I'm trying to bootstrap spot rates given coupon-paying bond data. To simplify my problem, assume we are working with only 3 given data, the price/coupon rate on semi-annual bonds maturing in 0.5, 1, and 2 years.
I can infer the 0.5 and 1 year spot rates from the given data. How do I infer the 1.5 and 2 year spot rates? If it simplifies the problem, assume that the spot rate changes linearly from 1 to 2 years.
Is there an analytic solution to find the 1.5 and 2 year spot rates? Do I need some iterative process?
Any leads on this problem would help. Thanks!