Combining lattice and regression methods for the evaluation of convertible bonds with soft call/put provisions

This work faces the problem of pricing Convertible Bonds embedding an m-out-of-n soft call/put provision. This provision gives the issuer/holder the right to call/put back the bond if the underlying stock price has passed at least m days (not necessarily consecutive) above (below) a pre-specified trigger over the last n days. We propose an evaluation model that embeds a stochastic evolution of both interest rates and stock prices, whose dynamics is approximated through lattice-based models. Then, to estimate the probability of activating the provision, we employ a proxy function estimated by combining Brownian bridge’s based simulations with regression techniques. Extensive numerical results illustrate the consistency of the proposed model.