Dynamic of future price models in mathematical finance

In this work, we focus on the future price models, introduced by Heath and Jara in 1998 in which interest rate contracts are studied as basic securities. We assume that future prices Fi (t1Ti); 1≤i≤p are moving like a linear combination of several independent Brownian motions where the Ti are their maturities. Firstly, we try to get a deep understanding of the correlation structure of the dynamic of these given p future prices. Secondly, for any given cap K>0, using Principal Component Analysis, we obtain the best m-estimator, 1≤m≤p-1, for (Equation in text) sense where Q in the martingale measure.

Keywords:

Future price model , correlation structure , best estimator , principal components.