Narrow Results

Latency (i.e. time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity, takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB) might undergo updates, so there is no guarantee that MLOs are filled. We develop a latency-optimal trading strategy that improves the marksmanship of liquidity takers. The interaction between the LOB and MLOs is modeled as a marked point process. Each MLO specifies a price limit so the order can receive worse prices and quantities than those the liquidity taker targets if the updates in the LOB are against the interest of the trader. In our model, the liquidity taker balances the tradeoff between the costs of missing trades and the costs of walking the book. In particular, we show how to build cost-neutral strategies, that on average, trade price improvements for fewer misses. We employ techniques of variational analysis to obtain the price limit of each MLO the agent sends. The price limit of an MLO is characterized as the solution to a class of forward–backward stochastic differential equations (FBSDEs) driven by random measures. We prove the existence and uniqueness of the solution to the FBSDE and numerically solve it to illustrate the performance of the latency-optimal strategies.

The objective is to develop a general stochastic approach to delays on financial markets. We suggest such a concept in the context of large Platonic markets, which allow infinitely many assets and incorporate a restricted information setting. The discussion is divided into information delays and order execution delays. The former enables modeling of markets, where the observed information is delayed, while the latter provides the opportunity to defer the indexed time of a received asset price. Both delays may be designed randomly and inhomogeneously over time. We show that delayed markets are equipped with a fundamental theorem of asset pricing and our main result is inheritance of the no asymptotic Lp-free lunch condition under both delay types. Eventually, we suggest an approach to verify absence of Lp-free lunch on markets with multiple brokers endowed with deviating trading speeds.