Scenarios and Stress Testing For risk management, regulation, models and fun

Philipp Keller

Scenarios

Scenarios

Historical

Scenarios

Synthetic

Scenarios

Company-

Specific

Scenarios

Reverse

Scenarios

Single-

Event

Scenarios

Forecast

Scenarios

Stress

Scenarios

Events

Implicit

Events

Single

Event

Sensitivities {E│P(E)<α}

{E│Capital(E)<0}

X ~ LN(x,α,β)

{E│Capital(E)<0}

Global

Scenarios

Multi-

Event

Scenarios

t=0

t=1

t=2

t=3

Scenarios: Possible, internally consistent

events, parameterized by a set of risk factors

Set of

Events

Uses of Scenarios

Reverse Stress

Testing

Emerging

Risks

Systemic

Exposure

Analysis

Scenario

based Models

Simulation /

Training

Communication

on Risks

ORSA

Model

Assessment

Strategic

Analysis

Recovery and

Resolution

Planning

Contingency

Planning

Impact of

Uncertain

Events

Defining Risk

Appetite

Assessing

Financial

Soundness

Extreme

Events

Setting Capital

Requirements

Impact of

Regulation and

Financial

Policies

Scenario-

based Planning

Assessing

Unquantifiable

Events

Crisis

Management

Model

Enhancement

Assessing

Concentration

Risks

Materiality

Assessment Incentivizing

Risk Culture

Scenario Analysis

• The quantification of the impact of a scenario depends strongly on the valuation standard being used.

• Illustrative Example: Solvency Ratios pre- and post stress test of a financial risk event for Solvency I, QIS 5 (using liquidity premia, matching adjustments etc.) and market-consistent

0%

50%

100%

150%

200%

250%

300%

Solvency I QIS 5 Market Consistent

Solvency Ratios

pre-stress post-stress

Solvency I ratios barely react to the stress test

QIS 5 solvency ratios react more but dampeners mitigate effects of stress events

In a market consistent framework, the impact of the scenario is strongest

The relative declines in solvency ratios as well as the relative solvency ratios between Solvency I, QIS 5 and market consistent valuation under a realistic financial market event.

The importance of valuation

Scenario Analysis

Source: IMF Country Report No. 13/124, May 2013: Belgium Financial System Stability Assessment

Regulatory uses: The IMF

Scenario Analysis Regulatory uses: Swiss Solvency Test 2007

-1 -0.5 0 0.5

Drastic drop of interest rates

Equity fall -60%

Real estate -50% and i.r. +1%

Stock market crash (1987)

Nikkei crash (1990)

European currency crisis (1992)

US interest rate crisis (1994)

Spreads widening - LTCM (1998)

Stock market fall (2001/2002)

Impact of Scenario / RBC

Life - Impact of Scenarios on RBC

High spread risk, which materialized in 2008+

Very high risk to falling interest rates, which is materializing since the 1990s

-2

0

2

4

6

8

1988

01

1989

07

1991

01

1992

07

1994

01

1995

07

1997

01

1998

07

2000

01

2001

07

2003

01

2004

07

2006

01

2007

07

2009

01

2010

07

2012

01

2013

07

2015

01

10 year Yield

Scenarios for Modelling

Historical data set with approximately 1’000 storm events in the last 100 years is enriched by • track sampling: 9 “daughter tracks” from one

“mother track” • pressure sampling: 9 additional pressure samples • uncertainty modelling: each event loss sampled

five times Generates 500’000 potential events

Track sampling

Pressure sampling

Historical tracks

Conceivable tracks

Uncertainty modelling

Where situated?

Vulnerability Value distribution Cover conditions

• Sums insured

• Cover limits

• Deductibles

• Exclusions

• etc.

How well built?

The exposure of a portfolio towards an event is the event loss

How covered?

Example Hurricane “Charley” Aug 2004

Generation of

possible events

Source: Swiss Re

Hurricane North Atlantic

Scenarios and Catastrophes

Vacuum Metastability Event

Entropic Death Brane Collision

Gammy Ray Burst Black Hole Collision

Supernova

Solar Flare

Asteroid Impact

The Big Rip

Stone Fall

Tsunami

Volcano

Earthquake

Tornado

Marine Catastrophe

Airplane Crash

Dam Collapse

Industrial Accident

Fire

Limited Capital Mobility

Financial Repression

Legal Uncertainty Compliance Culture

Financial Crash

Rogue States

Dictatorships

Autocratic Rules

Corruption

Nationalisation

Bad Governance

Demographic Change Resource Depletion

Climate Change

Collapse of Infrastructure

AI Uprising

Nanotechnology

Biological Hazards

Radiological Contamination

Artificial Biology

Nuclear War

Doomsday Equation Global Causality Violations Simulation Hypothesis

Alien Attack

Rapture

Artificial Moral Hazard

Limnic Eruption

The 1918 flu pandemic infected 500 Mio people and killed between 50 - 100 Mio of the infected. It caused a cytokine storm (overreaction of the immune system) which led to younger adults between ages 20 to 40 to die disproportionally while children and older people with weaker immune systems were less affected. Globally approx. 30% of all people were infected, and a total of 3%-6% of the world population died.

Deaths per 100’000 in each age group for the US population for 1911-1917 and for 1918

Massively higher mortality for people aged 15 to 44

World War Z, Paramount Pictures

Monty Python and the Holy Grail, Python (Monty) Pictures

A scenario has to be specified properly for it to be useful. Assuming a multiplicative mortality increase might lead to an impact that is positive (due to annuitants dying) while in reality the impact for most life insurers would be negative.

Scenarios: Pandemics Megadeaths by microorganisms

Scenarios: Attack by Aliens Relativistic death

Our galaxy consists of ~100bn stars and the number of planets is likely an order of magnitude higher, many of which must have the condition for life. However no signs of intelligent life have been detected yet (the Fermi paradox). One solution to the Fermi paradox is that self-replicating von Neumann machines destroy all life in order to inhibit competition. Alien civilizations then either are careful and do not emit signals or are being destroyed, e.g. by relativistic impactors (Relativistic Kill Vehicles) or by other means of planetary and solar destruction.

Light speed

Apparent position from Earth

Actual position

Relativistic speed

RKV

Mars Attacks!, Warner Bros Pictures Mars Attacks!, Warner Bros Pictures

A 1kg mass impacting at 99% speed of light would release an energy of ~132 megatons or twice the larges hydrogen bomb ever exploded. The detection time would be very limited if the RKV travels close to the speed of light. Even if detected, it would be futile to destroy it since even vapour or small particles would be highly destructive.

Scenarios: Autonomous Cars Self-driving networked cars will pose unique challenges to insurers. The programming has to cope with situations where the losses will have to be minimized and which require potential moral judgment. In addition, the type and number of accidents will change radically, requiring changes in the business model of insurers. Scenarios help to think about possible consequences, risks and opportunities.

Moral Dilemmas

? A

A

B

A

Scenario 1: Car A has to choose between crashing into different pedestrians and has make a value judgment

Scenario 2: Car A will crash into child unless car B rams into A, killing driver B

Scenario 3: Ruritania requires producers of self-driving cars to assign lower values to certain minorities

Scenarios: Tambora Eruption

Shift in thermohaline circulation

1816 Summer Temperature Anomaly

Tambora Eruption 1815

Immediate local

devastation, estimated

deaths 70’000+

100 km^3 of debris ejected into

atmosphere (~10 times Vesuvius)

Lung infections due to

sulfur acid and ashes

Global cooling, failed crops in Europe and North America and Yunnan,

China

Snow in June 1816 in North America

Floods and low temperatures in Europe

Disruption of the Indian monsoon

Shift in jet stream

Most livestock died during winter 1816/17 in the US

Doubling of mortality in Switzerland

1818 return to normal

climate situation

Cholera pandemic in India , China and Indonesia: 1817to 1824

Typhus epidemics in Ireland 1816 – 1819 (40’000+ victims)

Catastrophic collapse of ice dam in

Switzerland in 1818 (Gietro Glacier)

Source: Wikimedia Commons Source: Wikimedia Commons Source: Wikimedia Commons

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