Sea Bubble:
South Sea Bubble
South Sea Bubble:
South Sea Bubble
All the features
Conflict of interest – regulator was also the stockholder
Greed
Fraud
Promised excessive returns
New Economy concept
Leverage through partly paid sharesSouth Sea Bubble:
South Sea Bubble
South Sea Company didn’t do any trade in the South Seas
Took over UK’s National Debt
First Private/Public Initiative?
Good things did arise
Marine and other Insurance companies with significant initial capital
Notes introduced (Mississippi Scheme)
South Sea Bubble:
South Sea Bubble
Greater Fool Theory:
Greater Fool Theory
Increased over indebtedness
Bank deposits give higher yield than stock dividend
Only reason to hold stock is to sell at a higher price
Ford – when the lift operator “knows” more than you its time to get out
Wall Street Crash and Recession:
Wall Street Crash and Recession
Claim that no one could predict EVEN AFTER the event
Over Optimism turned to extreme pessimism
Money under beds and not in banks
No investment
Economy needed a kick start – New Deal
Wall Street Crash:
Wall Street Crash
Unpredictable – even after the event?1987 Crash:
1987 Crash
Once in every 10 universes! Once in every 10 UniversesInternet Bubble – New Economy:
Internet Bubble – New Economy Economic Value versus Financial Value
They should approximately equate
In a bubble the investors “assume” different economic scenarios to those outside the bubble
Interest rates are decreasing so use lower discount rate
What does risk adjusted mean?Internet Bubble – New Economy:
Internet Bubble – New Economy So much paper is sold at so high a price to so many investors
The market must be OK as it regulates itself!
Banks goal (set by SEC) to protect retail and institutional investors…but…
Banks didn’t want to loose their fees
Nick Leeson – winner of Ignoble Prize for Economics:
Nick Leeson – winner of Ignoble Prize for Economics
Other Ignoble Prizewinners:
Other Ignoble Prizewinners
The Copper Trader who didn’t know his buy button from his sell button (Cost 5% Chilean GDP)
The investors of Lloyds
Michael Milken
Honorable Mention
The IT Department of a Bank who put the Training Room computers on line2002 Prize:
2002 Prize To the executives, corporate directors and auditors of Enron,.…..,HIH Insurance, …..WorldCom, Xerox and Arthur Anderson, for adapting the mathematical concept of imaginary numbers for use in the business world
Decline and Fall of Ignoble winners:
Decline and Fall of Ignoble winners
Enron - “Laying” it on:
Enron - “Laying” it on
Enron Venture Capitalism:
Enron Venture Capitalism
You have two cows.
You sell three of them to your publicly listed company, using letters of credit opened by your brother-in-law at the bank,
then execute a debt/equity swap with an associated general officer so that you get all four cows back,
with a tax exemption for the five cows.
The milk rights of the six cows are transferred via an intermediary to a Cayman Island company secretly owned by the majority shareholder
who sells the rights to all seven cows back to your listed company.
The annual report says the company owns eight cows, with an option on one more. Noble Prize Winners:
Noble Prize Winners
Not immune – LTCM
Assumed volatility didn’t vary
Markets were perfect
Infinite Capital available (what’s leverage in any case ?)
No arbitrage
Whoops apocalypse
LTCM – A Noble Venture:
LTCM – A Noble Venture
The Regulator:
The Regulator
Throughout all the examples where was the regulator?
Six sigma does not work in these events
Never seen a Normal distribution in Financial Mathematics
Either self regulation or over regulation
The Regulator:
The Regulator
Self regulation – seen as opportunity to push business to the limit (and beyond)
Over regulation – prevents economic development and often an (over) reaction to a specific event
Corporate Governance – the latest buzzword
Acts like Sarbanes-Oxley
The Regulator:
The Regulator
Can’t happen in UK
Accounting more an art than a science
No GAAP
Reliance on Efficient Market Hypothesis
Prices move in a well defined way
No arbitrage
No bubble
UK Insurers:
UK Insurers
The Regulator:
The Regulator
US Laissez faire gave false feeling of wealth
Premises that Central bankers are supposed to control inflations and not set price
Prices inflated because interest falling and hence bubble
Inactivity by regulator oversees a fundamental change of wealth
Honey – they shrunk my pension
Mathematical Models:
Mathematical Models
Extreme Value Theory based on concept of continuous distribution with some relationships between events
I suggest that base on the analysis of irrational behaviour and the madness of crowds we need something else
Mathematical Models:
Mathematical Models The Efficient Market Hypothesis is rigorous but false because it is an artifact of the early years of econometrics
Economists sought to fit economic models into equations they could solve, possibly not realizing — being at best mediocre mathematicians — that linear and exponential equations, those soluble by mid-century economists, represented only a tiny fraction of the possible mathematical relationships that occur in nature.
Mathematical Models:
Mathematical Models Simple equations they had studied in school adequately reflected reality in only a small fraction of situations
the Efficient Market Hypothesis rested on a number of assumptions, made to simplify the equations into solubility, that were in fact demonstrably untrue
This leads to non linear assumptions – Catastrophe & Chaos Theory
Rene Thom – Catastrophe Theory:
Rene Thom – Catastrophe Theory
Catastrophe Theory:
Catastrophe Theory
Thom’s Theory itself could be considered a bubble
Chris Zeeman used the catastrophe to explain many things!
The financial model used in his paper used fundamentalists and chartists
But
We know from experience that crashes are a result over over optimism reverting to pessimism
Elliott Waves:
Elliott Waves
Elliott Waves:
Elliott Waves
Elliot Waves:
Elliot Waves
5 up and 3 down
The 5-3 pattern is the minimum requirement for, and therefore the most efficient method of, achieving both fluctuation and progress in linear movement when the only constraint is that the lengths of odd-numbered waves of each degree be longer than those of the even-numbered ones.
The Fibonacci is the mathematical basis for the Wave principle
The Golden RatioElliot Waves:
Elliot Waves Strong connection with complexity theory
Maybe not the perfect solution (it is the simplest)
Finance is a Complex Dynamical System
Dynamical Systems:
Dynamical Systems Insurance and Finance are nonlinear Complex Dynamic Systems
Standard deviation is not a measure of variabilty or management control
Six Sigma is inappropriate
Entropy is a better measure
Why Entropic Measures:
Why Entropic Measures Black Scholes equation is really a special example of a entropic formula and has been generalised
Generalise CAPM
Risk measures used in papers can be derived from entropic measures
Hazard Transform
Wang transform
Coherent risk measures can be easily generated from relative entropic measuresEntropy – the Way forward:
Entropy – the Way forward Operational Risk measurements
Pricing – Choquet Integral
A possible new tool for the profession
Brings geophysical and financial risks together
Mathematics of 30 years ago:
Mathematics of 30 years ago Catastrophe Theory Struggling
Chaos slowly becoming recognised leading eventually to complexity theory
Entropy understood
Shannons Theorem
Fisher Information Criteria
No computers
Mathematics Today:
Mathematics Today More Computer power
More mature
But should look back to find useful tools for todays issues