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 discusses ways to reduce sampling noise when simulating a Cox–Ingersoll–Ross interest rate process for option valuation. It recommends quasi-random sequences, with Niederreiter sequences given as an example, and control variates, suggesting a…
The document distinguishes a forward price from a forward interest rate. A forward price is the amount agreed today for purchasing an asset at a future date; a forward rate is an interest rate set today for borrowing over a future period. Although bond…
The document compares an equal-strike interest rate floor with a receiver swaption on the same underlying forward rate exposure and asks which is more valuable. Under single-curve pricing, the receiver swaption’s payoff is no greater than the sum of the…
The document considers how to fill gaps in cumulative default probability data across maturities and credit ratings. One proposed framework is to choose a probability matrix that stays close to a target, such as a calibrated estimate or a smoothness…
Yield curve PCA needs observations on a consistent tenor grid, but some markets have quotes at only a few maturities. The note compares running PCA on the sparse observed points with interpolating or extrapolating rates to create a fuller grid. The choice of…
The document explains why a bond futures contract may permit delivery of several eligible bonds instead of naming one specific issue. If a particular bond becomes scarce or unusually expensive relative to comparable bonds, restricting delivery to that issue…
The note asks why fixed-income practitioners use duration times credit spread, often called spread duration times spread, while an equivalent duration-times-yield measure is uncommon. It compares the rationale given for spread duration times spread with the…
The document considers whether a Libor Market Model volatility function, built from a maturity-dependent linear term multiplied by an exponential and then shifted by a constant, remains bounded. It assumes the parameters and the rate’s maturity are constants…
The document introduces the interpretation of a longer-tenor overnight indexed swap (OIS) rate. An OIS exchanges a fixed cash flow against a floating leg based on daily overnight rates; the cited answer identifies the Federal Funds Effective Rate and an…
The document explains why rising real yields make it more expensive for companies and consumers to borrow. A bond’s coupon divided by price is only a rough running-yield measure; for a zero-coupon bond, the price of a fixed future payment falls as its yield…
The document asks whether a lender and an equity holder in a simplified collateralized loan obligation should value their claims using the same risk-neutral probability measure. The lender receives an agreed payment ahead of the borrower, who keeps the…
The document asks how to compare daily five-day volatility estimates for two countries’ benchmark government bonds. Because both series use rolling windows, adjacent observations share most of their underlying price data and are serially dependent. Simply…
The document addresses whether MATLAB’s one-dimensional interpolation function can produce cubic spline interpolations for yield curve data. The response says that the built-in spline method is suitable for interpolating sampled curve values and identifies…
A Bermudan swaption allows exercise on multiple specified dates, giving it more exercise flexibility than a European swaption. The document notes that these products are actively traded rates volatility instruments and are used in callable bond structures: a…
The document explains how to revalue a swaption one week after observing its implied volatility in a rates volatility cube. The option retains its underlying forward swap and strike, while its remaining expiry shortens. Its value at the later date is…
The document explains how prices of European receiver swaptions relate to the risk-neutral distribution of the underlying swap rate. It corrects the idea that an out-of-the-money premium, compared directly with an at-the-money premium, gives the probability…
The document considers whether borrowing at a low nominal rate and buying goods whose prices rise with inflation creates an arbitrage. The answer explains that a consumer price basket is not a readily tradable investment: it includes perishable goods and…
The document examines a covered interest parity example involving Australian and US interest rates and a spot exchange rate quoted in US dollars per Australian dollar. The example applies the rate differential over the contract term to derive a forward…
The document asks how to translate a 90-day SOFR market rate into a comparable three-month LIBOR rate. It highlights a key timing distinction: SOFR for the accrual period is compounded in arrears, so the realized period rate is not known until the period…
The document discusses Hull’s formula for estimating a portfolio’s high-confidence default rate over a fixed horizon. It applies the inverse normal distribution to the probability of default and confidence level, with asset correlation entering through a…
The note explains a discrepancy between manually interpolated annual-compounded zero rates and rates returned between curve pillars by QuantLib. The key point is that the curve interpolates continuously compounded zero rates, even when its configured…
The document frames a portfolio stress test for zero-coupon bonds using key-rate DV01 exposures. Each maturity bucket has minimum and maximum allowed DV01 bounds, and the sum of the bucket exposures is subject to an overall limit. Given a stress vector…
The document explains that short-rate models describe the evolution of an instantaneous interest rate and use it to derive discount factors as expected accumulated discounting over time. Because the instantaneous rate is not directly observable, the response…
The document explains how to relate a short-rate model, such as Hull–White, to a simulated overnight rate. The central distinction is that the model’s one-day zero-coupon bond price is a discount factor, not itself the overnight rate. For a simply compounded…