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 question about extending a Vasicek short-rate simulation to the Hull–White model. It first presents the exact one-step normal transition for a constant-parameter Vasicek process: the conditional mean reverts toward a fixed long-run…
The document compares fair strikes for two LIBOR contracts that reference the same rate fixed at the first maturity but pay at different dates. It derives each strike from discounted expected payoff under the bank account numeraire, then uses a change to the…
The document compares two long-term U.S. Treasury bond futures for outright, long-biased trading. It presents Ultra Treasury Bond futures as having a more consistent volatility profile, attributing this to a more homogeneous deliverable basket and an…
The document derives a Cox–Ingersoll–Ross process by summing the squares of independent Ornstein–Uhlenbeck processes. Applying Itô’s formula to each squared component produces a mean-reverting drift with a constant term, while the combined stochastic term…
The document asks whether factor volatilities in the multi-factor Heath–Jarrow–Morton framework may be negative. It notes that the drift expression uses products of volatility functions, then reports a reference that explicitly assumes these functions are…
The document explains how to price a LIBOR cash flow fixed at time T and paid at T plus a tenor period. It addresses which numéraire is appropriate for changing from the risk-neutral measure and whether that change remains valid when the accrual period has…
The document derives the price and hedge for a European call on a longer-maturity zero-coupon bond using two bonds as trading instruments. Under deterministic bond volatilities, the forward bond price is modeled as lognormal under the appropriate forward…
A single-currency basis swap exchanges cash flows linked to two floating interest rate indices. The document points to QuantLib’s FloatFloatSwap instrument as the class for representing this structure in Python, contrasting it with a vanilla interest rate…
The document asks how to price structured products that depend on three-month EURIBOR, including constant-maturity swap spreads, range accruals, and target redemption notes, when discounting uses €STR. It proposes modeling the €STR short rate with a…
The document considers a three-year coupon bond with annual payments and a continuously compounded interest rate. It clarifies that continuous compounding must be handled consistently when discounting the coupons and principal. The posted response notes that…
The document gives a simple way to estimate the fixed rate on a forward starting interest rate swap from spot starting swap rates. It treats the longer term as a combination of an initial period, or head, and a later period, or tail. Under a chosen fixed-leg…
The document recommends Nelson-Siegel and related Diebold-Li models for parameterizing government yield curves. These models describe changing curve shapes, including rising, inverted, flat, and humped forms. Instead of assuming the curve is monotonic or…
The document explains why interest rate models often focus on short rates or forward rates rather than introducing a single model for an isolated long rate. The meaning of a long rate depends on the chosen maturity: rates at two, five, or ten years could…
The document evaluates a retirement contract by discounting its contributions and later benefits to the same date. It treats the payments as end-of-year cash flows, calculates the present value of the 40 annual contributions, discounts the retirement…
CDS index series begin with constituent default swaps set to a five-year tenor. As time passes, the series’ remaining maturity declines, so a contract entered into later has the time left on that series rather than a fresh five-year term. This is the key…
The document discusses how market participants price American options on Eurodollar futures and when a European-option approximation may be adequate. It contrasts tree-based models that represent early exercise with the simpler European treatment often used…
This exchange examines a mismatch between QuantLib and Bloomberg pricing for a Czech koruna interest rate swap. The questioner reports matching fixed-leg dates and the par rate but differing floating reset rates, cash flows, and net present value. A…
The discussion explains why equity volatility and credit default swap spreads may move together, focusing on structural models of a firm’s capital structure. In the basic Merton framework, equity behaves like a call option on firm assets, with debt repayment…
The document asks whether a futures price can fall below spot if interest rates turn negative, starting from the cost-of-carry relation for an asset with no dividends. The response points out that a negative futures basis does not require negative interest…
The document addresses how to locate recent US corporate defaults. Its answer points readers to the Credit Derivatives Determinations Committees, which publish decisions on credit events, including bankruptcy determinations for named companies. This provides…
The document considers a claim that pays one unit if default occurs before maturity and seeks to express its value as an integral over possible default times. The proposed representation combines the default-time density, formed from the hazard rate and…
The document collects questions about calibrating one- and two-factor Hull–White models to cap prices, calculating instantaneous forward rates for the drift function, and obtaining short-rate paths after calibration. The replies distinguish the model’s short…
The document asks how to select the mean-reversion parameter in a one-factor Hull–White model when pricing Bermudan swaptions. It describes a calibration approach based on the ratio of standard deviations of two forward rates with a shared expiry and…
The document addresses how to distinguish cap and floor claims in broker-provided spread option data organized by strike. It cautions against classifying the instrument solely from the sign of an absolute strike or by comparing that strike with a forward…