Pricing of Options on Forward Bonds and Constant Maturity Treasury (CMT) : A Monte Carlo Approach

This paper proposes a new Monte Carlo technique for pricing options on forward bonds, by diffusing the bond-related Yield To Maturity (YTM). The framework stands for both sovereign and corporate bonds. We price both in stochastic and local default intensity (Hazard Rate Function). We actually calculate the initial value of the forward yield, we calculate the volatility of the forward yield, and we write the diffusion of the forward yield. Pricing the forward yield to maturity is equivalent to pricing the related forward bond, as the bond price is linked to the yield to maturity price through a basic formula that we will recall in this paper.As direct application we price options on Constant Maturity Treasury (CMT) in the Hull and White Model for the short interest rate. Tests results with Caps and Floors on 10 years constant maturity treasury (CMT10) are satisfactory.The approach here is new and original, as it is the fi rst time, on our knowledge, that an arbitrage free framework is proposed for pricing options on CMT and forward bonds