Using Volatility Surface Parameters to Measure Option Risk

Summary

The document considers how to describe option risk across an implied volatility surface. Standard Black–Scholes Greeks measure sensitivity to model inputs, but Vega is difficult to aggregate across options because an implied volatility move need not be identical at every strike and expiry.

It proposes parameterizing each expiry with quantities such as at-the-money volatility, skew, and curvature, then measuring option price sensitivity to shocks in those shared parameters. Such measures could align risk reporting with how volatility is quoted in markets such as rates and foreign exchange, where traders often transact at the money and at selected wing points. The text raises this as a question rather than presenting a formula, empirical result, or validated risk framework. In practice, the usefulness of parameter sensitivities depends on the chosen surface model and on how parameter shocks represent actual market moves.

Key ideas

• Vega is not directly additive across options when their implied volatilities move by different amounts.
• A surface parameterization can express risk through sensitivities to at-the-money volatility, skew, and curvature.
• Parameter-based risk measures may better match markets quoted at selected volatility points.
• The proposal requires a surface model and a defensible definition of parameter shocks.

Tags

# Vol surface parameter risk


# Vol surface parameter risk












The traditional black-scholes greeks are risks with respect to the BS pricing model inputs. For a single underlying asset, they are all additive execpt for Vega, because the dImpliedVol that every option experiences is not necessarily the same.

This got me thinking about if there's a way to quantify IV risk in a parsimonious way across the full surface. If we take a SABR or SVI style parameterization, each expiry is parameterized by an ATM vol, skew, curvature, and potentially more parameters. These params are shared at least across the surface, so one could compute the sensitivity of the option price to shocks in these 3 parameters.

Is there a more scientific basis for this line of reasoning? I imagine in rates/fx where vols are quoted only for ATMs and a few select wing points, one would rather quantify those risks than fixed-strike IV risk.

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