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

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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