SERVING THE QUANTITATIVE FINANCE COMMUNITY

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Vsg
Topic Author
Posts: 1
Joined: November 10th, 2004, 9:04 am

Let us consider a risky bond.There seems to be a formula linking its asset-swap spread (denoted Sas) with its Z-spread (Sz) :Sas - Sz = (M-1) x (1/MD - 1/RD)where M is the market price of the bond,MD the sensitivity of the bond price to a change in the bond couponRD the sensitivity of the same coupon-paying riskless bond.I have found this formula in Risk Magazine, but I cannot find any proof for it.Can anyone help me ?

BLOBY
Posts: 113
Joined: May 17th, 2004, 5:07 am

More generally, what's exactly the diffrence between Z-spread and ASW ?Why there is a big diffrence between these two measures for a high yield bond (dirty price far above par) ?

quantman
Posts: 160
Joined: February 6th, 2002, 12:22 pm

Here's a very good pdf paper explaining how to calculate these measures and the difference between both is explained slide 29.Hope this helps.
Attachments
CDConference2004_Credit_Derivatives_101.zip

BLOBY
Posts: 113
Joined: May 17th, 2004, 5:07 am

Thanks a lot !! Finally an interested article on negative basis and measure of spread.....

BLOBY
Posts: 113
Joined: May 17th, 2004, 5:07 am

Quantman, do you know basically why the payoff at maturity of a bond, in term of his spread, is equivalent to :Z-spread (or ASW ??) x cach invested and not Z-spread x nominal ???

quantman
Posts: 160
Joined: February 6th, 2002, 12:22 pm

Personally,I'd rather use Z-spread x nominal than Z-spread x cash invested. What do you mean by cash invested ? For me what you invested in was the nominal amount of the bond.

BLOBY
Posts: 113
Joined: May 17th, 2004, 5:07 am

no, for me cash invested = nominal * bond price (with accrued).

zrj
Posts: 48
Joined: December 29th, 2003, 3:59 pm

because of that ol 'YTM' - Yield2Mat... u spend P = bond price to get F = face value, after T units of time... if u know the discount curve, u're left with the... z-spread. a.s.a.t.

sankar2
Posts: 1
Joined: January 8th, 2006, 5:43 am

Z Spread is the constant spread to the Zero Swap curve that one has to apply so that the discounted value of cashflows will equal present dirty price of Bond. ASW ( Gross Spread in Bloomberg) equals discrepancy between the bonds market price and its implied value computed by discounting its cashflows using the zereo swap curve. You need to divide this discrepancy by duration to convert it to a yield spread
Last edited by sankar2 on January 13th, 2006, 11:00 pm, edited 1 time in total.

Posts: 9
Joined: April 6th, 2005, 8:43 pm

QuoteOriginally posted by: sankar2Z Spread is the constant spread to the Zero Swap curve that one has to apply so that the discounted value of cashflows will equal present dirty price of Bond. ASW ( Gross Spread in Bloomberg) equals discrepancy between the bonds market price and its implied value computed by discounting its cashflows using the zereo swap curve. You need to divide this discrepancy by duration to convert it to a yield spreadConcerning ASW of Bloomberg, what is the theory behind to compute all valuations using swap rate's zero coupon? Sankar2, after you calculated the yield spread, would you use it plus coupon to calculate the price of a new bond? By the way, how fixed cpn and initial floating cpn of swap are calculated by bloomberg? floating cpn can be calculated by discount factors, but my computed number of the initial floating cpn is close but not the exact compared to bloomberg.Thanks a lot!
Last edited by ada on January 17th, 2006, 11:00 pm, edited 1 time in total.

cksh2005
Posts: 130
Joined: December 13th, 2005, 10:59 pm

ASW on Bloomberg is the Par-Par asset swap spread, you can replicate that calculation in Excel:There are four cashflows:cashflow(1): Fixed Coupons of Bond (with full first stub coupon) [on bond coupon payments dates]cashflow(2): Floating Libor Payments (with short first stub) [on floating libor payment dates]cashflow(3): Upfront Payment (=Dirty Price of Bond- Par of Bond) [on settlement date]cashflow(4): Libor Spread (=ASW spread of Bond) [on floating libor payment dates](1)+(4)=(2)+(3)Solve for (4) to get zero PV.Hope this helps.

Discage
Posts: 19
Joined: September 24th, 2005, 7:24 pm

I just construct a fair pricing model for bond vs cds trades. It works for most part of the credit curve except that I got negative zspread on the very short end for a few reference entities. I remember read from this forum somewhere talked about negative basis between cds and bonds, but it doesnt seem negative zspread is possible by its definition. Does it mean the bond is being penalized by high cash price or I need to reconsider my model? does negative zspread make sense at all?

cfornarola
Posts: 172
Joined: December 6th, 2004, 3:00 pm

Hi Discagenegative Z-spread makes sense.You should encounter it for bonds issued by issuer with high credit quality and high ranked collateralFor example Pfandbriefe or jumbo pafndbriefe maturiting up to 3-5 years can have negative Z-spread.I think for your model you can also refer to: Lehman Brothers May 2001 publication- "Explaining the Basis: Cash versus Default Swap".Hope this helpChiara

Discage
Posts: 19
Joined: September 24th, 2005, 7:24 pm

Hi Chiara,Thanks for your reply. The bonds I am modelling are all have high default risk, which is why we use cds to arbitrage. Where can I find the paper you mention? Could you post it if you have? Much appreciated.Discage

cfornarola
Posts: 172
Joined: December 6th, 2004, 3:00 pm

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