## Bond Spread

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*FinPricing provides probably the most comprehensive valuation models for financial products, including computation of:*

- Bond Accrued Interest Calculator
- Bond Coupon Rate Calculator
- Bond Price Calculator
- Bond Yield Calculator
- Bond Duration Convexity Calculator
- Bond Spread Calculator
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Credit risk arises because the bond’s value in one year can vary depending on the credit quality of its issuer. In general, we know that the value of this bond will decline with a downgrade or default of its issuer – and appreciate if the credit quality of the obligor improves.

Bond spread allows the measuring of the difference between a risky bond and a risk-free one. There are several ways to define the credit spread:

- Evaluate the yield-to-maturity (YTM) to retrieve the market price. The difference between this YTM and the YTM of a risk-free bond with the same redemption table is frequently referred to as “the credit spread of the bond”.
- Evaluate the spread to add to the zero coupon rates of all maturities to retrieve the market price.
- Use the Credit Default Swap rate that is actually paid to buy a protection against credit default for that bond.

One may either calculate the spread from the market price, or the theoretical value from the YTM (or the yield curve) and from the credit spread.

In practice, Bond spread, also called bond credit spread, Z-spread (Zero-spread), or option adjusted spread (OAS), is the constant spread added to the discount curve in order to recover the bond's price. Unlike yield to maturity, bond spread does account for the term structure of interest rates. As such, it is a good measure to compare bonds issued by a company that may differ in terms of maturity, coupon rate, or seniority. It should also faciliate comparisons of bonds from different regions and sectors.

The bond price can be computed as

where

- t is the valuation date
- i is the i-th cash flow
- r_i is the continuoups compounded interest rate for period i
- T_i is the coupon payment date of the i-th period
- s is the bond spread
- P is the principal or face value
- c is the coupon rate

The s in above formula is called the bond spread that makes the model price equal to the market quoted price.

As bond spread is a measure to compare a bond price to a benchmark interest rate curve, it relects the credit risk and liquidity risk of the bond. It tells investors whether a bond is cheap or expensive. It is also a return indicate for people who are willing to bearing credit and liquidity risks. Since bond spread plays such a fundamental role in trading and risk managemenet, it is essential for a good understanding to the definition and information of credit spread.

The interest rate curve can be treasury curve or LIBOR curve. If the treasury curve is used for discountig, the bond performance is bencharked to Treasuries. In contrast, if the LIBOR curve is used, the bond is compared to the funding curve as LIBOR represents the funding cost in the market. Given LIBOR replacement, the new funding curve is the secured overnight financing rate (SOFR).

Since bond spread reflects a parallel shift of the spread against LIBOR or SOFR, only the spread is bumped rather than the whole yield. Therefore, the bond spread takes into account the shape of the term structure of LIBOR or SOFR rates.

Also bond spread assumes that cash flows can be reinvested at LIBOR/SOFR + spread rates. Consequently future expectations of interest rates are taken into account. However, there still remains reinvestment risk as it is not possible to lock in this forward rate today.

Another popular credit spread measure is CDS spread. CDS spread reflects credit spread only. From credit spread perspective, CDS spread is cleaner than any of bond spreads. Bond spread can be referred to as CDS spread plus liquidity spread. Also the CDS and bond markets are distinct. Bond market carries various supply and demand effects.

Since credit and liquidity risks are embedded within a bond, bond spread can be interpreted as a measure for investors to determine how much they are being paid to compensate for risks.

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