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Computational Management Symposium 2004

Long Term Policy Making for Operational Risk management

in the Basel II framework

University of NeuchatelRoom ALG Session 16

Duc PHAM-HI,

Head of IT Dept.,prof. Computational Finance,

E.C.E engineering school, Paris, France


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31/03/2014 Duc Pham-Hi 2

Focus is on Risk management in Banks

Definitions (New Basel Accord)

"risk of loss from failed or inadequate process, systems or people,

resulting from internal or external events"

Basel II means profound changes

quantification of op risks for mandatory Capital reserves involvement of top management, held accountable

very large compliance projects

Operational Risk in banks

7 event categories

quantitative approach


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31/03/2014 Duc Pham-Hi 3

Operational risk: Advanced Model Approach

Loss distribution approach

hope for lower Capital requirements

risk control performances watched by Rating agencies

Probability

Loss occurences

individual Loss

amount

Monte Carlo

Simulation

etc.

Probability

Total loss

Mean Threshold

Probability


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31/03/2014 Duc Pham-Hi 4

Basel II, computation-wise

Basel II for the Top banks : Advanced Model Approach

Pillar 1: capital at risk calculation

use of all 4 inputs mandatory, but internal data scarce

allocation between part and whole?

source of risk is absent from model

Pillar 2: control and supervision governance and management role are not modelised

consistency and rationality: no objective way to judge

General:

procyclicity

look-back

etc

Conclusion : crying lack for a theory of dynamic risk control to build a

rational framework


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31/03/2014 Duc Pham-Hi 5

2 kinds of risks

"Business losses" are frequent, and small, and :

rather regular

both positive and negative

"Catastrophic losses" are rare and very large and

unpredictable

only negative ("no free lunch" effect)

Levy process for modeling risk state

Ordinary

business losses

Negligible losses

Extraordinary

catastrophic

losses


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31/03/2014 Duc Pham-Hi 6

Bank activity variables for modeling business

Small and frequent losses

Rare but very large losses

after application of Ito's formula, where :

is the compensated Poisson random measure,

(dz) is the Lvy measure, with condition

All operational losses

Revenue income process

Wealth is resultant of losses and gains

ttBXX ex

p0,11

tLXX exp0,22

21 dXdXdX

dtdR

tdBXdX 11

**

R 122 ),(

~)1()()1(

R

z

z

z dzdtNedtdzzebXdX

)(),(),(~

dzdtdzdtNdzdtN

1),(1

z

z dzdte

dXdRdW


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Parameters for modeling Management

Key Risk Indicators and Scorecards on Business Environment :

indicates level of danger/volatility

Scorecards on Internal Control

How effective does Management transform budgets into Loss

reduction

Approximation

Assmussen & Rosinski

Cumulated large losses as finite number of jumps, in practical

)(

1

tN

jt xX

t

t


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Reducing small losses

through better process management

where tis the loss reduction factor whose cost is expense

(more fraud detection, personnel, etc.)

Reducing impact of catastrophic events through insurance, or

recovery plans, at cost

where losses xj may be capped or reduced

Impacts on system

Risk state description: effects of management / environment

Wealth WWealth

W+dWTransition Probability

Control

variables ,

Environt var.

)()( ttF

)(

0

)()(tN

jt xKLG

amountfixedHwherexHxK jj )(),(inf)(

1)(0).()( HwherexHxK jj


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Introducing rationality and control

Wealth evolution is :

State of wealth at time :

Economic value depending on policy

where is the given of a pair ( (t) , (t)) .

Objective is to maximise:

)(

1

1 )()()()(tN

j

jtt xKdBXdtRdW

0

),,),(,,( ttttdWW

dttWUrtJ0

)()exp(

dttWUrtEV0

)()exp(max


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Other related problems :

Refer to Cramer-Lundberg : Ruin theory

Goal to stay afloat becomes constraint


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How to solve : 3 choices of methods

Pure HJB, G-HJB :

Galerkin + Viscosity

consistent with events classification

Neural / Learning

Adaptive: Reinforcement LearningNeural, supervised

QMC or MCMC exploratory

Has to back test and stress test anyway Scenario exploration thru parameters : Markov chaining events

instead of Experts panel imagination.

Classic dilemma : explore or exploitation : genetic programming

(splice & dice)

kkrJ


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Using Hamilton Jacobi Bellman to model risk ?

Introducing processes

Optimal control gives the big picture

Modeling processes

Process decomposition

Equation for risk genesis

Introducing Value

Optimal control equations

Solving for strategies

Solving for price of risk

Feature based reasoning


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31/03/2014 Duc Pham-Hi 13

Drawing help from Techniques of process modeling

Classification as Top down or Bottom up

Or, as either Process / Factor :

process analysis

causal networks

connectivity matrix

factors identification

risk indicators - and predictive models CAPM like and volatility models

actuarial techniques

empirical loss distribution

distributional form parametricized by historical data extreme value theory

Hamilton Jacobi Bellman is related to process

but transition matrix in Markovian case can be related to Bayesian

networks.


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31/03/2014 Duc Pham-Hi 14

Banking processes and losses separation

Need for a separate process model and a Losses model...

Risks identification is different from risk evaluation

one is cost, other is production

capital at risk evaluation is not (always) risk evaluation

Risk evaluation cannot be done properly without risk reduction

which cannot be treated if generation mechanism not seen

parameters for risk source easier to catch at op level

De facto schizoid treatment separating identification

that combines back together

at time dimension

cost reduction, management from Y to Y+1

at investment cost dimension

allocate CaR according to marginal efficiency of capital, not at

highest ex post costs therefore justify event type cats as axis


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31/03/2014 Duc Pham-Hi 15

Modeling hypotheses and issues

Standard approach (not AMA) and line of business

Basel II is profit center orientated, not back office... but operational risk stems from back office

modeling correlation errors if share back office processes

markovian hypothesis

homogeneity issue on local risk-adjusted returns on capital across

different business lines

Elements for the process model

profit generation rate

estimates of

risk level factor stochastic variable

is a LDA type : Extreme value theory to help here.


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31/03/2014 Duc Pham-Hi 16

Long history of solving HJB

Known cases Linear Quadratic

in Merton's problem and Black Scholes context

New : with Levy processes, but with HARA and CARA

utility function : explicit solutions

But still, classic obstacles

Unknown P(x,y) --> POMDP in Markovian case

Curse of dimensionality

Too large sets {y} for each x Too large sets { } for each x

Too strong nonlinearities


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31/03/2014 Duc Pham-Hi 17

Learning : quick sampling of state space wrt. rewards

Neural techniques on features

Mixing SDE with NN-based volatilities

To use Q-learning, philosophy is Action-Reward : use of at :

at= (xt) ,

Then

Taking null terminal value, the value function is the total of what can be

expected in the future (here discount is not present).

Introducing a discount rate and taking the expected value :

),(),( axrEaxR

0)),(,()),(,(

t tt dttxxrtxxV

0

0))(,()(t

tt

t xxxxrExV


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31/03/2014 Duc Pham-Hi 18

Rationality of the risk center is to seek maximum of value, starting from state t

x0, to "learn" policy maximising V over set A of admissible actionssatisfying

where V (x) is the the consequence of following policy from initial situation x

Value for a given strategy is sum of immediate reward and discounted flow of

possible future rewards, depending on the transition :

Solving for optimal policy requires dealing with nonlinear equation

Solving for strategies or for value of risk ?

0

* ))(,())(,(minarg)(t

tt

t xxrExxRx

)(min)( 00*

xVxVA

0

))(,())(,()(t

tt

t xxrExxRxV

y

tyxtt yVPxRxV )(..),()( ,11


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31/03/2014 Duc Pham-Hi 19

Solving for strategies is non-linear, we turn to solving for value (G is terminal

value)

by reasoning in terms of discrete time. Alternately, in terms of discrete states y, as

possible outcomes of state x, and introducing action at:

We iterate on V since the problem is linear.

let tbe the proxy for V at time t ; we iterate thus :

Q-learning is particularly easy to set up and is model-free

Solving for risk with Temporal differences

),,()1),((min),( tuxGtxfVtxV Uu

y

yxPxyxP 0),(,1),(

ya

yVyxPxarV )(),(),(min*

y

tt yyxPxrxV )(),(.),(min)(1

),().,(),(),(1 ayQyspasgasQ tt


20/22

31/03/2014 Duc Pham-Hi 20

Optimal control gives the big picture

Control using investment

mechanism for Capital at Risk deduction justifiable. give keys for allocation

Joining bottom-up and top-down management

clear rules of engagement for both operational and senior management on

budget

Remedy scarce data : How ? e.g by reinforcement learning,

greedy algorithm: not necessarily CPU consuming

by justifying online sampling

compensate scarce "experience points" with observations-weight

modifications (ANN like techniques - filtering) allow use of Monte Carlo by process even where no history was available

Regulator oversight advantage

secure model validation


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31/03/2014 Duc Pham-Hi 21

Even if not solving to 100% it's setting the framework

Separate roles of parameters from variables

See role of Business Environment & Internal Control

Adaptive learning

Online sampling


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31/03/2014 Duc Pham-Hi 22

Adressing gaps in today's risk management theory

Temporal dimension :

growth related risk (agressive strategies)planning

Allocation problem : J = Jk

Home Host

business line arbitrage

Adaptive :

online sampling

learning

Operational Real Time hedging : future scanning with high quality

inhomogenous Poisson time

identification of chains of events as patterns

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