Mapping Portfolio Instruments to Risk Factors for Delta-Normal VaR

Summary

The document explains how to represent equities, foreign exchange forwards, and options in a variance-covariance VaR framework. Its central recommendation is to map each instrument to the underlying risk factors that drive its value rather than treating every instrument as a standalone price series. An equity position maps to issuer equity risk and, when its currency differs from the portfolio currency, foreign exchange risk. A forward maps to spot foreign exchange and the relevant interest-rate factors in both currencies.

Options require a nonlinear approximation: the answer proposes delta-gamma exposure and inclusion of equity, interest-rate, volatility, and possibly foreign exchange risks. Payoff structure and quanto features can affect the mapping. The approach is presented as an approximation, with limitations for nonlinear derivatives and longer horizons; it may be unsuitable for portfolios with many options or assets with skewed distributions. The exchange gives conceptual guidance rather than a full calibration recipe, covariance construction, or worked VaR calculation, so instrument-specific risk mapping and model validation remain necessary.

Key ideas

• VaR inputs should represent the risk factors that drive instrument values.
• Equities can map to issuer equity risk and, when relevant, foreign exchange risk.
• Foreign exchange forwards can involve spot and interest-rate risks in both currencies.
• Options may be approximated with delta-gamma exposure plus volatility and other relevant risks.
• Delta-normal methods lose accuracy for nonlinear positions, long horizons, and skewed returns.

Tags

# VAR of portfolio containing options, equities and forwards


# VAR of portfolio containing options, equities and forwards












If we want to calculate VAR of a portfolio using variance covariance matrix (delta normal method), containing equities, forwards and options, how do we treat each asset class for making the variance covariance matrix:

- Equities - Take closing prices (I know)

- Forwards - Do we take spot prices orporated with interest rates or the forward rates calculated with Interest rate parity ?

- Options - No idea at all (please help me out)

Thanks.

## Answer by Nicholas (score 0, accepted)

https://quant.stackexchange.com/a/22606

RiskMetrics Technical Document. Chapter 6 - may help to grasp an idea of mapping instruments to relevant risk factors.

For example

- equity position can be mapped to EQ Risk (factor = issuerticker) and if equity_ccy is different from portfolio_ccy also FX Risk (factor = fxspotrate);

- fx forward can be mapped to FX Risk (factor = fxspotrate) and IR Risk (factors = rate_ccy1, rate_ccy2);

- for options you may approximate with delta-gamma position and map to EQ Risk (factor = issuerticker), IR Risk, Vega risk and if applicable FX Risk. Also be careful with details here (payoff type, quanto payoff, etc..)

Be aware that

> method is less accurate for options and other non-linear derivatives. It also becomes less accurate at longer horizons. Therefore not recommended for long horizons, for portfolios with many options, or for assets with skewed distributions.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.