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 clarifies how to calculate the probability of surviving the first year and then defaulting during the second when the hazard rate is constant. It distinguishes that joint interval event from a conditional probability of default given survival to…
The discussion examines whether greater risk aversion necessarily lowers the risk-free rate. One explanation uses the inverse relationship between bond prices and yields: stronger demand for Treasury bills can raise their prices and lower their yields,…
The document considers how to summarize a callable bond valued across stochastic interest-rate paths. It compares averaging the yield to maturity calculated separately for each scenario with first averaging scenario prices and then finding the yield implied…
The document explains how to calculate the year-end value of a deposit when the instantaneous force of interest is assumed to follow a cubic polynomial over the year. Four quoted rates at quarterly intervals determine the polynomial’s coefficients through…
The document asks whether monthly CPI releases move inflation-linked securities such as Treasury Inflation-Protected Securities (TIPS), and whether price responses depend on the difference between reported inflation and analysts’ expectations. It notes that…
This document explains how discounted cash flows connect to clean and dirty prices for an amortizing bond. Since amortization reduces outstanding principal, quoted prices are generally related to the unpaid principal rather than the original face amount.…
The document discusses how to infer the perturbation factor in a discrete-time Ho–Lee interest-rate tree when the initial bond term structure, risk-neutral up probability, and short rates are known. It gives a relationship between the logarithm of the…
The document presents a perpetual coupon bond valuation problem in a diffusion setting. Its pricing equation relates the required return times the bond price to the coupon and the price’s drift and curvature terms, with a boundary condition at a stopping…
The document works through a Ho-Lee short-rate model with a Brownian short rate and derives the zero-coupon bond price, its stochastic differential equation, and the discounted bond’s dynamics. It then constructs the forward-measure density from the bond…
The document compares term-premium estimates for Polish government bonds using daily and month-end monthly observations of the ten-year yield. The yields are interpolated from a Nelson-Siegel-Svensson curve built from bootstrapped zero-coupon yields, and the…
The document distinguishes a tenor-based forward LIBOR rate from an instantaneous forward rate. A forward LIBOR rate applies over a finite accrual period, such as a three- or six-month interval, and is calculated from the relative prices of zero-coupon bonds…
The document explains why a hedge does not automatically reduce exposure at default (EAD) for risk-weighted asset calculations. Basel capital requirements separate counterparty credit, market, and operational risk; an ordinary market hedge may offset market…
The document examines why par swap quotes reconstructed from a zero-coupon curve may fail to match the quotes used to build that curve. It describes bootstrapping a curve from deposit and swap helpers, extracting zero rates, then constructing swaps against a…
The note explains that a standard QuantLib bond yield calculation returns yield to maturity based on the bond reaching its stated maturity, even when it has callable dates. It shows a basic fixed-rate bond example that calculates yield from price and then…
The document raises a question about the risk-neutral valuation of a zero-coupon bond when interest rates vary over time. It compares a bond-pricing expression involving the ratio of discount factors with a general risk-neutral pricing formula, asking…
The document examines a currency-hedged excess-return formula attributed to Black and Litterman, focusing on why the hedge adjustment includes a factor of one plus the domestic short rate. The responses derive the hedge payoff by combining the foreign…
The document asks whether a premium bond necessarily has negative roll-down return, as several cited explanations claim. It distinguishes that claim from pull-to-par: on an upward-sloping yield curve, a bond that ages into a lower-yield maturity point may…
The discussion presents the Black formula for a caplet and asks how to differentiate its price with respect to the forward rate and volatility. It states the familiar forward delta as the discounting and accrual factors multiplied by the normal cumulative…
The discussion outlines a practical workflow for developing credit ratings or default-risk estimates from company fundamentals. First choose a target, such as observed defaults, agency ratings, or expert assessments, then assemble candidate financial…
The discussion asks whether ATM swaption volatilities indexed by expiry and tenor must satisfy no-arbitrage conditions. It explains that there are no direct no-arbitrage restrictions across such quotes because each swaption is written on a different…
The document distinguishes two ways to express interest rate sensitivity for a fixed income instrument such as an interest rate swap. Delta is a linear estimate of how much an instrument's price changes after a small move in the relevant rate; the discussion…
The document explores whether a bond could specify repayment in units of another security, such as stock or ETF shares, rather than in conventional currency. It frames the question both as a conceptual possibility and a legal one, then proposes an ETF whose…
The document asks how to build a USD zero-rate curve from short LIBOR tenors, forward rate agreements, and interest-rate swaps. The response recommends bootstrapping: first infer discount factors or zero rates at the short maturities, then use those results…
The document explains how to work with the joint distribution of two default events. The four intersection probabilities—both default, only the first defaults, only the second defaults, and neither defaults—must add up to one. Given a marginal default…