Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
5,701 documents
The note explains how to obtain a daily grid of forward rates from an interpolated overnight indexed swap curve in QuantLib. The original approach queried forward rates only at the curve’s node dates, so it returned a sparse set of values. The proposed…
The note describes how to convert an interest rate quoted with one compounding frequency and day-count convention into an equivalent rate under another convention. First calculate the accrual year fraction for the relevant dates under the source convention,…
The document presents a numerical question about applying the Merton structural credit model to estimate a firm's asset value, asset volatility, default probability, and recovery rate from equity value, debt, equity volatility, the risk-free rate, and time…
The document raises a portfolio-hedging question: how to account for correlations between international bond returns and foreign-exchange carry returns when choosing currency hedge positions. It defines the relevant series as asset log returns and carry…
The document asks how to calculate the conditional expected value and variance of the accumulated short rate between two future times under the Vasicek model. It begins with formulas for the integral from time zero to a given horizon, then obtains the…
The document concerns choosing which retail credit portfolios to retain or sell when only aggregate portfolio information is available and borrower-level records are not. Its response points toward loss given default (LGD) modeling as a relevant area of…
The document poses a valuation problem for a contingent payment tied to a bond’s credit-rating deterioration. It specifies a monthly rating transition matrix, a maturity horizon, continuous discounting, and a rule that pays when the bond first falls below…
The document explains how to interpret the three maturity-dependent loadings in the Nelson–Siegel model of the yield curve. Its factors represent level, slope, and curvature: the constant loading applies across maturities, while the other two functions shape…
The document explains why option values generally depend on both the underlying price and time, so they are described by a partial differential equation rather than an ordinary differential equation. It then gives perpetual American options as an important…
The answer explains the Federal Reserve’s discrete policy-rate decisions in terms of its data-dependent approach and mandate to support price stability and maximum employment. Inflation, employment, and output indicators arrive at different frequencies, so…
The example asks why a portfolio beta estimated by regressing portfolio returns on market returns might not equal the weighted average of the individual asset betas. It constructs portfolio returns from two bond price series using weights based on estimated…
The document considers whether a coupon bond maturing on the same date as a zero-coupon bond should have a higher or lower yield, given an upward-sloping set of zero-coupon prices. It explains that a bond’s yield to maturity is the single rate that discounts…
The document outlines an affine term structure model in which log bond prices are linear functions of latent factors. With as many observed yields as factors, the factor vector can be recovered from yields by inverting the model’s loading matrix, assuming…
The discussion addresses how floating-rate products changed after the transition from LIBOR to SOFR, focusing on floating-rate notes and interest rate swaps. For floating-rate notes, it describes using compounded SOFR fixings from the coupon period with a…
The discussion outlines a basic process for benchmarking a mortgage-backed securities portfolio. First, choose a relevant index, with U.S. mortgage benchmarks given as examples. Then compare portfolio data with benchmark data, taking care that the holdings…
The document clarifies terminology for describing an interest rate swap using two periods: the time from the relevant spot or evaluation date to the swap’s effective date, and the period from effective date to termination, commonly called the tenor. It…
The document explains why desks may use SABR alongside Black-76 or Bachelier pricing for vanilla swaptions and other interest rate options. In this account, the vanilla pricing formula supplies the option value, while SABR models how implied volatility…
The document raises a model-selection question for estimating potential future exposure (PFE) on a vanilla interest rate swap. It considers Monte Carlo scenarios from a one-factor Hull–White model and questions whether its parallel curve shifts can represent…
The discussion addresses how to calculate Bartlett-adjusted vega when a QuantLib SABR swaption volatility cube derives its forward rates internally from a spot curve. Since the cube does not expose forward rates as direct inputs, the proposed workaround…
The document explains why a cumulative return comparison between IEF, a Treasury ETF, and front-month 10-year Treasury futures can be misleading. A continuous series of front-month futures prices may show a price gap when contracts are rolled, even though…
The discussion examines an apparent futures cash-and-carry opportunity when a Treasury futures contract’s implied repo rate exceeds the actual financing rate. It explains that the spread is not necessarily risk-free: the trade uses balance sheet and…
The discussion explains how to calibrate a Hull–White interest-rate tree for valuing callable bonds. It recommends using swaption volatility quotes when those instruments resemble the embedded options in the bonds, and suggests constructing an equivalent…
The discussion considers how to estimate default probabilities and loss given default for small firms without traded bonds or equities, when market-implied credit measures are unavailable. It describes two balance-sheet approaches: a Merton-style structural…
The discussion addresses whether buying a Eurodollar futures contract produces a gain when its quoted price is unchanged from entry through expiration. Its central point is that a buyer who enters at 99.80 and settles at 99.80 has no price-based profit or…