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Workshop Managing Climate Related Financial Risks :

The frontier of Knowledge,

Some examples illustrating :

Complexity, Uncertainty and Compounded risks

Nicole El Karoui/Professor LPMA-UPMC,FDR, ILB Fellow

16 Décembre 2016, Paris

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Only Two ExamplesLong term yield curve simulating :

— Example based on Solvency II recommandations

Cohort effect based on population dynamics

— The present can impact the distant future in a surprising way— Population dynamics effect

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The essential steps of modelingDefine the objectives of the modelization

Different in Finance and Risk management, Insurance, ALM, Regulation, Climatefinancial risks

Define a minimal theoretical priniple

• In finance AOA, and Risk neutral probability measure, In Insuranceregulation, Market consistency

• In "climate", equilibrium point of view ?

Data bases, Modelisation, and Calibration

• Derivatives market prices,Historical data• C : Climate Data, Expert reviews

Model Choice, Simulation, Numerical methods

• Monte Carlo methods and simulation, or Statistics• PDE for Climate models

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Long Term DiscountingSolvency II Directives

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Conciliate Finance and InsuranceMarket-consistency

"A market consistent value of an asset or liability is its market value, if it is readilytraded on a market at the point in time that the valuation is struck, and, for anyother asset or liability, a reasoned best estimate of what its market value would havebeen had it been readily traded at the relevant valuation point.“ (Kemp M., 2009)

EIOPA’s risk-free interest rate term structures(05/16)

“The starting point in Solvency II is the economic valuation of the whole balancesheet, where all assets and liabilities are valued according to market consistentprinciples. The risk-free interest rate term structure [. . .] underpins the calculationof liabilities by insurance and reinsurance undertakings. EIOPA is required topublish the risk-free interest rate

In fact, the given information is the Ultimate Forward Rate

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Yield Curve uses in derivatives marketsStatic Point of view

Discounting future deterministic cash flows

• Daily curves• Calibrating every day by bootstrap on market prices of forward, futures,

swaps• Liquid maturities up to 30y

Measuring interest rate risk through sensitivities

Dynamic Point of view

Simulation for Pricing and hedging

• Develop models to simulate the curves in the future• In risk neutral universe, for pricing and hedging of interest rates derivatives,

basically cap, floors and swaptions

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EIOPA Yields curve with UFR

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Simulation Issues In Insurance under Solvency IIReglementary Issue : Use Volatility given by Market Data

• The swaption volatility matrix at 31/12/2014,• associated with very low, even negative interest rate• Used for a EIOP a curve very different of the market data

Inconsistency between Market Data Volatility and EIOPA Yields Curve

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Conclusion relative to the discounting curvesKeep in mind the links between the model and the objective

A model is still a strong reduction of the reality

• Financial data parameters as volatility cannot be used outside of the context.• Difficult to have a "market consistent " valuation for other risks than

financial risk• The "artificial" risk neutral point of view but also the classical market

approximation minimize the impact of the long term risk premium• Long term Monte Carlo simulation are robust only under specific

assumptions.

Same difficulty for distant discounting in Climate risk

• Same difficulty when modeling climate risk, for the financial point of view• For example, discounting curves issued from the Ramsey rule cannot be

really used to simulated long term discount rate• Need to be more flexible, adaptative, in the optimization criterium

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Population point of view/Individual based ModelExample of Cohort effect, on the long term

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Hetereogenous Population DynamicsIndividual Based Model/Destinee at INSEE

Aim :Starting of micro evolution at the individual level and demographic patternsin birth and death to explain macro evolution of the general structure.

• IBM in Ecology— Population is structured by traits (i.e. individual characteristics) and by age— with demographic patterns in birth and death— Possibility for an individual to evolve during life (marriage, divorce,

professional evolution,...)— Random environment— Aggregation patterns yield to complex dependence

Challenges in Simulation

• Model deduced of generalized Poisson measure• Very time consuming simulation, but can be optimized

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Age pyramid 2009-2019

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Golden cohortGolden cohort : generations born between 1925 and 1945

— Cairns et al. (2009) : ra,t = (qa,t−1 − qa,t)/qa,tThe Golden cohort has experienced more rapid improvements in longevity thanearlier and later generations.

2 DATA 7

1970 1980 1990 2000

2040

6080

Year

Age

−2%

−1%

0%

1%

2%

3%

4%

Annu

al im

prov

emen

t rat

e (%

)Figure 3: Improvement rates in mortality for England & Wales by calendar yearand age relative to mortality rates at the same age in the previous year. Red cellsimply that mortality is deteriorating; green small rates of improvement, and blueand white strong rates of improvement. The black diagonal line follows the progressof the 1930 cohort.

2.1.2 The cohort eÆect

Some of the models we employ incorporate what is commonly called the “cohorteÆect”. The rationale for its incorporation lies in an analysis of the rates at whichmortality has been improving at diÆerent ages and in diÆerent years. Rates ofimprovement are plotted in Figure 3 (see, also Willets, 2004, and Richards et al.,2006). A black and white version of this graph can be found in the Appendix, Figure38.

In line with previous authors (see, for example, Willets, 2004, Richards et al., 2006)we can note the following points. In certain sections of the plot, we can detectstrong diagonals of similar colours. Most obviously, cohorts born around 1930 havestrong rates of improvement between ages 40 and 70 relative to, say, cohorts born10 years earlier or 10 years later. The cohort born around 1950 seems to have worsemortality than the immediately preceeding cohorts.

There are other ways to illustrate the cohort eÆect and these can be found in Ap-pendix A.

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Willets explanation by fertility (UK)"One possible consequence of rapidly changing birth rates is that the"average"child is likely to be different in periods where birth rates are verydifferent. For instance, if trends in fertility vary by socio-economic class, theclass mix of a population will change."

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Simple toy modelReference parameters

— Reference death rate d̄(a) = Aexp(Ba) with calibrated on french pop in 1927A ∼ 0.0004 and B ∼ 0.073

— "Upper class" : time independent death rate d1(a) = d̄(a) andbirth rate b1(a) = c 1{20≤a≤40} (c=0.1)

— Lower class : time independent death rate d2(a) = 2d̄(a) butbirth rate b2(a, t) = 4c1[20,40](a)1[0,t1]∪[t3,∞)(t) + 2c1[20,40](a)1[t2,t3](t)

Constant death rates but reduction in overall fertility between times t1

(=10) and t2 (=20)

Aim :compute standard demographic indicators

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Aggregate fertility— One trajectory with 20000 individuals (randomly) splitted between groups.

Estimation of aggregate fertility

0 5 10 15 20 25 30

0.0

0.1

0.2

0.3

0.4

year

num

ber o

f chi

ldre

n pe

r ind

ivid

ual a

ged

[20,

40]

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Life expectancy by year of birth— "Cohort effect" for aggregate life expectancy

0 5 10 15 20 25 30

5556

5758

5960

year of birth

life

expe

ctan

cy (a

t birt

h)

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0 5 10 15 20 25 30

0.0

0.1

0.2

0.3

0.4

year

num

ber

of c

hild

ren

per

indi

vidu

al a

ged

[20,

40]

0 5 10 15 20 25 30

5556

5758

5960

year of birth

life

expe

ctan

cy (

at b

irth)

• Death rates by specific group remain the same• But reduction in fertility for "lower class" during 10-20 modifies the

generations composition• the "upper class" is more represented among those born between 10 and 20

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What can be learned from this example ?From Climate point of view

• It is possible to simulate some complex data• The past can be have a strong impact on the distant future• In climate risk it is important to try to identify this kind of effect• Do not neglect the impact of the climate on the population, in particular

migration effect

An example of Numerical experimentation

— Allows to accelerated test

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ConclusionVery complex task

• Complexity induces non linearity, introducing large bias in a priori toosimple models

• The simplicity can only be used after identification of the main risk factors• Simulation tools have become more efficient

Adaptative Criterium

• To Integrate that decision criterion has to become more adaptative• To deal with the uncertainty of climate model and its impact of the risk

measure develop idea about vigilance, to detect in advance the futureevolution

Thank you for your attention

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