Square-Root Price Impact Modeling for Concentrated Derivatives Positions

Summary

The document frames a model-design problem for estimating the concentrated positions component of an additional valuation adjustment for derivatives. It proposes relating price or volatility impact to the volatility of valuation inputs, bid–ask spread variability, position size—potentially measured by vega—and average daily traded volume, also expressed in vega terms.

As a candidate, it cites a square-root impact relationship in which impact scales with a coefficient, volatility, and the square root of position size relative to market volume. It also mentions a VaR-based approach, but provides no derivation, calibration procedure, empirical comparison, or recommendation between the alternatives. The formula is therefore a starting point rather than a validated model; the document leaves parameter estimation, market-specific behavior, and the treatment of liquidity and uncertainty unresolved.

Key ideas

• The proposed adjustment concerns concentrated derivatives positions measured through sensitivities such as vega.
• The suggested inputs include valuation volatility, bid–ask spread variability, position size, and daily market volume.
• A candidate impact relationship scales with volatility and the square root of position relative to volume.
• The document also mentions a VaR-based approach but does not compare or validate either method.

Tags

# Market price impact in derivatives


# Market price impact in derivatives












I am trying to define a model to compute the Concentrated Positions AVA (Additional Valuation Adjustment), defined by the EBA in Article 14 of https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:02016R0101-20200626

To do this, for concentrated positions in derivatives (in terms of vega sensitivity, for example), the idea would be to define a model in which, considering the volatility of the valuation input, the volatility of the bid offer spread, the total concentrated position (or vega) and the average daily traded volume in market (vega), a price impact (or volatility impact) would be calculated.

Which model would be better to use? I've been studying a model based on the VaR metric and the following model given by literature

$$ I(q)=\epsilon⋅\sigma⋅\sqrt{{q/V}} $$

Thnks!

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