CDS Par Spread (Reduced-Form)
Computes the par (breakeven) spread of a Credit Default Swap in the reduced-form model with a constant hazard rate, setting the present value of the protection leg — which pays 1−R on default — equal to that of the premium leg. It shows the credit-triangle relationship s ≈ (1−R)·λ in practice. Enter the hazard rate, recovery rate, maturity, payment frequency and risk-free rate; the result is in basis points.
Result
—
CDS Par Spread (Reduced-Form)
Computes the par (breakeven) spread of a Credit Default Swap in the reduced-form model with a constant hazard rate, setting the present value of the protection leg — which pays 1−R on default — equal to that of the premium leg. It shows the credit-triangle relationship s ≈ (1−R)·λ in practice. Enter the hazard rate, recovery rate, maturity, payment frequency and risk-free rate; the result is in basis points.
Reduced-Form CDS Par Spread Calculator
A credit trader marking a five-year CDS at inception needs the spread that brings present value to zero for both sides of the trade. That is what this tool returns: the par spread of a Credit Default Swap in the reduced-form (intensity) model with a constant hazard rate. Reach for it to sanity-check a dealer quote, to back out a theoretical level from an implied default probability, or to see how much of the premium pays for default risk versus expected recovery.
The model treats default as the first jump of a Poisson process with intensity λ, so the probability of surviving to time t is exp(−λt). The protection leg is the present value of (1−R) weighted by the default density at each instant. The premium leg is the spread times the risky annuity — the PV01 — which sums discount factors against the probability of surviving to each payment date. Set the two legs equal, solve for s, and you have the par spread. Keep the assumptions in view: a flat, time-constant hazard, deterministic recovery, and a fixed risk-free rate. No upward-sloping credit curve, no stochastic intensity, no correlation.
Enter the hazard λ (or the default probability that implies it), the recovery rate R, the maturity in years, the premium payment frequency, and the risk-free rate. The output is the par spread, usually read in basis points per year, alongside the risky annuity used in the calculation. For a quick gut check, lean on the credit triangle: s ≈ (1−R)·λ. With λ = 2% and R = 40% that lands near 120 bps; the calculator's exact figure sits close, with a small adjustment from discounting and the spacing of premium payments.
Related Tools
Spread Duration (Numerical)
Computes the spread duration of a bond by finite differences, repricing the instrument for an up and a down move in the credit spread: (V− − V+)/(2·V0·Δs). While duration measures sensitivity to changes in the risk-free rate, spread duration isolates sensitivity to the credit spread, the premium the market charges for issuer risk. It's essential for managing credit portfolios, where spread risk often dominates. Enter the base price, the prices with higher and lower spread and the spread change used.
G-Spread (Government Spread)
Computes the G-spread, the difference between a bond's yield and the yield of a government bond of comparable maturity. It's the most direct measure of a bond's credit risk premium: how much extra the market demands to lend to a corporate issuer instead of the treasury. The result comes in basis points, the standard unit of the credit market. Enter the bond's yield and the reference government bond's yield.
DVA — Debit Valuation Adjustment
Computes the DVA (Debit Valuation Adjustment), the mirror image of CVA seen from the other side. While CVA discounts value for the risk of the counterparty failing, DVA recognizes the counterintuitive benefit of the institution's own default risk: if it might not pay its obligations, that effectively reduces the liability. It's the piece that makes derivative pricing symmetric between the two parties. The calculation follows the same structure as CVA, but uses the expected negative exposure and the own default probability. Enter the exposure and credit data.
Par Swap Rate
Computes the par swap rate from discount factors: the fixed rate that makes the interest rate swap's value zero at inception, equating the fixed and floating legs. The formula is (1 − last discount factor) divided by the sum of discount factors weighted by the period. It's a swap's market quote and the basis for marking existing positions to market. Enter the list of discount factors by payment date and the year-fraction of each period.
Box Spread (Arbitrage)
Computes the fair value and arbitrage of a box spread: combining a call spread and a put spread at the same strikes, creating a fixed payoff of (Kh − Kl) at expiry, equivalent to a riskless bond. The fair value is that payoff discounted: (Kh − Kl)·e^(−rT). If you set up the box for less than that, you lock in a risk-free profit. The tool returns the payoff, the fair value and the arbitrage against the cost you enter. Enter the two strikes, the rate, the term and the cost.
CVA — Credit Valuation Adjustment
Computes the CVA (Credit Valuation Adjustment), the discount applied to a derivative's value to reflect the risk of the counterparty defaulting. After the 2008 crisis, it became central to pricing: the market value of a swap or option is no longer the risk-free theoretical one, but that value minus the CVA. The calculation sums, period by period, the expected exposure times the default probability, discounted to present value and adjusted by the loss given default. Enter the expected exposures, the hazard rate, the recovery and the discount.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.