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 presents a QuantLib example that builds a US Treasury yield curve from four quoted yields using fixed-rate bond helpers, then compares the ten-year input quote with the curve’s ten-year zero rate. The displayed figures differ, prompting a…
The document explains how investors' expectations of lower future interest rates can contribute to an inverted yield curve. If investors expect rates to fall, they may buy longer-term bonds, whose prices rise as yields decline. Since long-term bonds…
The document compares nominal spread, zero-volatility spread (Z-spread), and option-adjusted spread (OAS) for risky bonds relative to a risk-free curve. A nominal spread compares yields to maturity but does not reflect the shape of the spot curve. A Z-spread…
The document discusses pricing a European option when the short interest rate follows a stochastic process such as the Vasicek model. It points to affine pricing methods associated with Bakshi, Cao, and Chen: when the risk-neutral conditional characteristic…
The document examines why a rate inferred by compounding short-term LIBOR fixings can differ from the rate suggested by a Eurodollar futures quote for a roughly comparable period. It explains that three- and six-month LIBOR reflect unsecured lending for…
The document explains how exchange-rate changes affect the realized return of a euro-based investor trading US Treasury futures without delivery. Its answer treats futures P&L as the daily gains or losses credited to a USD account. When the trade is closed,…
The document asks how to estimate a country’s default probability when its historical record contains no defaults. The proposed starting point is a logit regression using macroeconomic variables, but the absence of default observations leaves the model…
The document frames parameter calibration for the Cox–Ingersoll–Ross interest rate model as a maximum likelihood problem. Its parameters govern mean reversion, the long-run rate, and volatility; the proposed baseline optimization requires each parameter to…
The document discusses whether a risk team can replace lognormal volatility inputs with normal ones in a RiskMetrics-style parametric VaR model when interest rates can become negative. One response recommends estimating volatility from historical changes in…
The document examines why a numerically estimated delta for a zero-coupon bond call may differ from the analytical delta under a Vasicek-based option formula. It describes using central differences on option values as the underlying bond price changes, and…
The document asks why an SDE’s drift changes when the pricing measure changes while its diffusion coefficient is written identically, in the context of changing numeraires in interest rate models. It proposes that quadratic variation is determined by the…
The document explains why a zero-coupon bond price can be stochastic even when it is defined as a risk-neutral conditional expectation. The key distinction is that conditioning on information available at time t produces a value measurable with respect to…
The document discusses the shifted lognormal approach to applying Black ’76 swaption pricing when swap rates can be negative. The method shifts both the swap rate and strike by a constant so the model's effective lower bound moves below zero. The question…
The document asks why a floating-rate note’s price might rise even as its discount margin widens, given the intuition that a higher required return should lower bond value. The response gives a brief possible explanation: if the note is trading below par, it…
The document describes how to infer zero-coupon discount factors from a sequence of par swap rates. It gives the relationship between a forward swap rate, the discount factors at its payment dates, and the accrual fractions. In a simplified example with…
The document discusses valuing a binary contract that pays a fixed amount if a specified credit event occurs before expiry and nothing otherwise. Its quoted premium is described as an approximate market-implied chance of bankruptcy. One proposed approach…
The document explains how a quoted CDS spread can imply a risk-neutral default probability when paired with assumptions about recovery and discounting. In a simplified one-year example, the protection buyer pays an upfront premium and receives the difference…
The document works through an HJM consistency question for a forward rate modeled as an exponential function of time to maturity times a scalar diffusion, plus a deterministic term. Applying Itô’s formula gives the forward-rate diffusion and drift. The HJM…
The document explains implied cross-currency basis as the adjustment that reconciles FX spot and forward prices with interest rates in two currencies. Substituting OIS rates into a covered-interest-parity relationship lets a trader infer an FX-OIS basis from…
The document examines how an investor might assess real estate debt funds that report steady positive returns and high yields, including funds lending through mezzanine structures. It questions whether distributions described as returns adequately show…
The document discusses key rate duration (KRD), which measures a fixed-income instrument’s price sensitivity to a change at a particular point on the yield curve. It asks why an MBS might show a large short-tenor KRD and a mix of positive and negative KRD…
The document asks whether an MBS can be valued by combining a noncallable bond with one or more swaptions, and whether swaption prices can help estimate the implied volatility of the mortgage security’s embedded options. It frames MBS as bonds whose cash…
The document explains why ownership records alone may not determine what happens to a client’s securities or cash if a custodian or prime broker fails. The outcome depends on account arrangements, legal contracts, and whether assets were kept separate,…
The document presents a Python function that generates paths for a Cox–Ingersoll–Ross (CIR) process. It updates the rate at each time step using the mean-reversion drift and a random shock scaled by the square root of the prior rate and the time increment.…