CMS spread range accrual

noncommutate · April 3rd, 2007, 4:50 am

HelloI need to price a CMS spread range accrual, say CMS30 - CMS2 >0.If I use libor market model together with Monte Carlo simulation, I have to simulate the forward rates for every day. It's very time-consuming.......Is this the way you do it?or could anybody suggest a efficient method to me? Thanks

Paolos · April 3rd, 2007, 7:34 am

Two faster alternatives:A) Differentiate Margrabe's formula w.r.t. -CMS2 to obtain the pricing formula for a digital spread option. Apply it for every dayB) Solve numerically the integral representing the payoff. You can find the formula for the integral in Pelsser ("Efficient methods for valuing interest rate derivatives" p.153). Apply it for every dayRemember that if you choose A) or B) you must correct the CMSs expected values using convexity (and timing) adjustments before applying the methods.Hope it helps.P.

alvinkam · April 5th, 2007, 9:31 am

A simpler answer is to just sample the observations more coarsely, i.e. once a week. I doubt this would affect your price much. For added accuracy you may also get daily points through interpolation of your weekly sampling. Tried and tested.

horacioaliaga · April 13th, 2007, 6:07 pm

Numerix has this CMS Range Accrual as part of the standard examples

BlueDonauRive · September 4th, 2007, 11:32 pm

QuoteOriginally posted by: horacioaliagaNumerix has this CMS Range Accrual as part of the standard exampleswould you like to give me the link?thanks

xquant · November 16th, 2007, 2:16 am

hi alvinkam, i test monthly/bi-weekly/weekly/daily simulation, results don't change more...i think monthly simulation can fit practical need

hjs · October 29th, 2008, 6:46 pm

The error that you get from doing monthly instead of daily will depend on how the forward indices move. If you miss a quick change in spread (and hence the moneyness of the corresponding digital, then you can introduce significant error in the corresponding coupon. This error can be mitigated by adapting the spacing according to the changes in the spread.