We consider the issue of pricing by simulation puttable and callable convertible bonds. Call times are typically subject to constraints, called call protections, that prevent the issuer from calling the bond during certain (random) time intervals. From the mathematical finance point of view, such bonds can be studied as certain type of game options with call protection. This leads to consideration of doubly reflected backward stochastic differential equations with an upper barrier, which is only active during random time intervals. A major practical concern is that call protection is typically monitored at discrete times, in a possibly very path-dependent way, which leads to highly-dimensional pricing problems.

We shall present certain recent results regarding valuation and hedging of convertible bonds subject to call protection and discrete time monitoring.