Pricing Corporate Bonds with Z-Spreads and Credit Models

# Pricing of fixed income securities


# Pricing of fixed income securities












When it comes to pricing fixed income securities like corporate bonds, what do practitioners usually use to get the price?

I can see two ways: (1) use yields-to-maturity, which equals government treasury yields with similar maturity plus some credit spread. this YTM applies to discount all cash flows. (2) use the entire term structure of zero-coupon rates, then plus some credit risk premia for each horizon, discount each payment using adjusted zero-coupon rates?

I am curious which is the norm.

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/81020

I'm thinking not of the scenarios when a corporation wants to issue a bond and needs to know how much coupon to pay in order to price it close to par, burt rather some bond hasn't traded recently in the secondary market, and someone needs to figure its fair price from looking at other bonds.

Many folks will start with (1) when they need something quick and dirty.

But corporate bonds sometimes have large cash flows before maturity, e.g. coupons in the double digits, or large amortizations. Looking at the risk-free rate only at maturity of the bond and ignoring the risk-free rates at the time of the other cash flows is less than great. Therefore in practice most folks will estimate the bond's Z-spread, from looking at the Z-spreads of other bonds of this issuer or similar issuers having observable quotes. Discount the bond's cash flows with risk-free curve shifted up by Z-spread. This is very easy on Bloomberg terminal. This isn't very different from "(1)" if the bond's cash flow at maturity is much larger than the other cash flows, or if the risk-free curve is flat, but much of the time these makes a material difference. This is why you usually see Z-spread communicated on corporate bonds runs, rather than any yield spreads. Z-spread fluctuate less when risk-free rates move.

Some folks also look at the methodology in Rutkowski and Duffie-Singleton, which is VCDS on the Bloomberg terminal - estimate the probabilities of default, with term structure, and loss given default from observable market quotes, and then price the bond as if it were a credit derivative - discount each cash flow using the default probability and loss given default as well as risk-free rates. The result usually isn't hugely different from using Z-spreads, and you won't see this communicated on runs.

## Answer by nbbo2 (score 0)

https://quant.stackexchange.com/a/81019

When a corporation is thinking of issuing a bond, the CFO will contact an investment bank and ask some questions, including what kind of interest rate would we pay? A newly hired IB employee will do a quick study to see in recent years what kind of spread comparable companies (in term of maturity range, credit rating, perhaps industry) have been getting in recent years. Then in will be sumarized as a a range of possible spreads over Treasuries, i.e. your method (1). If the company want to go ahead the real work begins; the IB will contact a number of big investors to ask "would you be interested in buying ACME 5 year bonds at a YTM of X?" and a final figure will be agreed. Some up or down adjustments may have to be made, so ultimately it is the capital market (the investors) that decides the spread.

From a theoretical point of view (2) makes sense, it is likely that there are different credit spreads at different maturities. However, there is no way that I know of to estimate a different risk premium for every month in the future, though in principle it makes sense. The company will usually have an idea what kind of maturities they want, so full generality is usually not needed.