I will present a simple model of market microstructure which explains the concavity of price impact. In the proposed model, the local relationship between the order flow and the fundamental price (i.e. the local price impact) is linear, with a constant slope, which makes the model dynamically consistent. Nevertheless, the expected impact on midprice from a large sequence of co-directional trades is nonlinear and asymptotically concave. The main practical conclusion of the model is that, throughout a meta-order, the volumes at the best bid and ask prices change (on average) in favor of the executor. This conclusion, in turn, relies on two more concrete predictions of the model, one of which can be tested using publicly available market data and does not require the (difficult to obtain) information about meta-orders. I will present the theoretical results and will support them with the empirical analysis.

Many financial arrangements reference market prices that are yet to be realized at the time of contracting and consequently susceptible to manipulation. Two of the most common such arrangements are: (i) market-on-close contracts, which reference the price prevailing at the end of an execution window, and (ii) guaranteed VWAP contracts, which reference the volume-weighted average price (VWAP) prevailing over the execution window. To study such situations, we introduce a stylized model of financial contracting between a client, who wishes to trade a large position, and her dealer. Market-on-close contracts are generally not optimal in this principal-agent problem. In contrast, we provide conditions under which guaranteed VWAP contracts are optimal. These results question the usage of market-on-close contracts in practice, explain the usage of guaranteed VWAP contracts, and also suggest considerations for the design of financial benchmarks. The presentation is based on joint work with Markus Baldauf (University of British Columbia) and Joshua Mollner (Northwestern University).

The risk and return profiles of a broad class of dynamic trading strategies, including pairs trading and other statistical arbitrage strategies, may be characterized in terms of excursions of the market price of a portfolio away from a reference level. We propose a mathematical framework for the risk analysis of such strategies, based on a description in terms of price excursions, first in a pathwise setting, without probabilistic assumptions, then in a Markovian setting.

We introduce the notion of $\delta$-excursion, defined as a path which deviates by $\delta$ from a reference level  before returning to this level. We show that every continuous path has a unique decomposition into such $\delta$-excursions, which turns out to be useful for the scenario analysis of dynamic trading strategies, leading to simple expressions for the number of trades, realized profit, maximum loss, and drawdown.  As $\delta$ is decreased to zero, properties of this decomposition relate to the local time of the path.

When the underlying asset follows a Markov process, we combine these results with Ito's excursion theory to obtain a tractable decomposition of the process as a concatenation of independent $\delta$-excursions, whose distribution is described in terms of Ito's excursion measure. We provide analytical results for linear diffusions and give new examples of stochastic processes for flexible and tractable modeling of excursions. Finally, we describe a non-parametric scenario simulation method for generating paths whose excursions match those observed in a data set.

This is based on joint work with Anna Ananova and Rama Cont (Oxford).

The workshop will take place August 25-28 in Berlin. More information will be posted here soon. The lead organiser is Dirk Becherer.