After a longer while, QuantAtRisk is back to business. As an algo trader I have been always tempted to test a gap-on-open trading strategy.
There were various reasons standing behind it but the most popular one was always omni-discussed: good/bad news on the stock. And what? The stock price skyrocketed/dropped down on the following days.
When we approach such price patterns, we talk about triggers or triggered events. The core of the algorithm’s activity is the trigger identification and taking proper actions: to go long or short.
That’s it. In both cases we want to make money. You may be asking what will by my next question? Well... Rest assure that we all need to learn the math, before we risk a penny.
Like for Example : Proposition 5.15. Let {ξn}n∈N be a sequence of independent N0-valued random variables, all of which share the same distribution with pmf {pn}n∈N0 and generating function Pξ(s). Let N be a random time independent of {ξn}n∈N. Then the generating function PY of the random sum Y = PN k=0 ξk is given by PY (s) = PN (Pξ(s)).
If you have any problem understanding the proof of Proposition 5.15, then go back a few pages and learn the Axioms again... Thank you.
-> Sources.
