On the supply side of the market, there are a handful of vendors who are leading the way.
These include Algorithmics, Fermat, SAS and SunGard. The common factor amongst the
leaders is the ability to offer multiple solutions across the ERM (enterprise risk management)
spectrum and coverage across multiple assets/products. These integrated offerings
provide significant value for financial institutions looking for a cost-effective ‘one-stopshop”
for a range of risk and compliance solutions. The market is also segmented along
specific verticals and geographies.
Sustainable profit and value development over time should be maximized given a certain
risk level, taking into account the aforementioned constraints. On the other hand, we can
seek to minimize the risk given a targeted profit level. To do so, many banks are using risk
adjusted techniques such as RAROC and RORAC.
In the context of this article, risk is defined as the variation (standard deviation) of key factors
such as profit, value, capital requirements and liquidity.
The success of our technique (to be presented below) is to be gauged on whether we are
able to quantify the risk for future time periods. This suggests the need for a distribution
of the forecasted profitability (Earning @ Risk), values (Value @ risk) and liquidity cash
flows (Liquidity @ Risk). Value is understood as nominal value, amortized cost or fair value
according to the FASB/IFRS.
Risk factors to be taken into account
Risk factors can be classified into exogenous and endogenous risk factors. The former
includes the GDP, stock market indices, default rates, inflation rate, and the unemployment
rate. The latter includes the strategies and decisions taken by a bank. For example, a
bank may decide to offer teasers for certain instruments as was the case for sub-prime
mortgages. A bank may decide to package mortgages into asset-backed securities or to buy
a collateralized debt obligation.
Clearly, there are also correlations between the various risk factors. The default rate is a
function of the GDP and the employment rate. The economy has a complex relationship
with the stock market, whereas the behaviour of the stock market is generally a forerunner
of that of the whole economy.
The choice of risk factors to be taken into account depends on how far a bank wishes to
proceed. Eventually, a bank will focus on those risk factors most relevant for its own business
Risk
• market
• credit
• strategic
• liquidy, etc
“To get profit without risk, experience without
danger, and reward without work, is as
impossible as it is to live without being born. “
– A P Gouthev
Constraints
min. capital
min. liquidity
Profitability / Sustainable Value Creation
model. A mortgage bank may include the interest rate level, GDP, house prices and default
rates. An investment bank will have a finer granularity regarding the types of industries in
which they invest. A credit card institution may predominantly take into account the GDP.
It is appealing to simulate as many risk factors as possible, in order to increase the precision
and accuracy of the forecast. However, this leads to the risk of losing focus and having an
overly complex model which is difficult to validate.
Figure 5 illustrates the relationship between the main risk categories.
Figure 5: Relationship between Main Risk Categories
Contract-centric approach/unified financial analysis
The main elements of the forecast are the financial instruments (contracts) such
as mortgages, bonds, saving deposits, derivatives, and much more. The forecasted
development (simulation) must be contract-based in order to model the relationship of
variations of the risk factors, such as economic cycles, and strategic decisions, against the
future profitability, values and cash flows.
The contract-centric approach should also apply for new business (simulated forward
financial instruments of the whole balance sheet). Once we have the simulated financial
events of every financial instrument, such as interest payments, amortizations, repricing,
defaults, and recoveries, we can easily derive cash flows, profit and loss, and other values.
Example: with a contract-centric approach for the new business, we are able to map the
relationship between the duration of new mortgages and the interest rate level. Clients
tend to choose longer periods for fixed rate mortgages when interest rates are low, and
shorter periods when interest rates are high. In addition, the volume of variable mortgages
tends to increase, when clients expect decreasing interest rates and decrease when they
expect increasing interest rates.
Figure 6: Contract-centric Approach
Any financial analysis is finally a combination of liquidity, value, income, sensitivity and risk
analysis. Only a unified (contract-centric) approach allows their calculation in a consistent
and correct manner.
Dynamic simulation/forecasting
As previously mentioned, we need to have a going concern approach in order to reliably
quantify future risks. This going concern approach is based on forecasted risk factors,
the existing financial instruments, forecasted financial instruments (new production),
assumptions about the client behaviour, and the strategy of the financial institution. In the
following set-up, we assume that we simulate a whole balance sheet. In case we simulate
only a portfolio, then the description must be adjusted accordingly.
The (static) input data:
• Financial instruments (assets, liabilities, derivatives): If possible, we need to use the
contract characteristics and not pure cash flow patterns. Using just cash flow patterns
will lead to losing the functional relationship with the risk factors.
• Current prices and values (risk factors) for interest rates, FX rates, indices, administrative
rates, etc.
• Macroeconomic factors such as inflation rates and GDP
• Credit risk data such as PD, migration matrices and LGD
t
Financial events
e1 e2 e3 en
Liquidity Value
Income Sensitivity
Risk
• Correlations between the risk factors to be included
• Counterparty information
Assumptions about:
• Client behaviour, which may include:
• Default/migration probabilities
• Early termination/prepayments
• Prolongation/roll-over of existing contracts
• Demand for new types of financial instruments
• Structural changes within the balance sheet
• Surrender behaviour
• The strategy of the financial institution, which may include:
• Launching of new financial instruments
• Launching of new services
• Funding policy
• Pricing of/teasers for financial instruments
A simulation engine, which allows:
• forecasting the risk factors into the future using a stochastic simulation process like
the LIBOR market model
• forecasting the set of new financial instruments taken into account the forecasted risk
factors, client behavior and the strategy of the financial institution.
What-if scenario
Now, we would like to present a simple simulation with a what-if scenario. For simplicity, the
risk factors in this example are restricted to interest rates, default probabilities and migration
probabilities.
A what-if scenario is a scenario, where we define the evolution of the risk parameters
manually. The extension using stochastic processes will be presented in the next section.
First, we define a forecast of the term structure for the subsequent 24 months. Of course,
any other time horizon and interval structure could also be used. We assume that the rate
level is increasing over time. The starting point at t0 is a low rate level, which ends with a
high rate level at t24. Through experience, we know that the higher the rate level, the higher
the default probabilities of our clients. Also, a higher default probability implies a change in
the migration matrix.
We also know that the higher the rate level, the higher the risk of prepayment of existing
loans. Furthermore, the prepayment is faster:
• the longer the remaining term to maturity
• the higher the spread between the loan rate and the market rate
• the better the alternative refinancing possibilities
• the lower the previous interest rates
• the lower the economic activity.
The prepayment behaviour can then also be adjusted with seasonal effects.
The relations can be estimated using a past time series of the variables and an econometric
technique such as the Ordinary Least Squares estimation.
Another effect we can simulate is the structural change in the balance sheet; retail clients
tend to decide more for fixed rate and long lasting mortgages and less for variable ones.
This means that the volume of fixed rate mortgages will increase and the volume of variable
mortgages will decrease.
As a bank, we may offer protection for our clients against the interest rate increase by
selling caps for variable mortgages. Instead of the mortgage rate’s increase according to the
market conditions, we offer a cap at, for example, 6%, but ask for an option premium.
The simulation engine takes into account all these discussed parameters and forecasts all
events of the financial instruments including cash flows, income and value.
In Figure 7 below we show one simulation path without credit risk effects and another with
credit risk effects (defaults).
Figure 7: Example Simulation Path
The extension of what-if using dynamic Monte Carlo simulation
As discussed above, we need to simulate not only one path, but many paths in order to get
a distribution of cash flows, income and value. The best way to do this is to apply economic
scenario generators, which simulate the risk factors as realistically as possible. This is in
contrast to arbitrage free models, for example, the LIBOR market model. Although arbitragefree
models are superior for option pricing, they do not reflect reality, since the evolution of
the risk factors hardly follows any arbitrage-free conditions.
All events of existing and newly generated financial instruments depend on one specific
t
P & L Credit risk free
With losses
Ma rket
s c ena rio
new business
new business
existing business
existing business
scenario or path. To say it another way round: every scenario, or path generates its own set
of events and newly generated financial instruments.
The final result is summarized in Figure 8. We get distributions for the cash flows, income
and value for each point in the future (e.g., each future end of the month). Having such a
distribution, we can calculate the variance (standard deviation), and quantify the simulated
risk factors.
Figure 8: Example Distributions
Although the technique is very powerful and close to reality, we need to carefully think
about the following aspects:
• Increasing the number of risk factors and model parameters may increase the accuracy,
but also the danger that we lose focus. Ultimately, it would be preferable to focus on
the most relevant factors and parameters. Trying to generate a sufficient number of
scenarios may require several thousand simulations. This would need a more advanced
technology infrastructure such as parallel processing (grid computing).
• We already need to optimize the simulation in terms of performance for medium-sized
banks. This
Sustainable profit and value development over time should be maximized given a certain
risk level, taking into account the aforementioned constraints. On the other hand, we can
seek to minimize the risk given a targeted profit level. To do so, many banks are using risk
adjusted techniques such as RAROC and RORAC.
In the context of this article, risk is defined as the variation (standard deviation) of key factors
such as profit, value, capital requirements and liquidity.
The success of our technique (to be presented below) is to be gauged on whether we are
able to quantify the risk for future time periods. This suggests the need for a distribution
of the forecasted profitability (Earning @ Risk), values (Value @ risk) and liquidity cash
flows (Liquidity @ Risk). Value is understood as nominal value, amortized cost or fair value
according to the FASB/IFRS.
Risk factors to be taken into account
Risk factors can be classified into exogenous and endogenous risk factors. The former
includes the GDP, stock market indices, default rates, inflation rate, and the unemployment
rate. The latter includes the strategies and decisions taken by a bank. For example, a
bank may decide to offer teasers for certain instruments as was the case for sub-prime
mortgages. A bank may decide to package mortgages into asset-backed securities or to buy
a collateralized debt obligation.
Clearly, there are also correlations between the various risk factors. The default rate is a
function of the GDP and the employment rate. The economy has a complex relationship
with the stock market, whereas the behaviour of the stock market is generally a forerunner
of that of the whole economy.
The choice of risk factors to be taken into account depends on how far a bank wishes to
proceed. Eventually, a bank will focus on those risk factors most relevant for its own business
Risk
• market
• credit
• strategic
• liquidy, etc
“To get profit without risk, experience without
danger, and reward without work, is as
impossible as it is to live without being born. “
– A P Gouthev
C
model. A mortgage bank may include the interest rate level, GDP, house prices and default
rates. An investment bank will have a finer granularity regarding the types of industries in
which they invest. A credit card institution may predominantly take into account the GDP.
It is appealing to simulate as many risk factors as possible, in order to increase the precision
and accuracy of the forecast. However, this leads to the risk of losing focus and having an
overly complex model which is difficult to validate.
Figure 5 illustrates the relationship between the main risk categories.
Figure 5: Relationship between Main Risk Categories
Contract-centric approach/unified financial analysis
The main elements of the forecast are the financial instruments (contracts) such
as mortgages, bonds, saving deposits, derivatives, and much more. The forecasted
development (simulation) must be contract-based in order to model the relationship of
variations of the risk factors, such as economic cycles, and strategic decisions, against the
future profitability, values and cash flows.
The contract-centric approach should also apply for new business (simulated forward
financial instruments of the whole balance sheet). Once we have the simulated financial
events of every financial instrument, such as interest payments, amortizations, repricing,
defaults, and recoveries, we can easily derive cash flows, profit and loss, and other values.
Example: with a contract-centric approach for the new business, we are able to map the
relationship between the duration of new mortgages and the interest rate level. Clients
tend to choose longer periods for fixed rate mortgages when interest rates are low, and
shorter periods when interest rates are high. In addition, the volume of variable mortgages
tends to increase, when clients expect decreasing interest rates and decrease when they
expect increasing interest rates.
Figure 6: Contract-centric Approach
Any financial analysis is finally a combination of liquidity, value, income, sensitivity and risk
analysis. Only a unified (contract-centric) approach allows their calculation in a consistent
and correct manner.
Dynamic simulation/forecasting
As previously mentioned, we need to have a going concern approach in order to reliably
quantify future risks. This going concern approach is based on forecasted risk factors,
the existing financial instruments, forecasted financial instruments (new production),
assumptions about the client behaviour, and the strategy of the financial institution. In the
following set-up, we assume that we simulate a whole balance sheet. In case we simulate
only a portfolio, then the description must be adjusted accordingly.
The (static) input data:
• Financial instruments (assets, liabilities, derivatives): If possible, we need to use the
contract characteristics and not pure cash flow patterns. Using just cash flow patterns
will lead to losing the functional relationship with the risk factors.
• Current prices and values (risk factors) for interest rates, FX rates, indices, administrative
rates, etc.
• Macroeconomic factors such as inflation rates and GDP
• Credit risk data such as PD, migration matrices and LGD
t
Income Sensitivity
Risk
• Correlations between the risk factors to be included
• Counterparty information
Assumptions about:
• Client behaviour, which may include:
• Default/migration probabilities
• Early termination/prepayments
• Prolongation/roll-over of existing contracts
• Demand for new types of financial instruments
• Structural changes within the balance sheet
• Surrender behaviour
• The strategy of the financial institution, which may include:
• Launching of new financial instruments
• Launching of new services
• Funding policy
• Pricing of/teasers for financial instruments
A simulation engine, which allows:
• forecasting the risk factors into the future using a stochastic simulation process like
the LIBOR market model
• forecasting the set of new financial instruments taken into account the forecasted risk
factors, client behavior and the strategy of the financial institution.
What-if scenario
Now, we would like to present a simple simulation with a what-if scenario. For simplicity, the
risk factors in this example are restricted to interest rates, default probabilities and migration
probabilities.
A what-if scenario is a scenario, where we define the evolution of the risk parameters
manually. The extension using stochastic processes will be presented in the next section.
First, we define a forecast of the term structure for the subsequent 24 months. Of course,
any other time horizon and interval structure could also be used. We assume that the rate
level is increasing over time. The starting point at t0 is a low rate level, which ends with a
high rate level at t24. Through experience, we know that the higher the rate level, the higher
the default probabilities of our clients. Also, a higher default probability implies a change in
the migration matrix.
We also know that the higher the rate level, the higher the risk of prepayment of existing
loans. Furthermore, the prepayment is faster:
• the longer the remaining term to maturity
• the higher the spread between the loan rate and the market rate
• the better the alternative refinancing possibilities
• the lower the previous interest rates
• the lower the economic activity.
The prepayment behaviour can then also be adjusted with seasonal effects.
The relations can be estimated using a past time series of the variables and an econometric
technique such as the Ordinary Least Squares estimation.
Another effect we can simulate is the structural change in the balance sheet; retail clients
tend to decide more for fixed rate and long lasting mortgages and less for variable ones.
This means that the volume of fixed rate mortgages will increase and the volume of variable
mortgages will decrease.
As a bank, we may offer protection for our clients against the interest rate increase by
selling caps for variable mortgages. Instead of the mortgage rate’s increase according to the
market conditions, we offer a cap at, for example, 6%, but ask for an option premium.
The simulation engine takes into account all these discussed parameters and forecasts all
events of the financial instruments including cash flows, income and value.
In Figure 7 below we show one simulation path without credit risk effects and another with
credit risk effects (defaults).
The extension of what-if using dynamic Monte Carlo simulation
As discussed above, we need to simulate not only one path, but many paths in order to get
a distribution of cash flows, income and value. The best way to do this is to apply economic
scenario generators, which simulate the risk factors as realistically as possible. This is in
contrast to arbitrage free models, for example, the LIBOR market model. Although arbitragefree
models are superior for option pricing, they do not reflect reality, since the evolution of
the risk factors hardly follows any arbitrage-free conditions.
All events of existing and newly generated financial instruments depend on one specific
t
As s ets
L iabilities
....
at t24 at t1 at t0
Aaa . B . C D
Aaa 0.7 . 0.3 . 0.02 0.01
.
B 0.1 . 0.6 . 0.07 0.05
.
C 0.01 . 0.1 . 0.5 0.3
D 0 . 0. 0 1
Aaa . B . C D
Aaa 0.7 . 0.3 . 0.02 0.01
.
B 0.1 . 0.6 . 0.07 0.05
.
C 0.01 . 0.1 . 0.5 0.3
D 0 . 0. 0 1
....
Aaa . B . C D
Aaa 0.7 . 0.3 . 0.02 0.01
.
B 0.1 . 0.6 . 0.07 0.05
.
C 0.01 . 0.1 . 0.5 0.3
D 0. 0 . 0 1
Migra tion
Default
probabilities
D
A aa 0.01
...
B 0.05
...
C 0.3
D 1
D
A aa 0.012
...
B 0.06
...
C 0.2
D 1
D
A aa 0.02
...
B 0.055
...
C 0.33
D 1
....
P & L Credit risk free
With losses
Ma rket
s c ena rio
new business
new business
existing business
existing business
© Chartis Research Ltd 2008 Page 14
scenario or path. To say it another way round: every scenario, or path generates its own set
of events and newly generated financial instruments.
The final result is summarized in Figure 8. We get distributions for the cash flows, income
and value for each point in the future (e.g., each future end of the month). Having such a
distribution, we can calculate the variance (standard deviation), and quantify the simulated
risk factors.
Although the technique is very powerful and close to reality, we need to carefully think
about the following aspects:
• Increasing the number of risk factors and model parameters may increase the accuracy,
but also the danger that we lose focus. Ultimately, it would be preferable to focus on
the most relevant factors and parameters. Trying to generate a sufficient number of
scenarios may require several thousand simulations. This would need a more advanced
technology infrastructure such as parallel processing (grid computing).
• We already need to optimize the simulation in terms of performance for medium-sized
banks. Thisrequires the aggregation of financial instruments in such a way that there will
be a large reduction in the number of financial instruments without any unacceptable
loss of information. Based on our practical experience, we can reduce the number of
instruments by a factor of 50 to 100 (for saving deposits the factor can be as high as
100,000). The number of paths can be reduced by using techniques such as stratified,
antithetic path generations.
The dynamic simulation results in a distribution for the cash flows, values and income. For
each of these, we can derive the Liquidity at Risk, the Value at Risk and the Earning at Risk.
The risk is defined as the variance/standard deviation of each distribution.
The final result can only be achieved by:
• applying a going concern approach, in order to simulate reality closely.
• using a contract-centric approach, not only for the existing financial instruments, but
also for the simulated ones.
• using functional relations between the exogenous and endogenous risk factors,
including client behaviour and the strategy of the bank, with respect to the events of
the financial instruments.
