Value at Risk: Market Risk Models
Han Zhang
Director, Head of Market Risk Analytics
Corporate Market and Institutional Risk
August 23, 2013
University of North Carolina at Charlotte
Value at Risk
 What is VaR
In its most general form, the Value at Risk measures the potential
loss in value of a risky asset or portfolio over a defined period for a
given confidence interval.
 What does it mean
1-day 99% VaR at $10 mm for an Equity Portfolio
 How to calculate it
If the equity portfolio only has one stock from IBM, we collect for
example one year of stock price history on IBM, and calculate the
daily returns, and then apply such returns to the holding to
calculate the profit and loss (P&Ls), after that the vector of the
P&Ls are sorted in order, the 1% tail on loss side is the VaR.
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List of Models in Risk Analytics (RA)
 General Value at Risk (General VaR)
 Stress General VaR
 Debt Specific Risk (DSR)
 Equity Specific Risk (ESR)
 Incremental Risk Charge (IRC)
 Stress Testing
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What are all these models doing
 General VaR captures the risk from general market moves;
 Stress General VaR follows the same methodology as the
General VaR, but it captures the risk from a most stressful time
period;
 Additional to General VaR, DSR and ESR model capture the
idiosyncratic moves from individual names, plus the event risk
specific to the name;
 IRC captures default and migration risk beyond 10-day and to
1-year specific to the name;
 Bank conducts stress tests (forward looking assessments) to
gain information about the impact of adverse market events on
its positions.
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Model Coverage and Usage (Trading)
 Covers all covered trading positions:
– Interest rate
– Equity
– Commodity
– FX
– Credit products
– Structure products
 The models are used by
– Market Risk Oversight to monitor the risks/limits for trading
desk
– Market Risk Reporting Team to report bank’s Regulatory
Capital
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VaR method
 VaR method
– Variance - Covariance
– Historical Simulation
– Monte Carlo Simulation
 P&L calculation method
– Delta-gamma approximation
– Grid approximation
– Full revaluation
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