Panaggio, et.al., arxiv.org, Symmetry breaking in optimal timing of traffic signals on an idealized two-way street, here. One of the best chorale arrangements by Monte Python is “I Like Traffic Lights.”
Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal world, traffic signals would be timed such that consecutive lights turned green just as vehicles arrived, eliminating the need to stop at each block. Unfortunately, this “green wave” scenario is generally unworkable due to frustration imposed by competing demands of traffic moving in different directions. Until now this has typically been resolved by numerical simulation and optimization. Here, we develop a theory for the flow in an idealized system consisting of a long two-way road with periodic intersections. We show that optimal signal timing can be understood analytically and that there are counter-intuitive asymmetric solutions to this signal coordination problem. We further explore how these theoretical solutions degrade as traffic conditions vary and automotive density increases.
King Kong, Wall Street Oasis, Day in the Life of an Options Trader, here. This is old and making the rounds again.
12:00 – company announces a profit warning, unfortunately you have a short gamma position and the stock is down 5%. This is one of the situations you hate to be in. The stock is down 5% and because of the short gamma you are long a lot of delta. Now do you sell the shares 5% down or hold on and hope it rallies back. As a personal rule I like to keep my delta’s from my short gamma’s to a certain limit, and I hedge so that it never crosses that limit. You do not want to be stuck with a stock that drops 20% in a day and you just sit there watching it.
This is also important that you know everything about your short gamma’s, more so than your long’s, because if something gaps down you need to know what your pnl and delta is. With longs its fine because its positive pnl, but negative pnl always brings more senior attention. You also need to make sure you know not just your local risk, but your risk as spot moves. Because in a client flow book you have thousands of positions, your risk can quite easily flip as parameters move. That is why you need to look at your risk in three dimensions, time and spot. Its what makes derivatives more interesting than delta one products, but it also takes a bit more effort in terms of risk management.