Hi all,I need your help for pricing a product with this payoff: payoff= 7% * n/N where N is the number of days on wich we have (CMS10Y-CMS2Y)> barrier, and n is the number of fixings per Year (daily fixing ==> n ~ 250 ) Maturity: 3Y , and there is no payment before maturity (no coupon during the lifetime of the note).Can you give some advice, papers helping me in pricing this option. Thks

- pascal2006
**Posts:**26**Joined:**

The pricing of range Accrual is usually done with Monte Carlo method.You have to simulate your reference rates ( in your case CMS10Y and CMS2Y) at each observation dates.You can done this directly by simulating the CMS10Y and CMS2Y rate or compute them from a simulation of libor rate for example.Then you have to run your Monte Carlo as usual.

If I use Monte Carlo simulation, I have to simulate CMS 10Y & CMS2Y for every day. It's very time-consuming.......

MC simulation is best avoided for this kind of payoff. If the option is american/bermudan, then you need a term structure model. it is best to price this in a pde or a tree. if you just want to price the straight payoff, i.e. it is not american/bermudan, then with suitable assumptions on your CMS rate stochastics, this payoff reduces to a sum of expectations, there is nothing fancy about this. You should always start out by writing the formula: p(t)/N(t) = E{p(T)/N(T) | F_t}, no matter what you do. Then start sticking in your payoff as it appears on the term sheet, no do some algebra. The payoff will reduce to a sum of binary options, etc...

The Payoff can be written as a sum of CMS Spread digital options. And I want to know if there is a closed formula for this payoff to avoid Monte Carlo Simulations

that depends what modeling assumption you make about the underlying(s) your payoff is on. btw, this is always the case for any derivative. people very often ask, "how do you price this?" or "is there an analytic solution?". These questions are meaningless. the question should read: "assuming this stochastic for the underlying, is there an analytic solution for that payoff there?"for your deal, if you assume that your spread is governed by arithmetic BM, then Bachelier's theory will allow you to price it. this is unlikely to be very useful in practice though, in real life I mean, because of skew.

I think i'll two methods: -First will be FFT assuming that CMS2Y & CMS10Y governed by geometric BM -second will Bachelier Model assuming the spread (CMS10Y-CMS2Y) governed by arithmetic BM

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Last edited by alanxyz on March 30th, 2008, 10:00 pm, edited 1 time in total.

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