list
Senior Member
Posts: 2034
Joined: Oct 2005

Wed May 30, 12 10:51 AM


see that the Bloomberg USD OIS curve (curve 42) consists of OIS quotes up to 5y and from 7y onwards are constructed from a rather complex construction. I am wondering if anyone knows the theory behind it?  I have a feeling that construction of the OIS is a trick. Primary and the 1st step is developing floating leg of the OIS. How to calculate the day valued geometric average based on a broadly extended data of the forward rate. For example in more simpler setting we have a spot FF rate r ( 0 , 5 ), where 0=today Monday , 5= closest Friday. There are 2 ways for construction. We can solve the equation for geometric average which for given 5 days presents the same return as r ( 0 , 5 ) and the second way. It is a tricky one. We use r ( 0 , 5 ) for a day and calculate its geometric average. The second way represents something that at certain degree different than initially FF defined r ( 0 , 5 ). I could be mistaken but my intuition suggests that the second approach was chosen for the construction of geometric average day compounded floating rate of the OIS.
When we prove in calculus existence of the limit of the sequence ( 1 + r / n ) ^n it was proved that this sequence is monotonic increasing. For n = 1 it relates to simple interest rate r over say [ 0 , T ]. This interval can be split into months , weeks, or days and compounded interest corresponds to geometric average. If r is the simple interest for next 5 days then indeed each day have interest 'r' and no one can prohibit to calculate compounded rate over the same period and calculated swap rate over the same period. Thus starting with the fixed rate r ( 0 , 5 ) over [ 0 , 5 ] we arrive at other fixed rate that can be called here OIS if it is drawn from FF rate. This OIS would be higher than r ( 0 , 5 ) and investor buying fixed payed more
Edited: Wed May 30, 12 at 04:34 PM by list

