Category: Uncategorized
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How Treasury STRIPS Algorithms Turn Coupon Bonds into Zero-Coupon Cash Flows: Stripping, Reconstitution, Discount Factors, No-Arbitrage Checks and Duration
How the U.S. Treasury STRIPS program separates each eligible note, bond or TIPS principal and interest payment into independently tradable zero-coupon components, how those components can be reconstituted, and how discount-factor replication, duration, liquidity and tax effects create verification tests and limits.
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How Black-76 and Bachelier Swaption Algorithms Price Rate Optionality: Forward Swap Rates, Annuities, Lognormal vs Normal Volatility and Negative-Rate Diagnostics
How payer and receiver swaptions reduce to option formulas on a forward swap rate multiplied by a swap annuity, why Black-76 uses lognormal percentage volatility while Bachelier uses absolute normal volatility, and how negative rates, shifts, smile calibration and parity tests expose model misuse.
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How Adjoint Algorithmic Differentiation Computes Derivatives Greeks at Scale: Computational Graphs, Reverse Accumulation, Bump-and-Revalue Benchmarks and Nondifferentiable Payoffs
How AAD turns a pricing program into a reverse computational graph so one valuation can produce sensitivities to thousands of risk factors at a small multiple of valuation cost—plus tape memory, Monte Carlo noise, discontinuous payoffs, regression boundaries and validation against bump-and-revalue.
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How Matched-Maturity FTP Algorithms Split Repricing Risk from Contingent Liquidity: Dual Horizons, Behavioural Deposits and Stress Consistency
A focused deep dive on matched-maturity FTP: split short repricing from long liquidity horizons, assign behavioural maturity to deposits, price contingent draws, and test stress-model consistency.
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How CreditRisk+ Algorithms Turn Loan Portfolios into Loss Distributions: Poisson Defaults, Gamma Sector Factors, Exposure Bands, Recursions and Tail-Risk Failure
How the actuarial CreditRisk+ framework converts obligor PD, exposure and recovery assumptions into a full portfolio loss distribution using Poisson default counts, Gamma-mixed sector factors, exposure discretisation and recursive generating-function mathematics.
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How Smith–Wilson Yield-Curve Extrapolation Algorithms Build the Long End: Last Liquid Points, Ultimate Forward Rates, Wilson Kernels, Alpha and Convergence Diagnostics
How the Smith–Wilson algorithm fits observed liquid rates exactly, then extrapolates discount factors toward an ultimate forward rate using the Wilson kernel, a convergence-speed parameter alpha, and explicit long-end validation tests.
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How SABR Calibration Algorithms Fit Interest-Rate Volatility Smiles: Alpha, Beta, Rho, Nu, Hagan’s Approximation, Negative Rates and Calibration Failure
How SABR converts a forward rate and four stochastic-volatility parameters into an interest-rate volatility smile, then solves the inverse calibration problem with weighted least squares, parameter bounds, negative-rate shifts, arbitrage checks and stability diagnostics.
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How ISIN Check-Digit Algorithms Validate Securities Identifiers: ISO 6166, Letter Expansion, Modulus-10 Double-Add-Double and Reference-Data Checks
How a 12-character ISIN is structurally validated: country prefix, nine-character basic number, letter-to-number expansion, modulus-10 Double-Add-Double checksum, deterministic test cases—and why a valid check digit does not prove the security exists or is the intended instrument.
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How U.S. Treasury Auction Algorithms Allocate Securities: Competitive Bids, Stop-Out Yields, Single-Price Awards, Marginal Proration and Bid Limits
How U.S. Treasury auctions turn noncompetitive and competitive tenders into one stop-out rate or yield, pro-rate bids at the margin, enforce award limits and charge successful bidders one uniform price—plus diagnostics for edge cases and common misconceptions.