Two Vignettes in Computational Finance
7I will discuss two results in quantitative finance in which algorithmic arguments play a central role. In the first part, I will introduce the problem of order dispersion in dark pools, a relatively new kind of equities exchange in which traders seek to 'invisibly' trade large volumes at market prices. I will present a provably efficient algorithm for near-optimal order placement in dark pools. This algorithm is based on methods from reinforcement learning and the Kaplan-Meier estimator from survival analysis. In the second part, I will compare two different models for the arriving limit order prices in the standard continuous double auction mechanism of electronic trading. In one model, traders are seen as having 'fundamental' views on price, while in the other they form prices only relative to those of other traders. I will quantify a sense in which the former model has highly stable dynamics and the latter has highly unstable dynamics, and discuss some implications for the ongoing debate over high frequency trading. The talk will be self-contained, and the theoretical results illustrated by experiments on trading data. Joint work with Kuzman Ganchev, Yuriy Nevmyvaka, and Jennifer Wortman Vaughan (dark pools); and with Eyal Even-Dar, Sham Kakade, and Yishay Mansour (dynamic instability).