Reduced-Form Bond Pricer

Reduced-form risky bond pricing model with cash coupons, PIK accruals, hazard rates, survival probabilities and discounted expected cash flows.

Bond Inputs

Face Value

Cash Coupon Rate (%)

PIK Rate (%)

Maturity (Years)

Coupon Frequency

Risk-Free Rate (%)

Credit Spread (%)

Recovery Rate (%)

Bond Price

Yield

Hazard Rate λ

Annual PD

Cumulative PD

Expected Loss

Cash Flow Analytics

Period	Time	Face	Survival	Marginal PD	Cum PD	DF	PV	Marginal EL

Portfolio Analytics

Paste one bond per line using: Face,CashCoupon,PIK,Tenor,Frequency,RiskFree,Spread,Recovery. Decimal inputs are supported (e.g. 0.01 = 1%).

Total Notional

Portfolio Price

Annual PD

Cumulative PD

Expected Loss

Portfolio Breakdown

Bond	Face	Cash Cpn	PIK	Tenor	Frequency	Risk-Free	Spread	Recovery	Annual PD	Cum PD	Price	Expected Loss

Portfolio Stress Test

Annual PD Stress (+%)

Trade Notional

Stressed Portfolio Price

Stressed Annual PD

Stressed Cumulative PD

Stressed Expected Loss

Stress Expected Loss Sensitivity

Model Definitions & Formulas

Hazard Rate & Default Metrics

Hazard Rate (λ)

λ = Spread / (1 − Recovery)

Marginal / Period Default Probability

Default(t) = Survival(t−1) − Survival(t)

= e^−λ(t−1) − e^−λt

Annualized Default Probability

Annual PD = 1 − e^−λ

Cumulative Probability of Default

Cumulative PD = 1 − e^−λt

Survival Probability

Survival(t) = e^−λt

Valuation Framework

Discount Factor

DF(t) = e^−rt

Expected Cash Flow

Expected CF = Coupon × Survival Probability

Recovery Cash Flow

Recovery CF = Face × Recovery × Default Probability

Present Value

PV = (Expected CF + Recovery CF) × DF

Expected Loss

EL = PD × LGD × EAD

where LGD = 1 − Recovery