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TRANSFER AND GENERALISATION OF FINANCIAL RISK METRICS

TO DISCRETE EVENT SIMULATION

Arne Koors(a), Bernd Page (b)

(a) Department of Informatics, University of Hamburg, Germany

(b) Department of Informatics, University of Hamburg, Germany

(a) koors@informatik.uni-hamburg.de, (b) page@informatik.uni-hamburg.de

ABSTRACT

Quantitative Finance is one of the numerous application

fields of discrete event simulation. Because of special

requirements in this area, typically domain specific

simulation tools are applied, instead of general purpose

simulators. It appears fruitful and beneficial to provide

some of the risk metrics common in quantitative finance

for discrete event simulation in general, in order to

make use of them in generalised versions in further

domains. In this paper we describe transfer and

generalisation of risk metrics from quantitative finance

to general purpose simulators with regard to Semi-

Variance, Value at Risk, Expected Shortfall and

Drawdown.

Keywords: risk metrics, discrete event simulation

1. INTRODUCTION

The field of Quantitative Finance (also called

Computational Finance or Financial Engineering) deals

with computer-supported analysis of price histories of

asset values and the support of investment decisions in

financial markets. Next to Monte-Carlo-Simulation (i.e.

mathematical method, that solves complex problems

from probability theory numerically, based on repetitive

random experiments following the Law of large

Numbers, see Metropolis and Ulam (1949)) and related

methods, discrete event simulation is mainly applied in

two areas:

On the one hand, simulating the performance

of financial markets on micro level, i.e. down

to the level of single market participants

(Arthur, Holland, LeBaron, Palmer 1997; Lux

and Marchesi 2000; Levy, Levy, and Solomon

2000; Hommes 2006; LeBaron 2006).

On the other hand, evaluating particular

financial market trading strategies by

simulating, assessing and optimising them in

different historical market environments

(Chande 1997, Kocur 1999, van Tharp 2007).

In the context of this paper, we focus on the second

application area.

For the evaluation of trading strategies, special

purpose simulators are applied, so-called back testers.

Back testers differ from general purpose simulators in

the following aspects:

1. Instead of common random number generators,

historical time series are used as data sources

for security prices.

2. Entities in the sense of classical simulation

objects are not required, as only the behaviour

of defined trading strategies in the context of

inflowing market data is analysed. From a

conceptual point of view, these strategies do

not necessarily have to be represented as

entities.

3. Waiting queues and higher modelling

components such as processing stations or

transport stations are not explicitly required for

modelling, due to the immaterial nature of

financial strategies and their market orders.

Likewise, synchronization mechanisms for

different entities are usually not needed.

4. However, there are extensive requirements on

the characterisation of trading strategies, in

particular related to profitability and the risk

taken. Here, computation of manifold special

key figures developed in quantitative finance is

required for an extended reporting. To our

knowledge, most of these key figures and their

underlying concepts have not been regarded in

general purpose simulation so far.

* Event Modelling

* Activity Modelling

* Process Modelling

* Simulation Clock

* Scheduler

* Standard Statistics

* Reporting

* Experiments

* Optimization

* Entities

* Queues

* Stochastic

Distributions

* Extended Reporting

* Historical Timeseries

Discrete Event Simulators Back Testers

Figure 1: Commonalities and differences of general

purpose discrete event simulators and back testers

Proceedings of The International Workshop on Applied Modeling & Simulation, 2012

978-88-97999-07-2; Bruzzone, Buck, Cayirci, Longo, Eds.

100

Commonalities and differences between general

purpose discrete event simulators and back testers are

shown in the figure above.

In spite of the differences mentioned, back testers

and general purpose simulators are widely comparable

in structural terms. Further, the modelling and

simulation cycle as well as experiments are processed

equivalently. Back testers can be understood as a

special case of general purpose discrete event

simulators and therefore implemented by these, see e.g.

Golombek (2010) or Koors and Page (2011).

From a historical point of view, back testers have

developed concurrently to general purpose simulators

since the nineties, with rather limited mutual exchange

of ideas into both directions.

Risk metrics are an advanced aspect of back

testers, both serving for quantification of risk of a

particular trading strategy and for comparisons of

different trading strategies amongst each other. To us,

risk metrics do appear potentially useful for other

application domains as well.

In this paper, we aim at the transfer and

generalisation of established risk metrics from

quantitative finance into the world of general purpose

discrete event simulators.

This paper is structured as follows: In section 2, we

deal with the character of risk, seen from the

quantitative finance point of view. Parallels to

application fields of simulation are shown. We advance

to the concept of downside risk and motivate that the

idea of transferring financial risk metrics to general

application domains of simulation could be beneficial.

In section 3, we describe four central risk metrics of

quantitative finance in their original context first, and

then illustrate them by simulation queues. Advancing to

observation variables, we generalise the concepts and

transfer them into the field of general purpose discrete

event simulation. We outline the modifications and

enhancements we have carried out and discuss certain

implementation aspects. Section 4 summarises and

concludes the paper.

2. THE CONCEPT OF RISK IN QUANTITA-

TIVE FINANCE

2.1. Expected Value as Characteristic and Variance

as Risk

Yield and risk are the central concepts when evaluating

financial trading strategies by means of back testers.

Here, yield is understood as expected value of the

return of a trading strategy during a defined time span.

The trading strategy may carry out a number of

investment decisions during the simulated time frame,

so-called trades. The compounded return of all single

trades is the overall return of the strategy at the end of

the simulation. Its expected value is the yield of the

strategy.

The second central characteristic of trading

strategies is risk. Risk is defined as volatility, i.e.

variation of return around the expected average return,

following the fundamental thought pattern called Mean-

Variance-Framework introduced by Markowitz (1952)

into finance. Volatility mathematically corresponds to

the standard deviation of return.

General purpose simulation of discrete event

systems operates with mean and empirical standard

deviation as well, e.g. regarding queue length or

concerning the state space of observation variables in

general.

Attention should be paid to a shift in connotation

of the aforementioned concepts in finance: While the

expected value of return is considered as given and

characteristic for a strategy, variance always has a

negative connotation, in the sense of risk.

From this point of view, an expected queue length

x of a standard M/M/1-queuing system would be

considered merely a characteristic of the system. With

increasing variance of queue length (at a constant

expected value) the model would be estimated

increasingly risky, in the sense of higher uncertainty and

precariousness.

In this sense, risk can be understood as a metric for

the potential of a strategy or a model to leave a stable

equilibrium state into an undesired direction.

In many typical application fields of simulation,

the departure from an equilibrium state or from an

interval of tolerable states is also seen as critical, e.g. in

Queuing systems and production systems, if

queues run empty and machine utilisation sinks

towards 0, resp. conversely, if the available

waiting room capacity is exceeded and

therefore client orders are lost

Ecological systems, if necessary population

sizes or quantities of substance are fallen

below or exceeded, and the system collapses

Physical systems, if material strains are too

high, resulting in damages. Physiological

systems may suffer from underutilisation as

well, thus becoming inoperative in

consequence of non-use.

2.2. Downside Risk as Asymmetric Risk Conception

Deviations from the mean may be uncritical into one

direction, while undesired into the other direction. In

finance, only below-average returns (resp. above-

average losses) pose a risk for an investment, while

excess returns are welcome and may be ignored in

terms of risk assessment. Quantitative finance has

elaborated an asymmetrical risk metrics category called

downside risk, where only one-sided variations of return

in the sense of underperformance are considered as risk.

Asymmetric risk perceptions can also be found in

the application fields of simulation, with regard to

desired resp. undesired deviations from means or

system equilibrium states. Thus longer queues in

production, higher pollutant concentrations in

ecological systems or stronger physical strains will

generally be considered as more risky and less

desirable, while this is usually not true for the opposite

Proceedings of The International Workshop on Applied Modeling & Simulation, 2012

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cases. On this background of comparable asymmetric

evaluation preferences, downside risk metrics from

quantitative finance should be more suitable for risk

assessment in simulation application fields than

conventional symmetric standard statistics.

2.3. Practical Implementation

We would like to provide modellers of general discrete

event systems with additional tools, which allow them

to assess inherent “risks” of models more adequately,

following the concepts of quantitative finance. This can

help in understanding model dynamics more

appropriately and can deliver new fruitful approaches

and deeper insight concerning analysis and adaptation

of undesired model behaviour.

For this purpose, the four risk metrics from

quantitative finance discussed below are transferred into

our general purpose discrete event simulation

framework Desmo-J (www.desmo-j.de, Page and

Kreutzer 2005) as statistical extensions. This work is

currently carried out in the context of a bachelor thesis

in our working group Modelling and Simulation (MBS)

in the Department of Informatics at University of

Hamburg.

3. RISK METRICS

A risk metric is a concept to assess risk. In comparison,

a risk measure is the implementation of a computational

process, employed to calculate a certain risk

measurement. As we focus on the conceptual side of

risk, the term risk metric is used in this paper.

In this section we describe four central risk metrics

of quantitative finance in their original context first and

afterwards exemplarily illustrate them by simulation

queues. Advancing to observation variables, we

generalise the concepts and transfer them into the field

of general purpose discrete event simulation. We outline

the modifications and enhancements we have carried

out and discuss certain implementation aspects.

Formal definitions of the mentioned risk metrics in

their original financial context can be found in e.g.

Yang, Yu, and Zhang (2009); Lohre, Neumann, and

Winterfeldt (2009) or Giorgi (2002).

3.1. Semi-Variance

As stated above, only those trades yielding a below-

average return actually contribute to the downside risk

of a trading strategy. By contrast, trades with above-

average returns are welcome and do not increase

downside risk. Insofar, only those undesired return

deviations below expected return are accounted for in

the Semi-Variance concept. The computation is carried

out as for the standard variance, but observations above

the mean are skipped.

In the characterization of a queue, we can as well

assume that only one of the two possible deviation

directions from the mean queue length is preferable,

depending on the context. This means that in computing

Semi-Variance only time spans are to be considered,

where the average queue length is exceeded or fallen

below, respectively, depending on the preferred point of

view. (Commonly, there will be a preference for shorter

queue lengths.)

By this metric, we can gain a first impression and a

basis for comparison, with regard to the size of

undesired variations of queue length.

For the implementation of further risk metrics

described below, it is required to store all single

observations as time series, until the simulation has

ended. Thus the implementation of Semi-Variance

accesses the total sample collected at the end of a

simulation run, in contrast to the stepwise online

computation of standard statistics, as normally applied

in Desmo-J (Page, Lechler, and Claassen 2000).

In order to provide general applicability

concerning the direction of deviation perceived as risk,

we compute negative as well as positive Semi-Variance

and provide both of them separately on simulation

reports.

3.2. Value at Risk

The Value at Risk (VaR) of an open trade quantifies the

maximum loss (in absolute currency units) that will not

be exceeded at a given confidence level of 1 – , at the

end of a set period. In other words, VaR is equivalent to

the -quantile of the probability distribution of the

returns expected in the set period.

Probability Distribution

of Returns expected

in the Set Period

Value at Risk 0

Figure 2: Illustration of the Value at Risk metric

The basic return distribution for computation can

be determined by Historical Simulations, Monte-Carlo-

Simulation or the Variance-Covariance method

(Linsmeier and Pearson 2000).

Value at Risk is an important key figure in

banking: Under the Basel II accord, banks are legally

obligated to compute market risk in terms of the Value

at Risk metric on a daily basis, in order to ensure that

pre-set maximum losses won’t be exceeded within

certain time horizons.

Transferred to queues in general purpose discrete

event simulators, VaR indicates the minimum or

maximum queue length expected after a given

simulation time interval and at a set confidence level,

starting from the current queue length. This becomes an

important measurand, if certain queue lengths must not

be exceeded or fallen below, e.g. because of cost

restraints or capacity limits of the waiting room. Thus,

VaR gives a formative indication how to dimension a

waiting room at a given initial state, a set confidence

level and a designated time horizon, in order to meet

specific restrictions.

Proceedings of The International Workshop on Applied Modeling & Simulation, 2012

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In simulation practice, it should be avoided to refer

to the current queue length resp. the present value of an

observation variable, as these values permanently

change during simulation runs and therefore are not

eligible as fixed states of reference for the VaR

measure. Instead, we implement the VaR concept by

only considering the relative change of observation

variables compared to their previous states and call this

Delta at Risk.

In case of bounded state spaces, there is a risk of

distortion at boundary states and extreme states, such as

the length of a queue cannot fall below zero. In this

context, no further decrease of the queue length will be

observable next. In contrast, if the state of an

observation variable is far away from boundary states

and extreme states, their impact on the next

observations will be much smaller.

Without differentiation, this could lead to

overestimating the risk of increase of queue length in

cases of lengths > 0, as more length increment

observations starting from length = 0 would be regarded

than appropriate in the normal case.

Conversely, observations in the context of a queue

length > 0 would distort the representative basis of

future states for length = 0, as unrealistic length

decrement observations were included in the sample,

though for length = 0 a decrease of queue length below

zero is conceptually impossible.

The stated danger of reduced significance due to

insufficient consideration of marginal or extreme

contexts exists in the practical use of Value at Risk in

financial institutions as well. Often the present state of

financial markets is abstracted from, and the risk of loss

is calculated without consideration of the current

context. For example, the risk of high losses intuitively

is lower at the end of a financial market decline than at

the beginning of the same period, as most fearful

investors have already left the market at an earlier stage,

thus selling pressure eases. Nevertheless, the current

market environment normally is not considered when

calculating VaR.

As long as state change probabilities are

determined regardless of the context of boundary states

and extreme states, the VaR metric consequently runs

into danger of diminished significance.

We address this problem by calculating four

different Delta at Risks in simulation reports, according

to four contexts: On the one hand we determine the

Delta at Risk related to the most frequent and the

median state of all states observed during the simulation

run. On the other hand we compute two more Delta at

Risk measures, corresponding to the minimum and

maximum states observed. Using the example of

queues, output is generated for the expected alteration

of queue length considering empty, frequent, median

and maximal length queues.

The choice of the median state in the sense of a

representative average state is motivated by the

approach to analyse a state as far away from boundary

states and extreme states as possible, in order to provide

a largely unaffected Delta at Risk representing

intermediate states.

In case of non-symmetrical state distributions, the

most frequent state is situated closer to boundary states

or extreme states than the median state. Even though it

might be under (partial) influence of boundary states

and extreme states, the most frequent state may be

regarded as a better basis for significant conclusions in

certain contexts, as statements concerning this state may

have higher empirical correspondence.

The description above deals with the original and

probably most frequent application of VaR as a risk

metric for one-dimensional discrete state spaces (here:

currency units). In principle, the Delta at Risk concept

is canonically extendable to multi-dimensional or

continuous state spaces as well. In order to keep

simulation reports manageable, the mapping of sets of

multi-dimensional states or intervals of states to a one-

dimensional discrete state space should be considered,

though.

With this in mind, we continue to describe Delta at

Risk in terms of one-dimensional discrete state spaces,

as we expect this to be the most common use case.

A naive implementation of Delta at Risk of an

observation variable could compute and store the delta

of state size divided by the simulation time passed since

the last state change, as a quotient, at every change of

the observation variable. By sorting these rates of

change in ascending order, accumulating their

frequencies and normalising these, the distribution

function F(x) could be constructed, describing the

distribution of rates of change per reference time unit.

However, rates of change computed in this way

would base on variable length time intervals containing

only one actual change event, being scaled to a

reference time unit afterwards. Real consecutive

observations within real reference time intervals would

be ignored. Thus, extrapolations of short time intervals

could lead to excessive distortions when dealing with

longer time intervals.

Instead, we determine and store the size of state

change at every modification of an observation variable,

as compared to the state the variable had a fixed time

interval earlier. For this purpose the state history for (at

least) the time interval under consideration has to be

stored within a time series during the simulation run.

Subsequently, the recordings of these actual

relative state changes within the set time span, are

sorted in ascending order, accumulated and normalised

in frequency, yielding to a more realistic distribution

function F(x). This procedure takes into account that

subsequent state changes may neutralise each other

partially or entirely over longer time frames, as often

observed in practice.

For flexibility, n time spans of interest may be

passed as input parameters, leading to a risk analysis for

each of the time frames given, regarding the cumulative

outcome of all multiple state changes actually observed

within that time frame, recorded at every simulation

event concerning the observation variable.

Proceedings of The International Workshop on Applied Modeling & Simulation, 2012

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Beyond the original application in quantitative

finance, we extend the initially asymmetrical concept of

downside risk to both ends of the state space, as it

cannot be assumed that risk always is represented at the

left end of the state space. Thus, we appraise the

potential risk at the right end of the distribution

likewise. As a consequence the -quantiles for = 1%,

2.5%, 5%, 10% as well as for 90%, 95%, 97.5% and

99% are determined from F() and output on the

simulation report.

In sum, the Delta at Risk metric derived from

Value at Risk quantifies the maximum size of change

expected (i.e. risk, in terms of quantitative finance) with

regard to an observation variable, at a given confidence

level , after a set period, and according to four well-

defined reference states.

Typical conclusions based on the simulation report

were “At a confidence level of 97.5% and starting from

the observed median m, the queue length will

maximally increase by x entities and maximally

decrease by y entities after 10 minutes of simulated wall

clock time” or “Starting with an empty queue and given

a confidence level of 99%, the queue length will not

exceed z entities after 1 hour of simulated wall clock

time”.

3.3. Expected Shortfall

Value at Risk quantifies the maximum loss at a given

confidence level of 1 – , nevertheless a loss exceeding

VaR is not impossible, as long as > 0. The

shortcoming of the VaR concept is that it does not make

a statement about the amount of loss to be expected, if

the limit of Value at Risk is exceeded in critical cases.

This gap is filled by the metric Expected Shortfall

(also referred to as Conditional Value at Risk or

Expected Tail Loss, Rockafellar and Uryasev 2000). It

expresses the expected amount of loss for the fraction

of cases where VaR is exceeded. Hence, Expected

Shortfall is a metric to assess the potential extent of

damage for unlikely but possible cases of extreme

events (in terms of the choice of ). Expected Shortfall

is an important key figure used to describe the state

space beyond VaR when structuring finance products

with insurance nature.

Probability Distribution

of Returns expected

in the Set Period

Expected Shortfall 0

Value at Risk

Figure 3: Illustration of the Expected Shortfall metric

Here too, we generalise the quantitative finance

metric with regard to three aspects, for the purpose of

transferring the concept to general simulation

application domains: Firstly, we move from expected

absolute loss to expected relative state change of an

observation variable. Secondly, we consider minimum,

median, most frequent and maximum states as

references. Thirdly, both ends of the probability

distribution are regarded likewise, to remain flexible

with respect to where to attribute risk, depending on the

special application area.

In order to avoid confusion, the modified risk

metric is called Conditional Delta at Risk.

Conditional Delta at Risk is based on the same data

as Delta at Risk introduced above. In the course of

calculating Delta at Risk, the Conditional Delta at Risk

simply can be computed as the expected value of the

empirical probability density below (resp. above) the -

quantile of all observations.

Referring to queues, Conditional Delta at Risk

indicates the expected growth or contraction of queue

length for the remaining fraction of cases beyond the

confidence level. If a waiting room was dimensioned

taking account of the Delta at Risk metric, its overload

in the remaining fraction of cases is now appraisable.

A typical conclusion based on the simulation

report would be “If, starting with an empty queue and

given a confidence level of 99%, the queue length

exceeds the Delta at Risk of z entities after 1 hour of

simulated wall clock time, then an average queue length

of z + c entities can be expected”.

3.4. Drawdown Phases

The term Drawdown of a trading strategy relates to an

interim loss of asset value, after a new peak of asset

value was reached beforehand. Drawdown may be

given in absolute currency units or as a percentage of

the preceding peak asset value. A Drawdown Phase

often extends over several consecutive (mis-)trades and

thus cumulates their effects.

Drawdown Recovery starts at the point of

maximum interim loss. It lasts until the previous peak

asset value is reached again or exceeded.

-10%

0%

-20%

Jul 2011 Mar 2012Nov 2011

Drawdown

Drawdown Time Drawdown Recovery Time

Drawdown Phase

Figure 4: Drawdown Phase of the L’Oréal Share from

July 2011 to April 2012

Drawdown and Drawdown Time give an

impression of extent and speed at which the state of

observation variables may move into an undesirable

direction. Therefore, these key figures allow an

assessment of undesirable system dynamics in terms of

Proceedings of The International Workshop on Applied Modeling & Simulation, 2012

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vulnerability or susceptibility to disturbances. By

contrast, the Drawdown Recovery Time provides an

indication of the regenerative capacity of the analysed

system.

A financial trading strategy may experience a

multitude of Drawdown Phases over time. Especially

the Maximum Drawdown ever undergone is of

particular interest with regard to trading futures

contracts in financial markets, as this key figure

determines the required minimum margin of a trading

account, to withstand the highest Drawdown

encountered so far in the strategies history.

Drawdowns and their recoveries can only be

quantified ex post, when a Drawdown Phase is

completed and a new peak in asset value has been

reached. Moreover, a trading strategy is almost always

in a Drawdown, except from new peaks in asset value.

Hence it is of vital interest to analyse the structure of

Drawdowns to gain insight into the dynamics of

undesirable behaviour.

In the context of queues, a queue length of 0 may

be set as base level, corresponding to the peak asset

value in financial context. Then Drawdown, Drawdown

Time and Recovery Time characterise the dynamics of

formation and reduction of queues, regarding the queue

length as observation variable.

Since a multitude of Drawdown Phases per

observation variable is to be expected in simulation

runs, we extend the quantitative finance Drawdown

concept, as it originally focuses only on the extreme

case Maximum Drawdown resp. Average Drawdown.

To provide a quick overview of the total dynamics

of the system modelled, we classify all Drawdowns

according to their absolute extent and display their

distribution in a histogram. The number of histogram

bins is determined according to the rule of Freedman

and Diaconis (1981), after the simulation has ended.

Two additional histograms visualise the

distribution of Drawdown Times and Drawdown

Recovery Times in a similar manner.

For further orientation, we introduce a Drawdown

scatter plot, encoding Drawdown Time as x-coordinate,

Drawdown Recovery Time as y-coordinate and the

Drawdown extent as colour of a data point. Hereby

character and distribution of all Drawdown Phases

during the simulation run can be seen at a single glance.

Moreover, all Drawdown Pathways per

observation variable are superimposed in a joint

coordinate system. Thus, a good overview of the typical

and most severe Drawdown Phases is given, including

the Recovery sub-phases.

A second diagram visualises the superimposed

time series only of the Recovery sub-phases per

observation variable, providing a quick overview of the

regenerative properties of the system modelled.

Beyond the specified extended analysis of the

Drawdown concept itself, we generalise this risk metric

in three ways, in order to support its flexible and

unrestricted utilisation in simulation application

domains:

We consider both the setbacks and recoveries

on the way towards peak states (“classical”

Drawdowns) and complementarily the ascent

and descent phases on the way towards bottom

states. By this means, we again take into

account that the interpretation of a certain state

development direction as risky or preferable

cannot be predetermined for the manifold

application areas of simulation.

Furthermore, after determination of the median

state at the end of a simulation run, the time

series of observed variable states is divided

into phases below and above the median.

These phases are treated separately as

Drawdowns and Recoveries concerning states

below the median resp. as ascents and descents

concerning states above the median. This

supports the alternative point of view of

striving for a central state of equilibrium and

considering deviations from this balanced state

as risk. Since phases below and above the

median are treated separately, it remains free

whether risk is attributed to one or both

directions of deviation.

For non-symmetrical empirical distributions,

the same handling as above is applied, but this

time with reference to the state with the highest

frequency instead of the median state.

Accordingly, all advanced statistical and graphical

analysis mentioned (3 histograms, 1 scatter plot, 2 time

series diagrams) are provided for all six use cases of the

generalised Drawdown concept described above.

4. SUMMARY

In quantitative finance, specialized discrete event

simulators called back testers are utilized, in order to

evaluate financial market trading strategies. Here,

strategies are simulated in different historical market

environments and evaluated, compared and optimised

by means of a wide range of assessment criteria. A

significant assessment category is related to the risk

taken in following a particular trading strategy. In this

context, risk in terms of volatility is understood as a

metric for the potential to deviate from a characteristic

average rate of return. Additionally, quantitative finance

has elaborated the concept of downside risk in the form

of asymmetrical risk metrics, where only negative

deviations in the sense of underperformance are

regarded.

We propose to introduce the four most accepted

financial risk metrics of back testers into general

purpose discrete event simulators. We think that these

metrics open up new and fruitful views on model

dynamics in general and may specifically support the

evaluation and possibly optimisation of undesired

model behaviour. In particular, dimensioning of waiting

rooms as well as planning of processing capacities

should benefit from the generalised risk key figures.

Proceedings of The International Workshop on Applied Modeling & Simulation, 2012

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In order to support a preferably wide field of

application domains in discrete event simulation, we

extend the transferred metrics Value at Risk and

Expected Shortfall in three aspects: Firstly, we advance

from expected absolute loss of currency units to

expected relative changes of observation variables, to

allow deriving general statements independently from

particular current states. Secondly, we consider the

minimum, median, most frequent and maximum state of

observation variables in order to handle boundary and

extreme states separately. In this sense, the median of

an observation variable represents a state as far as

possible from extreme situations. For non-symmetrical

empirical distributions, the most frequent state is

regarded as well, as a maybe better basis for significant

conclusions. Thirdly, we account for both ends of state

distributions, since depending on the application

domain, risk may be regarded as deviation into different

directions, possibly also into both directions.

The third aforementioned generalisation is also

applied when transferring Semi-Variance to discrete

event simulation.

The second and third extension mentioned above

concern Drawdown Phases, too.

We aim at providing a concrete tool for the

modeller of general discrete event models, in order to

convey an impression of the value of transferring

quantitative finance risk metrics into other domains. For

this reason, our general purpose simulation framework

Desmo-J is extended by these concepts in a Bachelor

thesis at the working group of Modelling and

Simulation in the Department of Informatics at

University of Hamburg. We expect to provide a more

sophisticated risk estimation in the various application

domains of discrete event simulation as compared to

conventional standard statistics.

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AUTHOR BIOGRAPHIES

Bernd Page holds degrees in Applied Computer

Science from Technical University of Berlin, Germany,

and from Stanford University, USA. As professor for

Applied Computer Science at University of Hamburg he

researches and teaches in the field of Discrete Event

Simulation as well as in Environmental Informatics.

Arne Koors obtained his master degree in Computer

Science from University of Hamburg, Germany. Since

then he has been working as a software developer and

management consultant in the manufacturing industry,

primarily in the field of forecasting and demand

planning. Meanwhile he works as a research associate

and on his PhD thesis in the field of financial

simulations in the simulation group led by Prof. Page.

Proceedings of The International Workshop on Applied Modeling & Simulation, 2012

978-88-97999-07-2; Bruzzone, Buck, Cayirci, Longo, Eds.

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