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FRM Exam Part I · Corporate Bonds

Credit Spreads and Corporate Bond Pricing for FRM Part I

Updated 11 October 2026 · Fact-checked

A corporate bond is priced by discounting its promised cash flows at risk-free rates plus a credit spread. The spread pays you for default risk, liquidity and other risks. Yield spread, G-spread, Z-spread and OAS are different ways to measure that spread. In exams, you usually solve for price or spread.

Understand Credit Spreads and Corporate Bond Pricing

A government bond is treated as close to risk-free. A corporate bond promises the same kind of cash flows, but the issuer may fail to pay. Investors want extra return for that risk. That extra return is the credit spread.

Pricing is simple in principle. Take each promised coupon and the principal. Discount each one at the risk-free rate for its maturity plus the credit spread. The sum is the bond price. A wider spread means a lower price. A narrower spread means a higher price.

The spread is not only default compensation. It also covers expected loss, a premium for uncertainty about default, lower liquidity, and sometimes tax or embedded-option effects. Under a simple risk-neutral view with a flat hazard rate λ and recovery rate R, spread ≈ λ × (1 − R). That is a rough approximation, useful for quick checks.

There are several ways to quote the spread. The yield spread is the bond yield minus the yield of a benchmark government bond of similar maturity. The G-spread is the same idea, but the benchmark is an interpolated government yield at the bond's exact maturity. The Z-spread is a constant spread added to every point of the risk-free spot curve so the discounted cash flows equal the market price. The OAS (option-adjusted spread) is the Z-spread-like spread after removing the value of an embedded option, such as a call.

For an option-free bond, Z-spread and OAS are the same. For a callable bond, the call option benefits the issuer, so the Z-spread is larger than the OAS. The difference is the option cost, expressed in spread terms. OAS is found using an interest rate model, such as a binomial tree.

Key formulas to remember

Price with credit spread (annual)
P = Σ CFt ÷ (1 + zt + s)^t
zt is the risk-free spot rate for time t, s is the constant Z-spread. Solve for s by trial and error or a calculator.
Yield spread
Yield spread = YTM of corporate bond − YTM of benchmark government bond
Uses a single yield on each bond. Maturities should be close.
G-spread
G-spread = corporate yield − interpolated government yield at the same maturity
Interpolation removes the maturity mismatch of the plain yield spread.
Option-adjusted spread
OAS = Z-spread − option cost (in spread terms), for a callable bond
For a putable bond, OAS is larger than Z-spread. For an option-free bond, OAS = Z-spread.
Spread and expected loss approximation
s ≈ λ × (1 − R)
λ is the annual risk-neutral default intensity, R the recovery rate. It is an approximation, not an exact rule.
Risky bond price with default probability and recovery
P = [ (1 − q) × (promised payoff) + q × R × (promised payoff) ] ÷ (1 + r)^T
q is the risk-neutral default probability, r the risk-free rate. Discount at the risk-free rate because default risk is already in the cash flows.

How to solve Credit Spreads and Corporate Bond Pricing questions

Work out what the question gives you and which spread or price it wants. Then set up the discounting cleanly.

  1. 1Identify the task: price from a spread, a spread from a price, or a default probability from a spread.
  2. 2Identify the spread type. Yield spread and G-spread use yields. Z-spread uses the whole spot curve. OAS adjusts for an option.
  3. 3List the cash flows and their dates, including principal at maturity.
  4. 4Choose the discount rate: risk-free spot rate plus spread, or the risk-free rate alone if default is already in the expected cash flows.
  5. 5Compute the present value of each cash flow and add them up.
  6. 6If solving for a spread, compare your price with the market price and adjust the spread. Use a calculator's yield function when the curve is flat.
  7. 7For default questions, compute the expected payoff using default probability and recovery, then discount.
  8. 8Check sense: a bigger spread must lower the price, and a callable bond must have a Z-spread above its OAS.

Quickest way: Quick spread and price checks

When to use it: Use when the question asks for a rough spread, a price change, or which spread measure is larger.

  1. Use s ≈ λ × (1 − R) to link spread and default intensity.
  2. Use price change ≈ −modified duration × Δspread × price for small spread moves.
  3. For callable bonds, remember Z-spread > OAS. For putable bonds, Z-spread < OAS.
  4. For a one-period zero-coupon bond, price = expected payoff ÷ (1 + r), or face ÷ (1 + r + s) for a quick spread comparison.
  5. Eliminate options that break direction: wider spread means lower price.

Common mistakes in Credit Spreads and Corporate Bond Pricing

  • Treating Z-spread and OAS as always equal

    Both are constant spreads over a curve.

    Fix: They are equal only without embedded options. For a callable bond, OAS is lower than Z-spread.

  • Using the risk-free rate plus spread on expected cash flows

    Students mix two methods.

    Fix: Use promised cash flows with risk-free plus spread, or expected cash flows with the risk-free rate. Not both.

  • Confusing yield spread and G-spread

    Both are measured against government bonds.

    Fix: G-spread uses an interpolated government yield at the same maturity. A plain yield spread uses a nearby benchmark bond.

  • Forgetting recovery in default pricing

    Students treat default as a zero payoff.

    Fix: Add the recovery payment q × R × face to the expected payoff.

  • Applying s ≈ λ(1 − R) as exact

    It looks like a formula to memorize.

    Fix: It is an approximation for small intensities and ignores liquidity and risk premia.

Worked examples

Example 1

A one-year zero-coupon corporate bond has face value USD 1,000. The one-year risk-free rate is 3% (annual compounding). The risk-neutral probability of default is 4%, and the recovery rate is 40% of face. What is the bond price?

Show the solution
  1. Payoff if no default: 1,000, with probability 0.96.
  2. Payoff if default: 0.40 × 1,000 = 400, with probability 0.04.
  3. Expected payoff = 0.96 × 1,000 + 0.04 × 400 = 960 + 16 = 976.
  4. Discount at the risk-free rate: 976 ÷ 1.03 = 947.57.

Answer: About USD 947.57.

Example 2

A two-year bond pays an annual coupon of 5% on face USD 100. The risk-free spot rates are 2% for year 1 and 3% for year 2. The bond trades at a Z-spread of 1%. What is the price?

Show the solution
  1. Discount rates are 3% for year 1 and 4% for year 2.
  2. Year 1 cash flow is 5: 5 ÷ 1.03 = 4.8544.
  3. Year 2 cash flow is 105: 105 ÷ 1.04² = 105 ÷ 1.0816 = 97.0784.
  4. Add: 4.8544 + 97.0784 = 101.9328.

Answer: About USD 101.93.

Exam tips

  • Know the direction rules: Z-spread above OAS for callable bonds, below for putable bonds.
  • Read whether the question gives promised or expected cash flows before choosing the discount rate.
  • Remember the Z-spread is added to each spot rate, not to a single yield.
  • Use your calculator's cash flow functions to check price calculations quickly.
  • Watch units: spreads are in basis points, and 100 bp = 1%.

Practice questions from Corporate Bonds

Credit Spreads and Corporate Bond Pricing in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Credit Spreads and Corporate Bond Pricing: frequently asked questions

What is the difference between Z-spread and OAS?

The Z-spread is the constant spread over the risk-free spot curve that matches the bond's market price. OAS removes the value of any embedded option. For bonds without options, they are the same.

How do I calculate a credit spread for a corporate bond?

For a yield spread, subtract the benchmark government yield from the bond's yield. For a Z-spread, find the constant added to every spot rate that makes the discounted cash flows equal the market price.

How do I price a risky bond with default probability?

Compute the expected payoff using the default probability and recovery rate. Then discount at the risk-free rate. This works under risk-neutral probabilities.

What is the difference between yield spread and G-spread?

Both measure yield over government bonds. The G-spread uses an interpolated government yield at the same maturity as the corporate bond, which gives a cleaner comparison.