A Participation Calibrated Gamma Exposure Methodology for Index Options

<p>Gamma Exposure (GEX) is widely used to characterise option-market positioning, estimate dealer hedging pressure, and identify potential gamma-regime boundaries. As described in Section 4, the conventional framework aggregates option gamma using open interest and contract size while assigning a fixed positive contribution to calls and a fixed negative contribution to puts. This construction provides a tractable proxy for aggregate dealer positioning but implicitly relies on a stable relationship between option type and the sign of the passive book's inventory, an assumption that may not hold in structurally heterogeneous options markets such as India.</p> <p>Section 3 establishes the mathematical foundations for option gamma and implied volatility, while Section 5 develops the proposed Participation-Calibrated Gamma Exposure (PC-GEX) methodology to relax the fixed-sign assumption. PC-GEX infers the likely sign of passive gamma inventory from three jointly observable market signals: footprint order-flow direction, changes in open interest (ΔOI), and changes in implied volatility (ΔIV). These signals provide complementary information on trade aggressor direction, position formation or unwinding, and the option-demand component of price changes, allowing the methodology to distinguish inventory accumulation from position reduction without requiring direct observation of dealer books.</p> <p>The proposed framework further formalises this inference through an eight-case decision matrix and a cumulative inventory approach that assigns a GEX increment to each strike and observation interval before aggregating exposure across active strikes. The resulting PC-GEX measure therefore represents accumulated passive-book gamma conditioned on observed market activity rather than on a predetermined option-type sign convention. The mathematical formulation, including the GEX increment, cumulative strike-level exposure, and aggregate PC-GEX measure, is presented in the proposed methodology section. Empirical validation against conventional signed-OI GEX, using return autocorrelation and expiry-pinning distance as evaluation criteria, is reserved for subsequent work following systematic data collection and backtesting.</p>