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 explains how an issuer’s call right is incorporated when valuing a callable bond on a binomial interest-rate tree. Valuation proceeds backward from later dates: at each node, the model discounts the possible next-period bond values using the…
The document considers a Hull–White short-rate simulation using Euler–Maruyama to estimate the expectation of a terminal payoff. It distinguishes the error from using a finite number of simulated paths from the error introduced by approximating the…
The document explains why overnight repo rates can sit above the effective federal funds rate even though repo lending is secured. Its main explanation is market structure: interest on reserve balances reduces banks’ incentive to lend reserves, the federal…
The document explains how securities lending is arranged and priced, particularly for equities. Large holders may invite dealers to compete for lending their securities, while smaller participants commonly work through multiple prime brokers. Online services…
The document compares non-callable bank certificates of deposit with brokered CDs, focusing on the bank CD holder’s ability to withdraw early at par while paying an early withdrawal penalty. It models that feature as an American-style put embedded in a…
The document poses a fixed-income valuation question about a pay-fixed interest rate swap held for a year. It asks how a positive mark-to-market on the remaining swap, calculated as the difference between the original forward rate and the prevailing…
The document considers how interest rate forwards and swap floating legs change when their fixing dates differ from standard market conventions. It compares FRAs for the same accrual period with fixings at different lags and asks whether separate curves are…
The document explains why a forward-starting swap rate can be approximated from two spot-starting swap rates. In the example, the rate for a swap beginning after three years and lasting two years is estimated from the five-year and three-year spot swap…
The document asks whether the private-company Altman Z′ score can be translated directly into a bond rating or a one-year probability of default. It explains that the score’s original coefficients and zone thresholds were calibrated on an older sample, so…
The document discusses estimating a U.S. corporate bond’s price during London morning hours, when the U.S. bond market is closed. It proposes decomposing the bond into interest-rate and credit components, using the USD swap curve rather than Treasury rates…
The document considers funding a liability due in the future with a portfolio of four-year zero-coupon bonds and a perpetual annuity, using duration matching. It writes one duration equation at the initial date and another one year later, when the bond’s…
The document explains how to establish that a forward measure is a probability measure by weighting the risk-neutral measure with a positive, normalized random variable. It defines the measure of an event as the expectation of its indicator multiplied by the…
The document asks how a forward premium quote for an interest-rate cap relates to the usual spot premium. It describes the distinction as whether the caplet payoff is discounted to its payment date: the spot-premium expression includes a discount factor,…
The document examines why the yield inferred from a Treasury note futures contract can differ from the quoted yield on the on-the-run ten-year Treasury, and asks how futures carry affects DV01 calculations. The response attributes the gap to the difference…
The document asks whether Bermudan swaptions have a put–call parity relationship, how to think about optimal exercise, and whether one side’s decision to exercise determines the other side’s choice. It also considers a callable payer swap with opposing…
The document explains how the at-the-money level for an interest-rate cap or floor is determined and why volatility quotes are often organized around it. The relevant level is the forward swap rate for a swap with the same maturity, schedule, and other terms…
The document addresses obtaining downloadable, multi-year data for European companies to build a credit or default-risk model. Desired fields include company identifiers, country, industry classification, and year, alongside financial ratios, ESG measures,…
A short-rate model specifies stochastic dynamics for the instantaneous interest rate. Zero-coupon bond prices are derived from those dynamics as risk-neutral discounted expectations, and observable bond prices or cash rates provide the market data used to…
The document explains how market rates can be used to form measures of inflation expectations and expected real interest rates. It identifies inflation swap rates as the likely source of the cited medium-term inflation expectation measure, including the…
The document clarifies two uses of “forward interest rate”: a rate fixed today for borrowing or investing over a future interval, and a contract whose payoff depends on a short rate observed at a future date. It explains that these are distinct contract…
The document considers a borrower’s option to choose between a fixed-rate loan, a floating-rate loan, or cancellation after a decision window. It frames the choices as embedded options with value linked to the borrower’s credit spread, interest rates, and…
The document asks how to interpret quoted running and upfront market premiums at different tenors when working with preliminary data for estimating probability of default. It gives examples of five-year and eight-year quotes, each with a nonzero running…
The answer explains how to derive the time-dependent bond price function in the Hull–White extended Vasicek model. Instead of trying to obtain the target result by manipulating a later equation alone, it solves the first-order equation for the bond-price…
The document considers a simplified model for valuing inflation options embedded in inflation-indexed contracts with guarantees. The author already has a stochastic nominal interest-rate model, G2++, and wants inflation scenarios linked to it. One proposed…