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 frames the model-selection problem for pricing vanilla swaptions on fixed-versus-floating or floating-versus-floating legs. Requirements include multiple floating-rate tenors, OIS and LIBOR legs across currencies, mid-curve structures, and both…
This document presents a bond portfolio duration calculation and asks how to hedge its interest-rate exposure with a fourth bond. The accepted answer distinguishes Macaulay duration, which measures the weighted timing of cash flows, from modified duration,…
The document clarifies how long and short CDO tranche positions relate to credit exposure and credit protection. For cash CDO tranches, an investor buying a tranche takes on credit exposure and receives a spread as compensation. For a synthetic CDO, the…
The document examines the basis risks in a SEK–USD cross-currency swap collateralized in euros. It reasons from the collateral currency: discounting the SEK cash flows may involve a SEK–EUR basis, while discounting the USD cash flows may involve a USD–EUR…
The document raises a question about using a non-flat term structure when pricing options on bonds with a normal short-rate model. The author describes a proposed mapping for a ten-year bond: at each future point before maturity, use a zero-coupon yield…
The document explains the economic reason bid and ask sides may appear reversed when deriving implied interest rates from an FX forward. A long AUD forward is described as a sequence: borrow USD, exchange USD for AUD at spot, and lend AUD. Each leg has its…
This exchange asks why a German government bond future can have a quoted price far above the price of a cash government bond. The question considers yield-curve expectations, quotation conventions, and carry, and wonders whether coupon payments should make…
The discussion explains how price alignment interest (PAI), paid on variation margin, changes the funding interpretation of cleared interest rate swaps. With perfect collateralization, where collateral tracks the derivative’s net present value, the…
The discussion identifies potential benchmarks for US corporate and Treasury bond strategies over a historical daily sample. It distinguishes an investable exchange-traded fund from the index it tracks: the fund’s price history begins later, while the…
The note explains why multiplying the Vasicek short-rate SDE by the deterministic factor e^{at} produces the differential d(e^{at}r_t). Using the Itô product rule for e^{at} and r_t, the differential is the sum of e^{at}dr_t and r_t d(e^{at}). Since the…
This discussion addresses European swaption pricing under normal volatility, including how to derive a receiver swaption value from a payer value and whether an at-the-money strike equals the forward swap rate. The answer identifies the Bachelier formula as…
This discussion examines a negative yield returned by QuantLib for a fixed-rate bond when the user expected a small positive yield. The replies identify several input and convention issues to check: the coupon is divided by 100 after already being described…
The document asks how to price a long-maturity fixed-for-floating interest rate swap when the available LIBOR curve quotes extend only to short maturities. Its answer is to use quoted market swap rates beyond the end of the Eurodollar futures strip,…
The document works through the normalized gains process for a stock paying continuous dividends, using a bank account as numeraire. It starts with geometric Brownian motion under the real-world measure, applies a change of measure, and identifies the…
The document explains how interest rate derivatives use historical index fixings for dates already observed and projection curves to estimate future fixings. It then considers valuing a derivative at a simulated future date, when the fixing history available…
The document offers two book recommendations in response to a request for an accessible introduction to options derivatives. One answer points to a broad derivatives textbook covering options and futures. Another recommends a book on interest rate models,…
The document asks how to handle bonds that mature while backtesting a fixed-income portfolio strategy, particularly when trying to reproduce a published study. It focuses on how a maturing bond contributes to returns and how the portfolio should account for…
The question considers how to invest a large sum that will arrive at the end of year two and remain invested for two years. It provides continuously compounded zero-coupon yields across maturities and asks which approach offers the safest real-term…
The document explains how interest is handled when one party posts a US Treasury security as collateral for a derivatives contract. Unlike cash collateral, which may be returned with an explicit interest payment, securities collateral generally does not…
The document considers whether a noisy Ornstein–Uhlenbeck process with a moving reference band and a cooldown period has a financial interpretation. The band is reset when the process exits it, while a dead period prevents another update for a fixed time.…
The document distinguishes a decline in Federal Reserve mortgage-backed security holdings from the broader meaning of tapering. It explains that tapering generally refers to slowing the pace of asset purchases. A reduction in the Fed’s monthly MBS buying…
The document examines a mathematical issue in deriving the expected value of the Cox–Ingersoll–Ross short-rate process. Applying Itô’s lemma to an exponentially scaled rate gives a drift term that leads to the familiar expected-rate expression, provided the…
The document explains how to estimate pre-settlement risk, or potential future exposure (PFE), for a five-year interest rate swap. Although its question asks whether payments from the counterparty should be constant, the answer clarifies that exposure is the…
The document explains why a swap-based reference curve can be suitable for pricing USD interest-rate instruments, while emphasizing that the spread measure often matters more than the curve choice. It distinguishes the I-spread, which compares a bond’s yield…