Stress Testing Following P. Jorion, Value at Risk, McGraw-Hill Chapter 10
Daniel HERLEMONT
Need for Stress Testing VAR measures based on recent history can fail to identify extreme unusual situation that could cause severe loss Stress Testing
Stress Testing is required by the Basle Committee as well as recommended by the G-30 Derivatives Policy Group.
However the definition of Stress Testing is still vague ...
Daniel HERLEMONT
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Stress Testing can be defined as the process to identify and manage that could cause extraordinary losses Tools Scenario Analysis Stressing Models Policy Responses
Compared to VAR, Stress Testing appears simple and intuitive Daniel HERLEMONT
Contents Why Stress Testing is required increasing confidence level may not be sufficient ...
How to use scenarios to generate portfolios losses Scenarios analysis Stress models Management actions Daniel HERLEMONT
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Why Stress Testing ? - the 1987 crash The October 87 crash is a -20 sigma event ... Even if there are some time variation in volatility models, 20 sigma event are so far away that it should have never happen under normal model The 99% VAR would have totally missed the magnitude of actual loss Such event can be modeled through the use of Extreme Value Theory (EVT) Daniel HERLEMONT
Goal of Stress Testing Identify scenarios that would not occur under standard VAR models Simulating shocks that have never occurred (peso problem) or are more likely to occur that historical data suggest Simulating shocks that reflect permanent structural breaks or temporally changed statisticals patterns
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Implementing Scenario Analysis Define and select a scenario s obtained by a set of changes in risk factors All the securities are then re-evaluated using a full evaluation method similar to historical simulation, except that we don't generate all the distribution, and scenario receive equal small probabilities Daniel HERLEMONT
Generating Unidimentional Scenarios Traditional approach focuses on one variable at a time. For example, the G-30 Group recommend focusing on a set of specific movements: Parallel yield curve shifting by +/- 100 basis points Yield curve twisting by +/- 25 basis points Each of the 4 combinaisons of yield curve shifting and twisting Implied volatility change by +/- 20% Equity index value change by +/- 10% Currencies moving by +/- 6% Swap spread changing by +/- 20 basis points
Appropriate when portfolios depend primaraly on one source of risk
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Example - the SPAN system
Standard Portfolio Analysis of Risk (SPAN) set up by the Chicago Mercantile Exchange (CME) to determine collateral requirements, widely used by futures and options exchange to define margin requirements
SPAN is to determine portfolios values under a series of scenario. Then SPAN searches the largest loss and set the margin requirements at that level. Daniel HERLEMONT
SPAN Example
Manageable since SPAN consider only 2 factors Daniel HERLEMONT
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Multi-Dimentional Scenarios Analysis Mono-dimentional provides an intuitive understanding of the effects of movements in key variables, using a bottom up approah Problems: do not account for correlations
Multi-dimentional Defining a state of the world Inferring movements in markets variable This is a top-down approach
Perspective Scenarios Factor Push Method Daniel HERLEMONT
Conditional Scenario Method Systematic method to incorporate correlations across all variables consistently R* = extreme returns of key variables under extreme movements Perform conditional regressions
We can then construct predicted stress loss as
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Conditional Scenario Method- Example
Conditional Model provides better estimate of actual loss than Narrow (naive) model
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Historical Simulation
To some extent, extreme correlations can be inferred from historical events drawbacks: limited number of extreme events
Daniel HERLEMONT
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Systematic Scenarios Historical or prospective stress tests may not reveal the most dangerous states of the world With large portfolios, losses can arise from unexpected combinations of financial risk factors Approaches VAR Monte Carlo Analysis can be used to examine the worst loss from simulation Maximum Loss Criterion
Daniel HERLEMONT
Stress Testing Models critically examine all the steps in the generation of of risk measures, including stress testing models parameters Sensitivity Analysis: the effect of changing the functional form of the models (Derivatives can be priced using different models) Pricing models may fail in changin environments
One can test different models and take the worst case to mimizie model risk
options are near expiration and at-the-money with unstable deltas. (straddle, barriers, ...) .... these risk factors. âestimating the covariance matrix of risk exposure ...
Step 1: compute the covariance matrix from the correlation matrix and volatilities (given by ... Bond positions = distribution of money flows over time by.
The exception variable I, returns 1 if on day t if the loss on that day is larger than the VaR predicted for that day. If the VaR was not violated, then the exception ...
used time horizon formula that gives the expression of the N-day VaR in function ..... λ is found by picking the positive solution of the quadratic equation λ2Ïaa + ...
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