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 FORUMS > Student Forum < refresh >
 Topic Title: Specificity of yield curves Created On Mon Jun 20, 11 09:00 AM Topic View: Branch View Threaded (All Messages) Threaded (Single Messages) Linear

Tootient
Junior Member

Posts: 2
Joined: Jun 2011

Mon Jun 20, 11 09:00 AM

Hello,

I'm currently working on finding a fitting model of yield curve. And there's something I don't quite understand. I read for most models that there were used for the spot rates, swap rates, etc... But is it possible to use a model, "designed" for spot rates, to plot swap rates ? Why would it only be used for spot rates for example ?

I'm sorry if it's unclear, English's not my first language, I'll try to rephrase it if it's the case.

Thanks,

Edited: Mon Jun 20, 11 at 09:02 AM by Tootient

DavidJN
Senior Member

Posts: 1617
Joined: Jul 2002

Mon Jun 20, 11 08:00 PM

There are three different kinds of yield curves that people generally work with: par, zero and forward. Given any one of these you can derive the other two. What many people call spot rates are generally understood to be zero coupon rates, that is, rates that hold between now and future dates with no intermediate cash flows in between. A more general name for swap rates are par rates, they are observable rates traded in the marketplace and have periodic cash flows (coupons) between now and maturity. A forward rate is a rate that starts in the future and matures at a yet later date, a forward rate can be either par or zero coupon.

A good deal of yield curve modeling consists of transforming observable par rates into zero rates or forward. This is a static procedure in the sense that the transformaiton is done at one point in time.

A yield curve model is something different. Examples are the HJM, HW and LMM models. These model the stochastic evolution of the yield curve over time and take either the zero curve or the forward curve (depending on the specific model) as an input. Yield curve models are typically used to price derivatives based on interest rates.

So, are you building a zero curve from a par curve or are you interested in pricing derivatives using a yield curve model? Both?

Tootient
Junior Member

Posts: 2
Joined: Jun 2011

Mon Jun 20, 11 10:31 PM

First of all, thanks for your answer, it settles some things up in my mind
Quote

Originally posted by: DavidJN
There are three different kinds of yield curves that people generally work with: par, zero and forward. Given any one of these you can derive the other two.

Yep I forgot that there are formulas relating these three kinds of rates ! And I didn't know the yield curves were only for those 3.

Quote

A good deal of yield curve modeling consists of transforming observable par rates into zero rates or forward. This is a static procedure in the sense that the transformaiton is done at one point in time.

A yield curve model is something different. Examples are the HJM, HW and LMM models. These model the stochastic evolution of the yield curve over time and take either the zero curve or the forward curve (depending on the specific model) as an input. Yield curve models are typically used to price derivatives based on interest rates.

So, are you building a zero curve from a par curve or are you interested in pricing derivatives using a yield curve model? Both?

Sorry, I didn't get into much precision, because it's a work I want to myself as much as possible. But I'm selecting some stochastic models and the ones that really interest me are zero curves (I think it's called 'term structure' ?) from which I would like to get the (forward) swap/par rates. The data I'm given can be spot rates or swap rates, preferably the latter.
I also prefer models that are simply implemented, rather than very precise implementations.

Also, I've had my own idea on the question but I'd like to get a confirmation : what's the main advantage of a no-arbitrage model compared to an equilibrium model ?

And I need another confirmation : can short rates be used for a 6-month maturity ?

Sorry, last question... I've already read the chapters about yield curves in Hull's "Options, futures, and other derivatives", would you happen to have another good reference about yield curves, especially their calibration ?

Thanks a lot (it's not a problem if you don't answer to all the questions I'm just in a great period of doubt and need some double-check answers)

Edited: Mon Jun 20, 11 at 10:32 PM by Tootient

bwarren
Member

Posts: 128
Joined: Feb 2011

Tue Jun 21, 11 01:24 AM

"Term structure" just refers to the differences in something, e.g. interest rates, over different maturities.

You can derive forward rates from the zero curve without using a model. As DavidJN said, the models are used for modeling the future evolution of zero or forward rates.