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 document examines integrability conditions for a cumulative income process in a mathematical finance framework. It asks how an expectation under a risk-adjusted measure, involving the finite-variation component divided by a numeraire, relates to an…
The document asks whether forward rates derived from one compounding convention can be used to calculate discount factors under ACT/360. It presents a method for deriving a forward rate from two spot rates and maturities, then proposes a discount-factor…
The document raises implementation questions about valuing an interest rate swap in QuantLib. It asks how a piecewise log-cubic discount curve uses dates and rates supplied through rate helpers, including whether the curve interpolates between those inputs.…
The document asks how to build a forward six-month LIBOR curve in a multi-curve framework from three market inputs: par OIS rates, a fixed six-month LIBOR rate, and par swap rates on swaps with semiannual floating payments and annual fixed payments. It…
Co-terminal, or diagonal, swaptions share a common final maturity while their expiries step forward and their underlying swap tenors shorten. The document illustrates the structure with a callable bond that can be redeemed at regular intervals before…
The document explains why a futures contract’s implied repo rate may be higher when the short delivers on the last eligible date rather than the first. The key detail is that the invoice price includes accrued interest in addition to the futures price…
The document explains the distinction between US M1, which covers balances readily used for transactions, and broader M2, which also includes savings balances, time deposits, and retail money funds that can be converted to spendable funds. It describes how…
The document presents a QuantLib setup for building a USD OIS discount curve and a SOFR projection curve from deposit, futures, and swap quotes, then pricing swaps at matching quoted tenors. The author reports small differences between the calculated fair…
The note outlines several ways to think about future short-term interest rates. It emphasizes the role of central bank decisions, since short-maturity government yields tend to track policy rates such as the Effective Federal Funds Rate or the midpoint of…
The note shows how to choose the 5-year and 10-year weights in a 5s/7s/10s interest-rate butterfly so its exposure to the first two principal components is zero. It represents the portfolio’s key-rate sensitivities in PV01 terms, sets the 7-year position as…
The document derives the relationship between a real estate asset's cap rate, its discount rate, and income growth using a perpetuity model. With constant income, value is income divided by the discount rate; with income growing at a constant rate, value is…
The document addresses how to compare equity option implied volatilities across the transition from LIBOR to SOFR discount curves. Its answer points to contractual benchmark fallback conventions: a replacement risk-free rate can be paired with a spread…
The document discusses apparent weekday swings in the P&L of a short eurozone bond position, where settlement occurs after a lag. Its response explains the effect through settlement-date valuation: a short bond may appear to have a larger liability when its…
The document asks whether sovereign yield-to-maturity observations can be fitted directly to a yield curve, such as a Nelson–Siegel curve, using QuantLib or another open-source library. The response cautions that yield observations alone can produce…
This short exchange clarifies the payoff notation for a forward contract on a zero-coupon bond. Although the forward price quoted before delivery can vary over time as market conditions and remaining time change, the delivery price agreed when the contract…
The document compares linear interpolation of quoted rates with constant-forward-rate interpolation when constructing a rate curve for pricing American and European options. It highlights that linear interpolation can create discontinuities in instantaneous…
The document considers how to decompose the forward-looking yield of an index of agency fixed-rate residential mortgage-backed securities. The proposed framework adds a duration-matched Treasury yield, the option-adjusted spread, and an adjustment intended…
The discussion distinguishes Macaulay duration’s cash-flow-weighted timing calculation from the misleading idea that it measures how long it takes a bond’s cash flows to repay its price. For a perpetual coupon bond under a flat yield, the derivation shows…
The document asks how to simulate paths of two mean-reverting processes from their stochastic integral forms and conditional distributions. Its answer recommends discrete-time SDE approximation and gives the Euler–Maruyama update: each new value combines the…
The document explains why a floating-rate swap leg can be valued from the next payment and the discount curve without forecasting every future rate. Under a single curve where discounting uses the same benchmark as the floating coupons, a sequence of bond…
The document asks how much capital or trading volume is needed to move the 10-year Treasury yield by 10 basis points. It frames the question around a recent period of Federal Reserve rate hikes, noting that the 3-month to 10-year yield curve stayed inverted…
In a continuous-time pricing model, the risk-free asset grows at a deterministic rate, expressed as a differential equation with interest rate r. The answer interprets this asset as a bank deposit: its value earns interest without a random return component.…
This document explains what the iborStartDate argument represents in QuantLib’s FuturesRateHelper. It is the start date of the interest-rate fixing’s underlying accrual period, rather than the futures contract’s expiration date. The fixing itself is for a…
The document discusses extreme forward-rate paths in a lognormal Libor Market Model simulated under the spot measure. It notes that reducing the time step or switching from ordinary Euler to log-Euler discretization may fail to eliminate the problem. One…