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 two practical ways to estimate duration and related small-shock risk measures for callable bonds, where issuer exercise can change the bond’s expected cash flows. One approach assumes the issuer exercises at the yield-to-worst call date…
The document discusses how to identify common risk factors in private markets when asset prices are infrequently observed or unavailable. One suggested route is to describe companies using observable characteristics such as industry, business relationships,…
The document asks how to choose a probability measure when pricing derivatives with Monte Carlo simulation. It starts from risk-neutral valuation, where price is the discounted expected payoff, and notes that simulations may require modeling state variables…
This note explains why a plain floating-rate bond can have interest-rate duration close to the time until its next coupon reset. Under a single-curve assumption, future coupons are projected from forward rates and discounted using the same curve.…
The discussion describes how to think about risk in a single-currency swap exchanging floating payments based on different tenors, such as six-month and three-month rates. It separates sensitivity to changes in the tenor basis from outright rate delta. A…
The document explores representing Brazilian DI1 interest rate futures with rateslib for curve calibration and sensitivity analysis. It proposes a zero-coupon swap representation and distinguishes the futures’ annualized compounded internal rate of return…
The document explains why hedging a mortgage-backed security with a swap is complicated when the underlying mortgages can be prepaid. Because prepayments depend in part on future interest rates, the security’s outstanding principal and the matching swap…
The document compares the classical LIBOR Market Model (LMM) with a stochastic-volatility extension called SABR-LMM. LMM models a family of forward rates jointly, allowing their correlation structure to inform the pricing of products that depend nonlinearly…
The document explains the formula (1 − exp(−sT))/s by modeling a bond that pays continuously at a unit rate until maturity or default. With zero interest rates, no recovery, and a flat default intensity equal to the spread, the probability of surviving to…
The exchange explains how a deliverable bond moving from general collateral repo to special repo can affect its gross and net basis against a futures contract. Special financing lowers the bond’s carrying cost, which can attract demand and raise its price;…
The note explains how Treasury issuance and secondary-market trading contribute to observed bond prices and derived yield curves. New issues can trade in the when-issued market before auction, where investors quote yields. At auction, the Treasury sets a…
This document explains ways to calculate Macaulay and modified duration when a bond’s remaining maturity is not a whole number of years. One approach uses a bond analytics library to construct a fixed-rate bond with a maturity specified in days, then…
The document explains a data choice for studying market expectations of Federal Reserve policy. Actual 30-day Fed Funds futures reference the average effective rate over a calendar month, so they do not offer a contract with a continuously rolling 30-day…
The document frames three ways to convert a fixed-rate bond position into floating-rate cash flows while seeking to isolate the issuer spread: a par-par asset swap, a same-notional payer swap, and a payer swap sized to match the bond’s DV01. It explains the…
The document introduces mean-variance portfolio optimization, including a minimum-variance portfolio and a variance-minimizing portfolio constrained to a target expected return. It then describes practical variations: long-only holdings, caps on individual…
The document asks how to interpret a bond investment denominated in one currency when the investor hedges the currency exposure using a forward rate whose implied yield differs from the bond’s yield. It frames the question as whether a 10% bond yield…
The document examines how the value of an inflation-linked payment can differ from expected inflation multiplied by a discount factor when inflation and interest rates are correlated. It presents a simplified convexity adjustment for a fixing paid after a…
The document applies Itô’s lemma to an exponential function of an integrated short rate under the Vasicek model. It derives the stochastic differential of the intermediate process, then uses its drift and diffusion terms to obtain the dynamics of the…
The document answers whether a bond can begin amortizing after an initial period of interest-only payments. It confirms that such structures exist, while noting that they do not have a single standard name in the response. The timing and pattern of principal…
The document compares ways to calculate a bond’s yield to maturity from price when repeated updates make speed important. One approach computes yields for three selected prices, fits a quadratic price–yield relationship, and uses it to estimate yields for…
The document considers pricing a callable range accrual whose coupon depends on how often a spread between long- and short-tenor constant-maturity swap rates stays above a threshold. The question notes that a LIBOR Market Model can be slow and that a…
This derivation uses an exponential-affine form for a zero-coupon bond price in the Vasicek short-rate model and substitutes it into the risk-neutral bond pricing PDE. Matching the constant and rate-dependent terms yields differential equations for the time…
Junior tranches of a credit default swap index absorb losses before more senior portions, so a small change in the underlying portfolio can produce a much larger proportional change in the tranche’s value or spread exposure. The document illustrates this…
The question asks how correlations in credit default swap data should be interpreted, particularly when researchers use correlations between equity returns to build relationship graphs. The answer cautions that credit correlation can refer to distinct…