Curvature Risk as Loss Beyond Delta Under a Market Shock

Summary

The document introduces curvature risk within the Basel Committee’s sensitivity-based approach, which groups portfolio risk into delta, vega, and curvature components. It frames curvature as the additional exposure that arises when a price move changes a position’s delta, so a linear delta estimate alone does not capture the full profit or loss.

The accepted response describes the calculation conceptually: apply a specified shock to the underlying and measure the profit or loss left unexplained by the position’s local delta. The excerpt points to a regulatory document for formulas but does not reproduce them, specify the shock scenarios, or work through a numerical example. A second response likens the effect to the nonlinearity of the price-value relationship, though its use of “beta” is not established as the formal calculation. The material is therefore an introductory explanation, not a complete implementation guide.

Key ideas

• Curvature risk captures changes in a position’s delta as the underlying price moves.
• A delta-only estimate approximates value changes locally and can miss nonlinear effects.
• The curvature component is described as profit or loss beyond that explained by local delta under a specified shock.
• The excerpt refers to an external standard for formulas but does not provide calculation details.

Tags

# What is curvature risk?


# What is curvature risk?












The BCBS has presented a new standard approach for measuring risk for a portfolio, which is based on sensitivities, that is “delta”, “vega” and “curvature” risks.

> Delta risk measures the change in price resulting from a small price or rate shock to the value of each relevant risk factor. Vega risk is the risk due to variations in the volatility for options - computed as the product of the vega of a given option and its implied volatility; and curvature risk captures the additional risk due to movement in the delta when the price changes.

The text does not contain formulae: how is the curvature risk actually computed?

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/28024

The formulae are on p17 of the document attached to the link you included. http://www.bis.org/bcbs/publ/d352.pdf It's just the profit or loss due to a specified shock in the underlying, which is not explained by the local delta of the position.

## Answer by Wei (score 0)

https://quant.stackexchange.com/a/30808

From the description, is it beta? Changes of Delta is captured by Beta, cause the price and value relation is not linear, so by simply considering Delta, it omits the shape of the relation curve.

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