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Volatility Arbitrage

Express relative-value views across implied and realised volatility.

Reviewed 2026-08-10TheQuantBateman Research2 linked labs
01Intuition

Name the object before manipulating it.

Express relative-value views across implied and realised volatility. Fix the information set, units and market convention before using the relationship in pricing or risk.

ONE-LINE DEFINITION

Express relative-value views across implied and realised volatility.

02Mathematics

State the governing relationship.

PnL⁡hedged≈12∫0TΓtSt2(σreal,t2−σimp,t2)dt−costs\operatorname{PnL}_{hedged}\approx\tfrac12\int_0^T\Gamma_tS_t^2(\sigma_{real,t}^2-\sigma_{imp,t}^2)dt-\text{costs}
Notation and units

Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.

03Assumptions

Draw the boundary of the claim.

01

Definitions, units and information sets are fixed before the mathematical relationship is applied.

02

Rates and volatilities use decimal units and time uses year fractions unless stated otherwise.

03

The relationship is local to its stated assumptions and should not be extrapolated mechanically.

“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
04Market use

Connect the definition to an observable.

Volatility Arbitrage connects an observable EQ quantity to valuation, scenario analysis or hedge interpretation. The desk view depends on units, timestamp and quotation convention.

Intuition→Mathematics→Implementation→Desk risk
05Desk view
FRONT OFFICE VIEW

Translate the concept into a risk question.

State the convention, identify the observable and ask which EQ risk remains after the proposed hedge.

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06Related

Follow the nearest dependency.