What is GARCH and how it is used to model comovements in stock prices? What are some introductory papers for this topic?

Answer 1

Garch basically recognizes that certain series like stock returns do not have constant variance. Namely they go though period of Turbulence and tranquility. Ther will be short run variances (if you are in a tranquil period you are likely to stay there. etc..) The Variance process itself is some autoregressive function. The commonly used is GARCH(1.1)

Var(t) = rVar(t-1) + e where e is white noise. LR variance will be Var(o)/(1-r).

Wikipedia actually gives a pretty decent intro. Let me know if you would like to discuss further.