Jump risk and option liquidity in an incomplete market

PeiLin Hsieh, QinQin Zhang and Yajun Wang

Journal of Futures Markets, 2018, vol. 38, issue 11, 1334-1369

Abstract: This study investigates the effect of a jump risk on options’ bid–ask implied volatility (IMV) spreads. We introduce theoretical models assuming market makers encounter a Bernoulli‐type jump atnd optimize the mean‐variance utility by choosing the optimal hedging delta and price. We find, at a low jump arrival rate, the Black–Scholes–Merton dynamic hedging for diffusion volatility outperforms static hedging for both diffusion and jump risks. If dynamic hedging is implemented, the jump components nonlinearly affect bid–ask spreads. Our regression supports our theoretical conclusions, and for model‐free IMV, jump risk factors are characterized by t statistics above 7 with adjusted R 2 above 70%.

Date: 2018
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