I know two applications of local time in option pricing theory. First, it allows a derivation of Dupire's formula on local volatility in a neat way (i.e. without resorting to differential operator ...
Look at ACCT 340 @ http://www.gsb.stanford.edu/research/courses/acctg.html I've read some of the research papers written by the Professor, and the material is very interesting. However, I'm looking ...