Numerical techniques for pricing callable bonds with notice

The complex financial product we price consists of an ordinary coupon bearing bond, which includes the call option with previous compulsory notice for the issuer. Discrete coupon payments and the notice feature lead to price discontinuities at the coupon and call dates, so that the numerical solution of the Black-Scholes type equation requires specific techniques. The bond value, B=B(t,r), depends on time, t, and on stochastic interest rate, r, and verifies the Black-Scholes partial differential equation:∂B∂t+(u−λw)∂B∂r+w22∂2B∂t2−rB=0,0