i am modelling deferred annuities that require a yield curve for the next 50 odd years... any good ideas on a reasonable method of extrapolating the yield curve beyond the longest duration bond?Would a reasonable approach be to callibrate CIR to current market data, and use the bond price it implies for discounting payments over 25 years away and the actual implied yield curve for discounting payments that fall within this time period?Or am I best to fit a cubic spline to the implied yield curve and simply extrapolate from this?

QuoteOriginally posted by: tibbarany good ideas on a reasonable method of extrapolating the yield curve beyond the longest duration bond?Sure, assume whatever yield will give you the highest profit on the deal. Then when the deal is done, whatever you have set it at will be the yield curve...

Good suggestion!

QuoteOriginally posted by: tibbari am modelling deferred annuities that require a yield curve for the next 50 odd years... any good ideas on a reasonable method of extrapolating the yield curve beyond the longest duration bond?Would a reasonable approach be to callibrate CIR to current market data, and use the bond price it implies for discounting payments over 25 years away and the actual implied yield curve for discounting payments that fall within this time period?Or am I best to fit a cubic spline to the implied yield curve and simply extrapolate from this?No, don't use a spline for extrapolation. Make some simple assumption like the forward curve being flat from the last known point onwards.

no - it is not correct to assume forwards after 30y (the last liquid swap curve piont)... are flat.... on the contrary, the swap curve is very much downward sloping (spot) out after 30y .... the reason for this is that the duration increase for each additional year after say 30y is nominal while the convexity pickup is huge.... so barring a very natrually steep, upward-sloping curve (not now) or some price-insensitve market flow (illiquidity) the curve should theoretically slope downward in the long end to reflect the incremental convexity value.... as far as modelling the curve ot there , USD, EUR, and GBP swaps DO trade out to 40 and 50y but the market is illiquid.... .....you can get a general idea from the mid levels in the brokeres, though..... if you are using bond (credit) yields in your curve, you will want to look at comparables - the french govt and some bluec chip USD corporations (disney, IBM) have 50y issues outstanding.....the other alternative is to model the value of the convexity pickup but this wont inclucle the credit component so i woud use the market swao and corp levels

You may want to have a look at Nelson-Siegel, Parsimonious Modeling of Yield Curves, Journal of Business 1987. And I agree with MattF that cubic spline is not a very good idea.

I meant assume the instantaneous forward rate is constant, not the forward rates themselves

but isnt the instanteous forward rate just an infintely short actual forard rate? therefore shouldn't the convexity issue below apply to the instanteous rate as well? i am not 100% certian here, but what is the distinction between say a 1 day foward rate and an instanteous forward rate as it applies to the duration/convexity issue?

Everyone is saying that the long end of the yield curve should naturally slope downwards (convexity etc.). I constructed the time series of the term structure and no downward slope (apart from a short period of inversion recently). Can anyone explain? P.S. Zero curve is bootstrapped from the swap rates (source -datastream).P. S.2. was going to post the graphs, but no idea hoe to add them to the reply? Can anyone help, please.

Hi sorry to bump this post up again. But noticed it was similar to my question.In the context of a developing market whereby swap rates are quoted up to 10 yrs only, the long end of the yield curve (constructed from swap rates)would only stretch out to 10 yrs. If one were interested in extrapolating it further, say to 15 years.i. assume flat i.e. zero coupons are flat beyond the last maturity (10yr). this is adopted in Mx.My question is: could i use bonds (ie graft bonds after swaps, employ the same bootstrap methodology) which have greater depth (maturities > 10yrs) to extrapolate the yield curve beyond 10 yrs.in summary<1y = depo rates1-10y = swap rates>10 yrs =bonds ? (grafted after swap rates)otherwise any other methodologies? any papers/references to consider would be greatly appreciated.thanks in advance.note that this would be irrelevent in developed markets, which have swap rates up to even 30yrs, illiquid it maybe but nontheless there are market quotes for these.