What is the Optimal Trading Frequency in Financial Markets?

Abstract

We thank the CFTC for providing summary statistics on four futures contracts and NASDAQ for providing summary statistics on 117 stocks that are used to calibrate the model.† Additional disclaimer related to CFTC: The research presented in this paper was co-authored by Haoxiang Zhu, an unpaid consultant of CFTC, who wrote this paper in his official capacity with the CFTC, and Songzi Du, an Assistant Professor of Economics at Simon Fraser University. (The majority of the paper was written prior to Haoxiang Zhu's affiliation with the CFTC.) The Office of the Chief Economist and CFTC economists and consultants produce original research on a broad range of topics relevant to the CFTCs mandate to regulate commodity futures markets, commodity options markets, and the expanded mandate to regulate the swaps markets pursuant to the Dodd-Frank Wall Street Reform and Consumer Protection Act. These papers are often presented at conferences and many of these papers are later published by peer-review and other scholarly outlets. The analyses and conclusions expressed in this paper are those of the authors and do not reflect the views of other members of the Office of Chief Economist, other Commission staff, or the Commission itself.

Are CDS Auctions Biased and Inefficient?

“…This result is shown in the static models of Vives (), Rostek and Weretka (), and Ausubel et al. (), as well as the dynamic models of Vayanos () and Du and Zhu (), among others. Appendix B reproduces the argument in a static setting, showing that the allocation inefficiency in double auctions is of order , where n is the number of auction participants.…”

“…Moreover, the dealers' quotes in Step DA‐1(b) could be useful for reducing information asymmetry. In models with asymmetric information and price impact, a lower degree of information asymmetry typically improves allocation efficiency (see Du and Zhu () and references therein).…”

“…The second line of summarizes the profit of trader i in the CDS auction: is the payout from CDS settlement, is the profit of trading the defaulted bonds, and is the inventory cost of creating the bond position in CDS auctions. This type of linear‐quadratic utility is also used by Vives (), Rostek and Weretka (), and Du and Zhu (), among others. The constants γ and λ that dictate the inventory costs are required to be positive, but can be arbitrarily small.…”

Order Protection through Delayed Messaging

“…With HFT now constituting a majority of transactions in major exchanges worldwide (SEC, 2014), those exchanges face competing incentives: they profit by accommodating HFT firms, yet still must retain traditional slower clients (O'Hara, 2015), many of whom feel that HFT puts them at a disadvantage. Some reform proposals intended to protect ordinary traders (e.g., by Budish et al (2015), Du and Zhu (2017), and Kyle and Lee 2017 The present paper contributes to the growing theoretical literature that addresses such questions. We develop an equilibrium model that spotlights the consequences of imposing a uniform delay on new orders while a class of previously submitted hidden liquidity-providing orders ("pegged" orders) are automatically repriced without delay.…”

Mechanism Selection and Trade Formation on Swap Execution Facilities: Evidence from Index CDS

“…This model of interdealer trading was solved in Du and Zhu (2017) and Duffie and Zhu (2017), as summarized in the next proposition.…”