The impact of option hedging on the spot market volatility

We theoretically model and empirically quantify the feedback effect of delta hedging for the spot market volatility of the forex market. We start from an economy with two types of traders, an aggregated option market maker (OMM) and an aggregated option market taker (OMT), whose exposures reflect the total outstanding positions of all option traders in the market. A different hedge ratio of the OMM and OMT leads to a net delta hedge activity, which introduces market friction. We represent this friction by a simple linear permanent impact model. This approach allows us to derive the dependence of the spot market volatility on the gamma exposure of the traders. Our theoretical model shows that the spot market volatility is increased (decreased) by a negative (positive) gamma exposure of the OMM, whereby the amount of the increase depends on the net delta hedge amount executed in the spot market. To empirically test this model, we first reconstruct the aggregated OMM's gamma exposure by using trade repository data and find that it is negative. The empirical analysis performed over the period from 21st October 2017 to 30th June 2018 using our reconstructed OMM data then strongly supports our theoretical model: The gamma exposure of the OMM turns out to be highly significant for the spot market volatility and, as expected, the spot market volatility is increased with the OMM's short gamma exposure. Quantitatively, a negative gamma exposure of the OMM of approximately −1000 billion USD (which is around what we observe from our reconstructed OMM data) leads to an absolute increase in volatility of 0.7% in EURUSD and 0.9% in USDJPY.