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 describes a zero-coupon-style claim on mortgage principal that pays when the borrower prepays or, if no prepayment occurs, at maturity. It models the prepayment time as a stopping time triggered when a mortgage reference rate falls below a…
The answer explains why a discount curve described as risk-free is used in derivative valuation even though the valued instrument can carry market and liquidity risk. It frames the curve as a reference rate for replication and comparison: in a replication…
The document addresses how to calculate a swap rate from a rolled curve in RatesLib. The questioner builds an EUR interest-rate curve from market quotes, solves for discount factors, and prices a swap at its initial start and maturity dates. They then roll…
The document explains how an interim coupon affects the no-arbitrage delivery price of a forward contract. Its example assumes a security worth 100 today, a one-year delivery date, a coupon of 5 paid after two months, and a fixed continuously compounded…
The document distinguishes the broad category of cash instruments from deposit rates used to calibrate a yield curve. Cash can refer to several short-term instruments, including deposits, Treasury bills, commercial paper, and repos; their yields differ, so…
The document asks how to quantify the relationship between bond yields and credit ratings when observations are unevenly distributed across rating categories, especially in lower-rated areas. The response suggests consulting high-yield bond indices with…
The document explains how an interest rate swap’s market value can respond to its projection curve and discount curve, particularly when the swap’s value is near zero. It separates the fixed and floating legs: fixed coupons are known and their present value…
The document explains why a parallel shift in a forward curve does not necessarily produce the same change in a forward swap rate. The effect depends on how the shift is defined: the answer defines it through overnight rates implied by discount factors, then…
The document proposes ways to fill an early gap in monthly total returns for a German government bond maturity bucket of ten years and above. One approach constructs a proxy using a chosen long tenor, with twenty years offered as a practical example. It uses…
The document discusses how to measure the risk left when a government bond is hedged with a bond future, even when their DV01s match. Matching DV01 addresses first-order sensitivity to yield changes, but does not make the positions behave identically. The…
The document explains why reaching a target portfolio percentage requires recalculating both the bond holdings and the total portfolio value after new money is invested. The example starts with a £40,000 portfolio holding 40% in bonds and asks how much…
The post asks whether a QuantLib vanilla swap needs an explicit curve-linking step when a discount curve handle has already been created. Its code builds a zero curve, applies a spread, uses a discounting swap engine, and constructs a swap, but does not show…
The post asks whether net present value (NPV) must fall as the discount rate rises, especially when cash flows include both positive and negative amounts. For a stream of positive future cash flows, the author says they can show NPV decreases with the rate,…
The document asks how to choose the exponent in a discounted-cash-flow formula when bond payments do not fall on a simple sequence of whole coupon periods. It gives a semiannual coupon bond example with a settlement date between payment dates, then contrasts…
The document collects approaches for computing Macaulay and modified duration from a bond’s cash flows. One method discounts each payment using its period-specific rate, weights the payment time by its present value, and divides by the bond price; modified…
This note examines how Bloomberg’s swaption volatility quotes relate to Black-model prices, focusing on a EUR cash-settled payer swaption. It defines the normal cumulative distribution and Black formula, then distinguishes the physical-settlement annuity…
The document asks why a stock-price diffusion changes when a model includes correlation between interest rates and stock returns. In the uncorrelated case, the stock diffusion coefficient is constant; in the correlated case described, it is scaled by the…
This note works through the drift of a forward LIBOR rate when changing between forward measures associated with two bond maturities. It identifies the rate multiplied by its maturity bond as a tradable asset, then uses the bond as numeraire to express the…
The discussion distinguishes independent increments from dependence on the current state and from correlated increments. It notes that Wiener motion has independent increments, while geometric Brownian motion’s price changes scale with the current price; the…
The document answers a request for an explanation or specification of the Gaussian short-rate model implemented in QuantLib. It points readers to a standard interest-rate modeling text for the model's broader treatment and to a technical paper for…
The note examines whether bond carry should include an expected loss for default, often expressed using default probability and loss given default. The answer explains that a performing bond’s market price already reflects market views about rates, default…
The note asks how an odd lot is defined in corporate bond trading and why the distinction matters for price discovery. It contrasts several definitions found by the questioner: a bond count other than 100, trades below $1 million, and a general threshold…
The document explains how to model a USD-denominated convertible bond whose conversion feature delivers shares priced in euros. If conversion delivers a fixed number of shares and all relevant thresholds are USD-based, the conversion value is a composite USD…
The document derives the expected value of a bank account when the cumulative short rate is normally distributed. Starting from the bank account’s exponential representation, it applies the moment-generating formula for a normal random variable to show that…