Value-at-risk models (VaR and Expected Shortfall) in low-liquidity markets

What it is about

Calibration and validation of market risk models, with value at risk (VaR) and Expected Shortfall, in settings where liquidity and price availability are limited.

Session summary

The speaker explains how to calculate the value at risk (VaR) of a fixed-income portfolio in a low-liquidity market such as the Dominican one. He starts with identifying the risk factors (the yield curve, exchange rate, credit spread, optionality and liquidity), how to map positions to those factors (by principal, by duration or by cash flows) and the three calculation methodologies: parametric, historical simulation and Monte Carlo simulation, with their strengths and limits. He recalls that VaR is a percentile that says nothing about what happens after an exceedance, can fail in crises and does not always meet the conditions of a coherent risk measure.

He presents conditional value at risk, or Expected Shortfall, as the alternative: it does measure how bad losses can be once VaR is exceeded, and it is where Basel regulation is heading. He devotes an important part to the liquidity risk of instruments: the bid-ask spread, the price impact of one’s own positions, market depth, and how to adjust the model with a liquidity-adjusted VaR and longer liquidation horizons. He closes with calibration through backtesting, the stress tests that complement it, and the governance and documentation of the model. The questions covered the effect of mark-to-market valuation on banks, expert judgment when a backtest fails and tests for balance-sheet interest rate risk.

Topics covered

• Risk factors and mapping of fixed income: principal, duration and cash flows
• Parametric, historical simulation and Monte Carlo VaR
• Limits of VaR and coherent measures: Expected Shortfall
• Liquidity risk of instruments and liquidity-adjusted VaR
• Backtesting (Kupiec and Christoffersen) and stress tests
• Governance, documentation and independence in model validation
• Questions: mark-to-market valuation, expert judgment and balance-sheet interest rate risk