Project Record

Credit Pricing and Model Validation Engine

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Primary source: https://ionitsa.com/projects/credit-pricing-validation-engine.md
Canonical page: https://ionitsa.com/projects/credit-pricing-validation-engine/

A tested CDS hazard-curve and fixed-rate bond valuation library that turns credit quotes into survival probabilities, full-revaluation P&L, and model-validation evidence.

Domains

Hedge FundCredit

Capability

Market & Risk Systems

Methods

Derivatives PricingCurve BootstrapNumerical MethodsStress Testing

Executive Summary

The existing credit strategies could size first-order hedges, lag signals and charge implementation costs, but their daily P&L still relied on supplied spread sensitivities. That left a basic research question unanswered: could the system price the underlying instruments and show when its approximation stopped being trustworthy?

I built an independent Python valuation library for that purpose. It calibrates a piecewise-constant hazard curve from CDS par spreads, calculates survival and default probabilities, values premium and protection legs with accrual-on-default, converts standard coupons to upfront points, and reports risky PV01. A separate fixed-rate bond engine calculates dirty and clean price, yield, Z-spread, credit-spread DV01 and rates DV01.

The implementation is paired with a deterministic stress study rather than an unsupported performance backtest. Across 15 spread scenarios, it compares full revaluation with the initial linear sensitivity and measures the resulting hedge-ratio drift. The result demonstrates credit instrument pricing, numerical calibration, model-risk controls and reproducible research. It also provides the valuation layer required by the broader bond–CDS and CDX projects.

What the engine prices

For a risk-neutral survival curve $Q(t)$ , recovery $R$ , discount factor $D(t)$ and CDS coupon $c$ , the protection buyer’s value is:

V_{CDS}=N\left[(1-R)\int_0^T D(t)(-dQ(t))-c\,A(T)\right],

where $A(T)$ contains scheduled risky premium payments and premium accrued when default occurs between coupon dates. The par spread makes the two legs equal:

s(T)=\frac{(1-R)\int_0^T D(t)(-dQ(t))}{A(T)}.

The hazard curve is piecewise constant. Each interval intensity is solved in maturity order so that the one-, three-, five-, seven- and ten-year market quotes are reproduced. A bisection solver keeps the numerical method explicit and auditable.

For a fixed-rate bullet bond, the dirty price at Z-spread $z$ is:

P(z)=\sum_i CF_i D(t_i)e^{-zt_i}.

The package inverts the same equation to recover Z-spread from price. Clean price is dirty price less accrued interest. Central differences provide credit-spread DV01 and rates DV01 independently.

Validation before research

The engine has tests for the model identities that should fail before a strategy result is trusted:

every input CDS quote reprices inside the declared tolerance;
survival stays between zero and one and never increases with time;
a par CDS has zero value;
low-spread CDS pricing approaches $s\approx\lambda(1-R)$ ;
risky PV01 agrees with a coupon finite difference;
standard-coupon upfront has the correct sign;
clean price plus accrued equals dirty price;
yield and Z-spread solvers recover their inputs;
rates DV01 and spread DV01 agree with central differences;
deterministic experiments reproduce exactly.

These are unit and property-style checks. The next validation tier is a golden test set against the official ISDA CDS Standard Model and a separately configured QuantLib implementation with all contractual conventions locked.

Approximation-error experiment

The first experiment prices a five-year, $1 million CDS and a five-year,$ 1 million face-value fixed-rate bond. Starting credit spreads range from 50 to 1,000 basis points. Each curve is widened in parallel by 25, 100 or 300 basis points. Recovery is fixed at 40% so the comparison isolates convexity and sensitivity decay.

The initial RPV01 and bond CS01 produce the linear estimate. The shocked hazard curve and shocked bond Z-spread produce exact repriced P&L. Under the largest shock, linear CDS P&L overstates the gain by as much as 12.43%, while linear bond P&L overstates the loss magnitude by 7.37%. The initially matched CS01/RPV01 ratio moves by as much as 4.01% across the grid.

Linear P&L versus full revaluation

This is not a discovery that first-order Greeks are useless. For the 25-basis- point shocks, CDS approximation error stays near 1% and bond error near 0.6%. The result identifies the operating boundary: the approximation is a useful daily attribution tool, not a substitute for revaluation through a credit jump.

Model boundary

The implementation is ISDA-informed but is not the ISDA CDS Standard Model and does not claim contractual cash-settlement parity. It uses year-fraction coupon schedules, a transparent integration grid and midpoint default discounting. Production valuation additionally requires exact step-in and settlement dates, business-day calendars, day-count rules, holiday treatment, RFR curve inputs, front-end protection and official test grids.

The bond engine prices fixed-rate bullets. Its Z-spread is not labelled OAS. Callable and putable bonds require an interest-rate model, exercise policy and option-adjusted valuation.

The reproducible package lives under research/credit-pricing-guide/. The companion article, How to Build and Test a Credit Pricing Engine Before You Backtest, is written as a step-by-step guide rather than a performance note.