There are tons of paper on constructing zero curves based on the information of treasuries.Is there a way to construct the treasury zero curve from libor rate/swap rates?

not sure if this answears your question but simplest ad-hock way is to calculate zeros from swap curve, then simply adjust for spread agianst treasury, or alternatively adjust for spread first then calculate zeros, if one are looking for getting the last basis point right, or a special point on the curve then no simple answear, how should you interpolate etc. linear, cubic spline, max smoothness, the list is long... if you use money market futures in part of the curve you also need to take into account convexity adjustments Find out what is market standard in particular market you are looking at, then see if you can improve on that. Do not trust market standard, but think three times minimum before you assume it is wrong, illiquied issues, or somone knowing something you don't is most common explenation. It is not that many years ago (15?) one could do close to risk free arbitrage in a few countires where people not yet had figured out how to calculates zero coupon rates. I assume that was the good old days....

I guess in any market the method of building a zero curve that gives best fit to markt prices of swaps priced using the zero curve will be optimal.

Thanks a lot!

QuoteOriginally posted by: Collectornot sure if this answears your question but simplest ad-hock way is to calculate zeros from swap curve, then simply adjust for spread agianst treasury, or alternatively adjust for spread first then calculate zeros, if one are looking for getting the last basis point right, or a special point on the curve then no simple answear, how should you interpolate etc. linear, cubic spline, max smoothness, the list is long... if you use money market futures in part of the curve you also need to take into account convexity adjustments Find out what is market standard in particular market you are looking at, then see if you can improve on that. Do not trust market standard, but think three times minimum before you assume it is wrong, illiquied issues, or somone knowing something you don't is most common explenation. It is not that many years ago (15?) one could do close to risk free arbitrage in a few countires where people not yet had figured out how to calculates zero coupon rates. I assume that was the good old days....Collector, how can I find the reasonable spread?

To help you decide on how to proceed you have to reveal what you are intending to use the curve for. Pricing bonds and derivatives on bonds? Relative value analysis? Risk management simulation? The key question is whether you want to be able to exactly replicate observable bond prices from the resulting zero curve. If so, I would be strongly inclined to work with treasury bond prices directly. If you are interested in relative value analysis you could solve for asset swap spreads using the swap curve. Depends on what you want to do with the curve.

>Collector, how can I find the reasonable spread?In a liquid market the spread is know in the market at any time, just call a market maker or look at screen. In very illiquid market with very few treasury bonds as market maker or trader you have to make up your mind on where you think spread should be, depending on positions on your book, liquidity in the issue etc.

allstar... vanilla swaps are very liquid and hence trade in very liquid markets of their own, possibly more liquid then treasuries themselves (not exactly sure of that)... therefore swap spreads are an implied result. as opposed to adding a spread to treasuries to determine a yield, just start straight from swap rates and assume that they are par priced bonds when interpolating to calcualte the rest of your zero curve. hopefully that answers your question.

QuoteOriginally posted by: bigslickallstar... vanilla swaps are very liquid and hence trade in very liquid markets of their own, possibly more liquid then treasuries themselves (not exactly sure of that)... therefore swap spreads are an implied result. as opposed to adding a spread to treasuries to determine a yield, just start straight from swap rates and assume that they are par priced bonds when interpolating to calcualte the rest of your zero curve. hopefully that answers your question.Thank you very much

yes - CMT forwards are constructed in this exact way - you start with forward swap rates and then subtract the treasury spread.... the only problem is that the "forward swap spread" is a very thinly traded and opaque market.... for a rough and dirty approach you can use spot treasury rates and spot swap spreads, but be aware that there are several fundamental problems with this. Probably the most significant is that the market swap spread is the swap rate minus the on-the-run treasury bond. the on-the-runs generally have a liquidity premium in their price (i.e. they will trade at a lower yield than an off-the-run treasury with the exact same maturity). Secondly, by building the treasury curve in this way, you are inherently assuming that the treasury can be financed (repo market) at LIBOR minus the swap spread, which can be very far from reality when treasuries (esp. on-the-runs) go on "special"

If you're trying to price swaps, I would suggest it is worth your time to write a proper swap bootstrapper. By proper bootstrapper, I mean one that generates actual swaps with actual dates and prices them to par using a solver routine. In your world you probably want to model cash and swaps. As a starter, you should determine all the cashflow dates, and use the forecast method to determine what the forward coupons are on the floating leg side. Discount all these coupons. Do the same for the fixed side and subtract these PV's. Your only variable should be the swap zero rate to maturity; use this to solve for a swap that prices to 0.0. You will have all sorts of practical issues like interpolation and holidays to consider.Have fun!

In all due respect, the nature of this topic is clearly beyond creating a simple bootstrapped swap curve....it's always helpful to first read the thread before commenting....

indeed... pls ignore my previous reply. it is slightly more complicated then backing out the implied spread.

bigslick - i wasn't referring to your comment... it was eredhuin's that i was alluding to....

johnself11 - understood... merely agreeing that there are a number of other details to take into consideration. stripping out spreads without adjusting for the details u mentioned would give an inaccurate reflection of the treasury zero.