We investigate how high-frequency trading (HFT) in equity markets affects options market liquidity. We find that increased aggressive HFT activity in the stock market leads to wider bid–ask spreads in the options market through two main channels. First, options market makers’ quotes are exposed to sniping risk from HFTs exploiting put–call parity violations. Second, informed trading in the options market further amplifies the impact of HFT in equity markets on the liquidity of options by simultaneously increasing the options bid–ask spread and intensifying aggressive HFT activity in the underlying market.

By employing a dynamic model with two limit order books, we show that fragmentation is associated with reduced competition among liquidity suppliers and lower picking-off risk of limit orders. Due to these countervailing channels, the impact of fragmentation on liquidity and welfare differs with asset volatility: When volatility is high (low), liquidity and aggregate welfare in a fragmented market are higher (lower) than in a single market. However, fragmentation always shifts welfare away from agents with exogenous trading motives and toward intermediaries. We empirically corroborate our model’s predictions about liquidity. Our model reconciles the mixed results in the empirical literature.