Decomposing Vega P&L with SVI-JW Parameters

Summary

The document asks how to break an option position’s Vega P&L into contributions from at-the-money volatility, skew, curvature, and related SVI-JW parameters. It proposes approximating the change in implied volatility with a first-order expansion in those parameters, then multiplying by Vega. The central issue is how to calculate the component contributions and explain a large residual.

The document provides no answer, worked example, market data, or validation of the proposed decomposition. It therefore identifies a quantitative options-attribution problem rather than establishing a method. Any use of the suggested expansion would depend on details such as the volatility quote convention, parameter definitions, and whether the linear approximation captures the full change over the measurement interval. The residual is reported as large, but its cause is not diagnosed.

Key ideas

• The document frames Vega P&L as Vega multiplied by a change in implied volatility.
• It proposes attributing that volatility change to movements in SVI-JW parameters.
• The proposed breakdown includes at-the-money volatility, skew, and curvature effects.
• A large unexplained residual motivates the question, but the document does not identify its cause.

Tags

# Vega P&L Attribution


# Vega P&L Attribution












I am trying to decompose Vega PnL into ATM vol, skew, and curvature components. To that end, I am building an SVI model and using the SVI-JW parameterization to attribute Vega PnL via the following formula:

$VegaPnL = Vega \times dVol \approx Vega \times (\frac{dVol}{dv_t}dv_t+\frac{dVol}{d\psi_t}d\psi_t + \frac{dVol}{dp_t}dp_t + \frac{dVol}{dc_t}dc_t + \frac{dVol}{d\tilde{v}_{t}}d\tilde{v}_{t})$

However, the results are not satisfactory — the residual is extremely large. What is the correct way to perform this Vega PnL breakdown, and where might the problem lie?

Thx

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