Jump Risk and Option Liquidity in an Incomplete Market

Abstract

We investigate the effects of return jumps on option bid-ask spreads measured in implied volatility. To explain bid-ask spread quoting behavior, we construct a general model with market makers trading in an incomplete market in which a Bernoulli-type jump could occur. Following a numerical analysis of equilibrium, we apply a nonparametric method to identify the jump components and then test the validity of our theoretical findings. Our results strongly suggest that, at a low jump arrival rate, the dynamic hedging of diffusion movement outperforms static hedging which considers both diffusion and jump risks together, and market makers should apply a dynamic hedging strategy most of the time. A testable implication of quoting behavior, which assumes market makers apply dynamic hedging, is ratified in our empirical work. Additionally, our regression shows that bid-ask volatility spread increases by 0.742% for a one-standard-deviation increase in our defined nonlinear jump factor and by 0.247% for the factor of diffusion volatility. We obtain a R² value above 80%, and the jump risk factor is characterized by t-statistics above 7, whereas diffusion volatility is only marginally significant. Thus, this paper theoretically explains why and how the jump risk affects options' bid-ask spread and empirically shows that the jump risk influences options' liquidity both statistically and economically.