November 1st, 2012, 8:38 pm
hi all,May I ask a question about the range accrual note/swap pricing? I am trying to price the callable RA note/swap under a short rate model with internal adjuster (do not want use LMM with MC).Let us assume the short rate model is fully calibrated, and tree is built, and libor index has been pre-computed on lattice nodesEssentially, when we price on the tree, for each coupon period [t, s], we need to estimate the indicator function E{I (LB<=L(observation point, observation point + tenor)<=UB) | t } for each node at time step tFor sure, we can exactly calculate the indicator function through the replication by digitals, however, if we reply on tree pricing, and compute the indicator function based on rolling back on the tree, how can we get accurate price?what I did is the following,for coupon period [t, s], let dt be the observation intervala) at time step s, set node values to dt*1 if the libor index falls into the range, otherwise 0b) roll back to step s-1, add values dt*1 if the libor index falls into the range, otherwise add 0c) until step tthen you will the effective accrual factor for each node and we use that for computing the exotic coupon.However, the problem for this approach is, it converges very slow...I've tried to smooth the range boundary (say allow tiny bullet spread similar to the one used in replicating with digitals), but it does not help...anybody has better idea?Thanks