Execution and cancellation lifetimes in foreign currency market

Abstract

We analyze mechanisms of foreign currency market order’s annihilation with a focus on the lifetime of these orders. Limit orders submitted in this market are approximately executed according to the random walk theory. In consequence, the distribution of execution lifetime can be approximated by a power law with exponent 1/2. Alternatively, limit orders submitted in foreign currency markets are roughly cancelled according to a mixed distribution; as a random walk with a tail following a power law. The cancellation lifetime distribution can be approximated by using a scaling relationship between the distance from mid-price and the random walk theory. In addition, we introduce the concept that market participants cancel orders depending on the market price’s movement which is represented as the movement of the mid-price. Taking into consideration market conditions when orders have been injected, market participants do not have symmetric decision rules. This behavior could at least partially explain the shape of price change distribution.