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 considers how to estimate a missing point in a swaption volatility grid indexed by option maturity and swap tenor. The questioner has quoted Black-model volatilities at selected maturities and tenors, and is unsure whether simple linear…
The document addresses how to think about interbank lending rates at tenors longer than the daily quoted LIBOR maturities, with a focus on rates beyond twelve months. Its answer suggests looking at yields on bonds issued by banks as the closest available…
The document derives the maturity default probability for a loan in a Vasicek-style credit risk setup. It models the borrower’s asset value as a geometric Brownian motion, solves for the logarithm of asset value at the horizon, and treats that log value as…
The document presents a simple way to allocate spot curve PV01 exposures across successive forward periods. It treats each spot maturity’s PV01 as evenly distributed over the annual segments from the present to that maturity. For example, the three-year spot…
The document explains the instrument used to delta hedge a swaption: an amount of the underlying forward starting swap. For a swaption expiring in one month on a ten-year swap, the hedge is therefore a forward swap that begins at expiry and runs for ten…
The discussion surveys interest rate benchmarks and swaps after the transition away from LIBOR. It distinguishes overnight risk-free rates from unsecured overnight rates and forward-looking term rates, naming examples across currencies. For USD, it describes…
The document asks whether Basel-style steepening and flattening shocks to a US Treasury curve need further adjustments before use in valuation or regression models. In particular, it raises the possibility that stressed curves could imply arbitrage…
The document explains why a cross-currency swap may appear to have no foreign-exchange exposure in a risk report. The reported EURUSD sensitivity is expressed per pip, so a small value shown with limited decimal precision can round to zero even when the…
The document asks why the Basel internal ratings-based (IRB) capital formula includes a maturity adjustment and how its form and coefficients are justified. It identifies the adjustment as a factor applied to unexpected loss, dependent on loan maturity and a…
The document asks how to differentiate the accumulated instantaneous forward rate from the current time to a fixed maturity in the Heath–Jarrow–Morton framework. The expression combines a moving lower integration bound with a stochastic forward-rate process,…
The document asks how to simulate returns for an allocation among equities, bonds, and cash, including how to handle a lower bound of zero for cash returns and how to combine return and risk assumptions for the two defensive assets. An answer suggests…
The question concerns a forward interest rate that is observed at one date but paid later, creating a convexity adjustment when moving between forward measures with different bond numeraires. The accepted response recommends replication pricing for this…
The discussion outlines a framework for valuing a cross-currency swap using currency discount curves, FX rates and forwards, calibrated market instruments, and the swap’s cash flows. The example sets up sterling and dollar curves plus a cross-currency curve,…
The document explains how premium accrual works for short-dated, SNAC-like credit default swaps under the 2015 roll convention. It distinguishes a three-month contract, whose premium leg has one coupon accruing from the prior standard date through maturity,…
The question concerns estimating a hedge ratio between daily changes in a swap fixed rate and changes in a bond-futures forward yield. Since the swap maturity stays constant while the cheapest-to-deliver bond ages, the underlying risk exposures can drift…
The document describes ways to determine whether a bond price is quoted clean or dirty when the convention is unknown. Clean price excludes accrued interest; dirty price includes it. One approach is to use the available yield to calculate a theoretical price…
The document asks for introductory resources on asset liability management (ALM) at life insurance companies. The questioner has economics, finance, and mathematical finance experience but is new to the insurance ALM field. The sole recommendation is a book…
The document concerns a QuantLib schedule intended to place bond coupon payments on fixed January and July dates. The schedule is built backward from maturity with semiannual periods, unadjusted business-day conventions, and a specified calendar. The author…
The document explains what a calibrated SABR model is used for in interest-rate markets. Its common role is to parameterize volatility surfaces for caps, floors, and swaptions. Because SABR specifies how volatility changes as the underlying forward rate…
The document asks how to apply Girsanov’s theorem to price a zero-coupon bond when the short rate follows a Vasicek process. The questioner changes measure so the rate appears to have zero drift, then simulates the transformed Brownian motion and…
The document asks how to interpret a swap in which one party pays three-month LIBOR while the other pays a rate equal to a fixed percentage minus twice LIBOR. Its proposed simplification is to subtract LIBOR from both sides of the payment comparison. This…
The discussion distinguishes futures-curve roll from the price effect associated with a bond futures contract’s cheapest-to-deliver bond. In common futures terminology, roll is measured by comparing prices of successive contracts. For bond futures, however,…
The document poses a fixed-income pricing question: whether a market instrument reveals the value of a claim that pays at a later date based on inflation realized over an earlier period. It expresses that value as an expectation of the nominal pricing kernel…
The document asks how to derive a time-independent pricing equation for a perpetual coupon bond that pays until default, with recovery at the default time. It models the short rate and default intensity as separate square-root mean-reverting processes driven…