Cross Variation of correlated Ito Processes
Posted: June 18th, 2010, 6:10 pm
Looking at the paper Pricing Treasury Inflation Protected Securities...In equation (3), page 339 we have the price of a treasury inflation protected bond defined asOn page 342, we should be able to use (13) and (16) - the dynamics of P_r(t,T) and I(t) - , to check that (15) - the dynamics of P_TIPS(t,T) - holds. For those of you too lazy to look in the paper : given the dynamicswe want to verifyDenote cross variation process asStochastic Integration by parts yieldswhereSo it's clear that the only way this will evaluate to the given dynamic of P_TIPS(t,T) is ifBut actually computing the cross variation, I get that we should have the opposite sign. That is I am probably missing something embarrassingly obvious in the computation. But can't see what it is right now.Thankful for any pointer in the right direction.Thanks!