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 difficulty obtaining stable parameters when calibrating a two-factor Hull–White interest-rate model to cap prices. The five parameters are two mean-reversion rates, two volatility parameters, and the correlation between factors.…
The document asks how to simulate a credit spread series that tends to tighten when stock returns exceed their average and widen when returns fall below it. It proposes a linear model: a positive baseline spread minus a positive coefficient times the…
The document considers how to estimate Treasury yields beyond the longest available bond maturities, using a theoretical 40- or 50-year yield as an example. The questioner reports that Nelson–Siegel and Svensson curve fits gave unsatisfactory, unstable…
The document discusses how to make yield curve stress shocks meaningful when the current rate level differs from the historical level used to define a shock. It contrasts applying a proportional change to rates, which can exaggerate moves at low levels, with…
This discussion examines why MATLAB’s actual/actual date-to-time calculation may not match QuantLib’s actual/actual day-count variants when code is ported between the two platforms. The example compares a period spanning 2006 to 2036 and reports different…
The discussion distinguishes terminology by context. In bond and swap trading, the terms notional and nominal may refer to the same reference amount used to calculate contractual cash flows. In macroeconomics, nominal commonly describes a rate or value…
The discussion explains why the risk-free rate can be expressed as the reciprocal of the summed prices of state-contingent claims. Each claim pays one unit of currency in one possible state and nothing in the others. Buying a claim for every state therefore…
The document explores how to include callable bonds in a historical-simulation risk model. For plain bonds, the questioner proposes applying historical changes in the currency zero curve and issuer or rating spreads, then repricing. Callable bonds add…
The document considers estimating a riskless interest rate from spot and forward or futures prices using the relationship between the forward price, spot price, rate, and time to maturity. Rearranging that relationship gives an implied rate from the…
The document raises a portfolio-construction problem from a life-insurance asset and liability model: whether a large bond portfolio can be represented by a smaller set of zero-coupon bonds with approximately matching cash flows. The motivation is to reduce…
The discussion considers whether a constant displacement can adapt a standard LIBOR market model to negative interest rates. It proposes applying the shift to the forward rates used in the diffusion and drift numerators, while the accepted response clarifies…
The discussion clarifies the difference between a cross-currency swap and a cross-currency basis swap, then illustrates how a basis swap can convert a foreign-currency bond exposure into a USD funding comparison. In the example, an investor exchanges USD…
A non-deliverable interest rate swap exchanges fixed and floating interest cash flows linked to one local currency, but settles the net amount in a deliverable currency such as USD or EUR. The example describes paying a fixed local-currency rate and…
The discussion asks whether a payer Bermudan swaption’s chance of exercise at its first exercise date rises or falls as interest rates increase. Its answer gives an intuitive example: for a payer option with a fixed strike and a flat curve, low swap rates…
The document explains that life insurers can face equity risk through both their investment portfolios and the products they sell. In the European Union, Solvency II does not impose a blanket ban on equity holdings. Instead, insurers must hold sufficient own…
The document explains how to translate a USD Libor curve into an equivalent EUR funding curve. Its central method is to convert EUR into USD at spot, accrue the USD cash at the relevant Libor rate, and convert it back to EUR at a forward FX rate. Comparing…
The document asks whether a central bank's published government yield curve is a forecast of future policy rates or a curve derived from bond market prices. The context is the fall and steepening of UK gilt yields after the Brexit vote, which the question…
The document explains how to extract a ten-year zero-coupon discount value from prices of two bonds with the same maturity but different coupon rates. Because the 8% coupon stream is exactly twice the 4% stream, subtracting twice the lower-coupon bond price…
The document asks how to build a USD multi-curve setup for trading Fed Funds and Eurodollar futures, with Fed Funds and three-month LIBOR forecast curves. It compares discounting from an OIS curve based on effective Fed Funds with using the Interest on…
The document derives a futures rate from the expected value of a money-market rate in a one-factor Heath–Jarrow–Morton framework. Using the bond-price dynamics, it obtains a convexity term expressed as an integral involving bond volatilities. The adjustment…
The post clarifies that marginal default probability, conditional default probability, and hazard rate describe related but distinct quantities. Over a time interval, marginal default probability is the unconditional probability that default occurs within…
The answer explains why the at-the-money caplet formula contains the forward rate for the accrual period. It assumes that this rate follows a lognormal process under the forward measure associated with the bond maturing at delivery. Discounting the expected…
The note addresses how to value an uncollateralized swap when the bank must fund its exposure. It describes two equivalent framing choices: discount cash flows using a curve that reflects the bank’s unsecured funding rate, or use OIS discounting as the base…
The document sets up a short-rate model with mean reversion, square-root diffusion volatility, and independent positive jumps whose sizes follow an exponential distribution. It presents the pricing PIDE for a security paying a function of the terminal rate…