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### callable range accrual pricing

Posted: **November 1st, 2012, 8:38 pm**

by **kelang**

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

### callable range accrual pricing

Posted: **November 2nd, 2012, 9:29 am**

by **spv205**

kelang - why are you pricing digitals on tree rather than in closed form at time t? that is surely the problem

### callable range accrual pricing

Posted: **November 2nd, 2012, 10:22 am**

by **kelang**

QuoteOriginally posted by: spv205kelang - why are you pricing digitals on tree rather than in closed form at time t? that is surely the problemYes you are right it is about the digital, and I agree it should use the closed form.I just want to see if it is possible to do so. I heard it can be done by smoothing the boundaries, but I never get stable numbers

### callable range accrual pricing

Posted: **November 10th, 2012, 5:22 am**

by **mj**

### callable range accrual pricing

Posted: **November 10th, 2012, 3:45 pm**

by **kelang**

QuoteOriginally posted by: mja Monte Carlo approach:

http://papers.ssrn.com/sol3/papers.cfm? ... 1285thanks mj, actually i solve the problem by doing some trick on the tree and it converges very fast for all cases. I also did some Monte Carlo simulation along with the tree (for benchmark purpose), which is much slower.will for sure try your approach, sounds quite promising.

### callable range accrual pricing

Posted: **January 12th, 2016, 8:46 pm**

by **Jhammer**

Hi Kelang,May I ask about the trick that speeds up pricing in your approach?Also, which measure is your pricing tree calibrated to? I assume it is calibrated to a forward measure. Now let say the tree is calibrated to risk-neutral measure, does anyone know any work-around to correctly price a callable range accrual using this tree?