statsbomb.com - Oliver Walker
A unique position, the goalkeeper. But also one of the most measurable, given a large aspect of their role is simply to keep the ball out of the net. It possibly gets overlooked just how much a good or bad goalkeeping season can impact the outcomes of a team's season relative to other positions on the pitch, with there often being a gap of 10-20 goals between the best- and worst-performing shot-stoppers in a league in any given season.Of course, in the modern game, goalkeepers are expected to do much more than save shots. A
ssrn.com - Alex Lipton, Marcos Lopez de Prado
When prices reflect all available information, they oscillate around an equilibrium level. This oscillation is the result of the temporary market impact caused by waves of buyers and sellers. This price behavior can be approximated through an Ornstein-Uhlenbeck (OU) process.Market makers provide liquidity in an attempt to monetize this oscillation. They enter a long position when a security is priced below its estimated equilibrium level, and they enter a short position when a security is priced above its estimated equilibrium level. They hold that position until one of three outcomes occur: (1) they achieve the targeted profit; (2) they experience a maximum tolerated loss; (3) the position is held beyond a maximum tolerated horizon.All market makers are confronted with the problem of defining profit-taking and stop-out levels. More generally, all execution traders holding a particular position for a client must determine at what levels an order must be fulfilled. Those optimal levels can be determined by maximizing the trader's Sharpe ratio in the context of OU processes via Monte Carlo experiments. This paper develops an analytical framework and derives those optimal levels by using the method of heat potentials.