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 asks how to interpret the local volatility shapes implied by a stochastic-local volatility specification related to SABR. In this setup, the forward rate is scaled by a power of its level, with the exponent controlling the backbone; the author…
The document clarifies how overnight indexed swap quotes relate to overnight index fixings and the construction of an OIS curve. The overnight rate in the swap formula is the relevant published index fixing, or its forecast for future dates; it is not simply…
The note explains how to estimate an overnight indexed swap rate from a fixed rate on an interest rate swap and a matching-tenor Fed Funds versus Libor basis spread. When the relevant swap schedules align—including dates, payment frequency, day-count…
The document explains why changing from a physical probability measure to an equivalent pricing measure can remove or alter the drift of an asset process while leaving its volatility coefficient unchanged. Using Girsanov’s theorem, it constructs a density…
The document explains how to turn observed zero-coupon yields into bond prices and estimate instantaneous forward rates from maturity changes. The proposed finite-difference calculation uses adjacent maturities to approximate the maturity derivative of the…
The document derives the relationship between a zero-coupon bond price and an interest rate that varies deterministically over time. Starting from the exponential of the negative integral of the short rate, it takes logarithms and differentiates with respect…
The document asks how to price a bond with an embedded option in a Black–Derman–Toy short-rate tree when the exercise date does not coincide with a time step. In the aligned case, the tree is built with a fixed step and bond values are rolled backward; at…
The document explains the change-of-numeraire result in asset pricing: when a positive asset is selected as numeraire, the price of another asset divided by that numeraire is a martingale under the associated probability measure. It starts with the cash…
The document presents a one-period binomial pricing question for an at-the-money caplet on a future one-year Treasury rate. The caplet pays if the rate rises to the upper of two possible outcomes. The question compares treating the yield like an equity price…
The document describes Markov-functional interest rate models as low-dimensional representations of the term structure built from functions of a Markov process. It notes their ability to calibrate to market prices and capture volatility smiles, while raising…
The document discusses a linear regression approach to forecasting corporate default rates from macroeconomic variables, using a historical dataset and scenario forecasts. The model selection goals are high adjusted R-squared and economic interpretability.…
The document examines how a short three-month SOFR futures position compares with a short single-period swap (SPS) over the same accrual period. Its answer emphasizes that the IMM dates and exact number of days matter when matching the instruments’ rate…
The question asks whether the normal or shifted log-normal model is the industry standard for pricing swaptions during negative-rate conditions, with the stated purpose of supporting credit valuation adjustment work. The response does not choose between…
The discussion explains why a risk-free rate appears in asset pricing and why its sign is not fixed. One account treats the rate as compensation for lending money and giving up access to it until repayment. Other explanations emphasize time preference,…
The discussion addresses why discount factors inferred from put-call parity across strikes may appear nonconstant. The key missing input is dividends: the basic parity equation without dividend treatment does not describe the relationship correctly when the…
The note asks for the risk-neutral dynamics of a zero-coupon bond whose price is exponential-affine in a short rate following a linear diffusion. It gives the time equations for the affine coefficients and compares applying Itô’s lemma to the bond price with…
This short discussion addresses how to calculate the maturity amount for an overnight index swap over a short accrual period. It distinguishes a simple interest calculation over the full period from compounding a sequence of overnight rates. The answer says…
This discussion explains why a bond’s coupon is not a reliable stand-in for its credit spread when assessing a CDS–bond basis trade. A coupon includes compensation tied to the bond’s cash flows and market interest rates, while the z-spread measures the…
The document poses a valuation question about floating-floating cross-currency basis swaps whose coupons reference overnight risk-free rates and whose discounting uses the same rate. It cites a par-value expression for a basis swap and notes that its…
The document describes a calibration problem for a Libor market model used to value a Bermudan swaption. The proposed volatility structure has a parametric time-to-maturity shape and period-specific scaling factors, while correlations follow an exponential…
The document explains how a 30/360 day-count convention affects discounting dated bond cash flows. Under this convention, elapsed time is computed by treating months as 30 days and years as 360 days, with details depending on the specific convention used.…
The document compares simple price proxies for estimating short-term price movement. One proposal weights the best ask price by bid size and the best bid price by ask size; the last traded price is offered as another useful predictor. These measures are…
The document explains how to value the EUR leg of a EUR-GBP cross-currency swap when GBP collateral is specified. The EUR leg needs both a three-month EURIBOR forward curve and a EUR discount curve that are consistent with GBP collateral. In theory, these…
The document explains how obligor asset correlations in a Vasicek single-factor credit model can be assigned under the Basel II Internal Ratings-Based framework. It presents a correlation rule that varies with probability of default, along with an adjustment…