I understand that a corporate bond can be priced by discounting its cash flows by Yield to Maturity to equate its market price.However, one of the reasons why YTM is not a good measure is that it assume coupons are re-invested and the bond is held to maturity.Therefore the cash flows can be discounted by a yield at each specific maturity, which is uses a spot curve.I am confused where this spot curve comes from. Secondly, a par curve can also be used. If different curves are used, will that affect the price.And I read that duration is the parallel shift in the yield curve. Which yield curve? Spot curve? Par Curve? Treasury curve? Does this matter which curve we use?Really confused...

the "par curve "is the curve which if used to price cash flows to par would give the par coupon. If you want to issue a bond today then the par curve embodies the yields that are required and the resulting coupon on your bond would make the price of the cashflows discounted at the "par curve" equal to par to 100.

Duration is a measure of the sensitivity to yield. All the other things that people talk about with the curves and everything is more poetry.I would highly recommend you read Antti Ilmanen's "Understanding the Yield Curve" series of papers.

To continue daveangel's explanation, the par curve for a given credit quality is a visible market curve that shows the coupon rates that would be required for coupon-paying bonds with different maturities to sell at par. The spot curve is a transformation of the par curve in which arbitrage-free zero-coupon rates are stripped out such that the set of par bonds reprice to par using the zero rates. As noted by Martinghoul, duration is simply a measure of local price sensitivity and it can be based on either the par or the spot curve. Since the measure of duration is one of local price sensitivity, you tend to get fairly similar results whether you use yield to maturity or zero coupon methods. Where they may start to differ is when you posit larger, especially non-parallel yield curve shifts.Spot curves are generally the way to go when you want to probe deeper into the financial economics of fixed income pricing, particularly if you are interested in relative value analysis.

Thanks, most people refer to the actual live Treasury curve as the par curve. If the definition that a par curve is that the yields would discount all cash flows to par, however Treasuries are not quoted by par???

QuoteOriginally posted by: blackscholesThanks, most people refer to the actual live Treasury curve as the par curve. If the definition that a par curve is that the yields would discount all cash flows to par, however Treasuries are not quoted by par???as treasuries are issued regularly the on the runs will be around par.

Ahhh thanks, that was the disconnect in my understanding.

Now a follow up question. If I have a theoretical spot price after obtaining the Treasury zero rate coupons to discount the cash flows, the price should equal the market price right? Otherwise, there's arbitrage? For example, if i have an IBM bond, the theoretical spot price should equal to what it's currently trade? Or is this not accurate?

You need to remove from your head the notion that the Treasury curve is the most important par curve. It is one of many.Another important example is the par swap curve. The swap curve a much cleaner par curve from an analytic perspective because it is comprised of a set of constant maturity instruments. Every day the quote for a 5-year par swap is exactly 5 years, subject to day count. Since governments do not issue bonds every day, there are issues with aging that present practical problems.You seem to remain fundamentally unclear about when to use what curve. If you discount the cash flows for an IBM bond using the Treasury curve you will most definitely not recover the market bond price, you will compute a price that is appreciably higher (assuming IBM has inferior credit to the US Treasury).To help inform yourself, read up on a topic called Option Adjusted Spread. This concept links the Treasury curve with non-government bonds.

Great, so if you add a constant OAS to the Treasury spot curve and discount all cash flows of let's say IBM, it should give you the market price of the bond. And the OAS is calculated by trial and errror by simulating interest rate paths and then figuring out the spread that would equate the discounted cash flows to the market price.

QuoteOriginally posted by: blackscholesGreat, so if you add a constant OAS to the Treasury spot curve and discount all cash flows of let's say IBM, it should give you the market price of the bond. And the OAS is calculated by trial and errror by simulating interest rate paths and then figuring out the spread that would equate the discounted cash flows to the market price.That's the general idea. In actual fact you may or may not actually simulate interest rate paths, but that is more of an implementation issue. And you can do the same thing starting with a swap curve instead of a Treasury curve, and get what some people would call a Libor OAS.