What is the recovery rate and why does it matter?

The recovery rate (R) represents the fraction of the notional amount that is recovered in the event of default. The standard assumption is 40% for senior unsecured debt, meaning creditors recover 40 cents on the dollar. Higher recovery rates imply lower loss given default and higher implied hazard rates for the same CDS spread.

What is the difference between buying and selling CDS protection?

The protection buyer pays periodic premiums and profits if the reference entity defaults (similar to buying insurance). The protection seller receives premiums and must pay (1 - R) times the notional if default occurs (similar to selling insurance). Buying protection is a bearish bet on credit quality, while selling protection is a bullish bet.

What is the CDS-bond basis?

The CDS-bond basis is the difference between the CDS spread and the bond's credit spread (z-spread). In theory, they should be equal, but in practice the basis can be positive or negative due to factors like funding costs, counterparty risk, delivery options, and market segmentation. Traders may exploit persistent basis differences through basis trades.

Credit Default Swap (CDS) Calculator: Spread, Premium & Default Probability

Enter Values

Notional Amount

Face value of reference obligation

CDS Spread

bps

Annual premium in basis points

Recovery Rate (R)

Standard: 40% for senior unsecured debt

Risk-Free Rate

Continuously compounded risk-free rate

CDS Tenor

years

Contract duration — = 20 payment periods

Payment Frequency

CDS Pricing Formulas

λ = s / (1 − R)

Q(t) = e^−λt | PD(T) = 1 − e^−λT

λ = Hazard rate | s = Spread | R = Recovery | Q = Survival prob

Calculator by Ryan O'Connell, CFA

CDS Pricing Results

Annual CDS Premium --

Periodic Premium --

Implied Hazard Rate (Risk-Neutral) --

Cumulative Default Prob (Risk-Neutral) --

Survival Probability --

Loss Given Default (LGD) --

Credit Quality (Rule of Thumb) --

Present Value of CDS Legs

PV Premium Leg --

PV Protection Leg --

Breakeven Spread (approx.) --

Payment Schedule Breakdown

Period	t_i (yrs)	Δt	Q(t_i)	DF(t_i)	PV Prem ($)	PV Prot ($)

Formula Breakdown

λ = s / (1 − R) | Q(t) = e^−λt

Step-by-step calculation with your inputs

Model Assumptions

Constant hazard rate (time-homogeneous default intensity)
Recovery rate is fixed and known at contract inception
Risk-free rate is constant across all maturities (flat term structure)
Defaults occur uniformly within each period (midpoint approximation)
No counterparty risk (protection seller always pays)
Continuous discounting: DF(t) = e^−rt
No accrued premium payment at default

For educational purposes. Not financial advice. Market conventions simplified.

Understanding Credit Default Swaps

What Is a Credit Default Swap?

A credit default swap (CDS) is a derivative contract that transfers credit risk from one party to another. The protection buyer makes periodic premium payments (the CDS spread) to the protection seller. In return, if the reference entity defaults, the seller compensates the buyer for the loss.

CDS contracts function like insurance against default. They are the most widely traded credit derivatives and play a central role in credit markets for hedging, speculation, and price discovery.

Implied Hazard Rate (Hull Ch. 25)

λ = s / (1 − R)
Where s = CDS spread (decimal), R = recovery rate, λ = constant hazard rate

How CDS Pricing Works

CDS pricing equates the present value of two legs:

Premium Leg: The PV of periodic spread payments, weighted by survival probability
Protection Leg: The PV of the expected default payment, (1 − R) × Notional

At the fair spread, PV(Premium Leg) = PV(Protection Leg). The implied hazard rate λ = s/(1−R) makes this equality hold in continuous time.

PV of CDS Legs

PV_premium = s × N × Σ [Δt × Q(t_i) × DF(t_i)]
PV_protection = (1−R) × N × Σ [(Q(t_i−1) − Q(t_i)) × DF(t_mid)]
Where Q(t) = e^−λt is survival probability, DF(t) = e^−rt is discount factor

Practical Applications

Hedging: Bond holders buy CDS protection to hedge credit exposure without selling the bond
Speculation: Traders buy protection on entities they believe will deteriorate (naked CDS)
Relative Value: Exploit mispricings between CDS spreads and bond credit spreads (basis trades)
Credit Indices: CDX and iTraxx indices provide diversified credit exposure via standardized CDS baskets

Note: The implied default probabilities from this model are risk-neutral probabilities used for pricing, not real-world default frequencies. Real-world default rates are typically lower because CDS spreads include a risk premium.

Credit Default Swaps Explained

Frequently Asked Questions

A credit default swap (CDS) is a derivative contract that transfers credit risk from the protection buyer to the protection seller. The buyer makes periodic premium payments (the CDS spread) and in return receives a payment if the reference entity defaults. It functions like insurance against a bond issuer defaulting on its obligations.

The implied risk-neutral hazard rate (λ) is derived from the CDS spread using λ = s / (1 − R), where s is the spread in decimal form and R is the recovery rate. The cumulative risk-neutral default probability over T years is PD(T) = 1 − e^−λT. These are risk-neutral probabilities used for pricing, not real-world default frequencies. Real-world default rates are typically lower.

The recovery rate (R) represents the fraction of the notional amount recovered in default. The standard assumption is 40% for senior unsecured debt. A higher recovery rate means a lower loss given default but implies a higher hazard rate for the same CDS spread, since λ = s/(1−R). The recovery rate directly determines the protection leg payout: (1 − R) × Notional.

The protection buyer pays periodic premiums and profits if the reference entity defaults (similar to buying insurance). The protection seller receives premiums and must pay (1 − R) × Notional if default occurs (similar to selling insurance). Buying protection is a bearish bet on credit quality, while selling protection is a bullish bet.

CDS spreads are quoted in basis points (bps) per year. For example, a 200 bps spread on a $10 million notional means the protection buyer pays $200,000 per year, typically in quarterly installments of $50,000. Wider spreads indicate higher perceived credit risk. The 5-year tenor is the most liquid benchmark.

The CDS-bond basis is the difference between the CDS spread and the bond's credit spread (z-spread). In theory, they should be equal, but in practice the basis can be positive or negative due to funding costs, counterparty risk, delivery options, and market segmentation. Traders may exploit persistent basis differences through basis trades.

Disclaimer

This calculator is for educational purposes only. It uses a constant hazard rate model with simplifying assumptions including flat term structure, fixed recovery rate, and no counterparty risk. Real-world CDS pricing uses term structures of hazard rates, market-implied recovery rates, and accounts for accrued premiums. This tool should not be used for trading decisions.

Credit Default Swap (CDS) Calculator

Enter Values

CDS Pricing Formulas

CDS Pricing Results

Present Value of CDS Legs

Payment Schedule Breakdown

Formula Breakdown

Model Assumptions

Understanding Credit Default Swaps

What Is a Credit Default Swap?

How CDS Pricing Works

Practical Applications

Credit Default Swaps Explained

Frequently Asked Questions

What is a credit default swap (CDS)?

How is the implied default probability calculated from a CDS spread?

What is the recovery rate and why does it matter?

What is the difference between buying and selling CDS protection?

How are CDS spreads quoted?

What is the CDS-bond basis?

Disclaimer

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