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 explains the inverse relationship between a bond’s price and its yield, while cautioning against treating one as the sole driver of the other. Price and yield are two ways of expressing the same information about a particular bond: when its…
The document explains the scaling on the premium side of a quarterly-pay credit default swap pricing equation. The factor of 10,000 converts a spread expressed in basis points into decimal rate units. The factor of four corresponds to quarterly installments,…
The document examines how the drift of a process ratio changes when the denominator is a numeraire. Its answer derives the dynamics of f/g using integration by parts and Itô’s rule, including the inverse-denominator term and the covariance between the…
The document derives a relationship between Australian-style and US-style forward rate agreement (FRA) payoffs. It rewrites the AUD payoff as the USD-style payoff multiplied by a notional adjustment, showing that the two forms can be matched by scaling…
The document addresses an apparent contradiction in descriptions of Federal Reserve reserves: reserves are liabilities held by commercial banks, yet banks can request physical currency from the Fed. The key accounting point in the accepted answer is that…
The document discusses why the standard Black formula cannot be applied directly to a zero-strike interest-rate floor: its log-forward-to-strike term is undefined when the strike is zero. The answers explain that model suitability depends on the forward…
The document explains how to calculate the scheduled monthly payment for a mortgage pass-through pool using its balance, gross weighted-average coupon, and remaining term. Convert the annual coupon to a monthly rate, then apply the level-payment annuity…
The response surveys embedded options and contingent cash-flow features found in bonds, loans, and preferred equity. Examples include step-up coupons, calls and puts, floating-rate floors and gearing, pay-in-kind coupons, dual-currency payments, and coupons…
The question asks whether short-window changes in bond yields can be approximated by dividing bond-futures returns by duration. The response does not derive that relationship or explain how duration maps a futures price move into a yield change. Instead, it…
The discussion explains why an FX forward calculated from two interest-rate curves may differ from a market quote. It recommends using the relevant zero-coupon rates for the forward’s maturity rather than compounding a one-year rate, and describes covered…
The document explains why the ratio of two zero-coupon bond prices, with maturities S and T where S is earlier than T, is a martingale under the T-forward measure. This property follows from the numeraire choice that defines the measure, so it does not…
The document addresses how to compare implied and realized volatility for swaptions when rates approach or fall below zero. The questioner uses broker-quoted normal at-the-money volatility, expressed in basis points, and finds that converting percentage…
The document addresses how a lifetime expected credit loss estimate should be allocated across future reporting quarters. The question asks whether a multi-year estimate should simply be divided evenly among the quarters, but the supplied answer does not…
The document presents a two-asset, two-factor diffusion model with a risk-free money market account. It gives the market price of the first risk factor as a function of the assets' expected returns above the short rate and their factor loadings, with the…
This document raises practical questions about constructing a credit curve for a single issuer, currency, and seniority class. It asks whether bullet and callable bonds should be combined, whether callable bonds with long final maturities but shorter…
The document examines whether borrowing short term and lending long term can reliably profit when the yield curve slopes upward. It explains that this maturity transformation resembles a traditional banking activity, but it is not arbitrage because the…
The document examines the Constant Maturity Swap rate used to drive the notional balance of a cancelable index amortizing swap in a Longstaff–Schwartz American-option example. It describes a two-factor Vasicek-type short-rate model and a CMS definition built…
The document explains why QuantLib’s Actual/Actual ISMA day counter can return different year fractions depending on whether coupon-period dates are supplied. In the bond example, the calculation date falls between the previous and next semiannual coupon…
The document explains why swaps do not share a single pricing formula: their fair terms depend on the underlying, cash flows, market conventions, and valuation framework. It distinguishes setting a contract’s fixed rate or strike at inception so its value is…
The question concerns the number of annual withdrawals needed to fund retirement from age 60 through age 89. Since both birthdays mark withdrawal dates, the sequence includes one withdrawal at age 60 and one at each subsequent birthday through age 89, for 30…
The document interprets notation for nominal wealth, real wealth, and the price level, then derives the relationship between nominal return, inflation, and real return. Real wealth is nominal wealth divided by the price level. If nominal wealth grows by the…
The document distinguishes LIBOR from an overnight policy rate such as the UK’s SONIA. LIBOR represents a term borrowing rate for a specified maturity, while the policy rate applies to overnight lending. The distinction explains why an overnight central-bank…
The document explains a curve trade described as buying five-year bonds and hedging with two- and ten-year bonds. The basic idea is to offset the purchased bond’s interest-rate exposure by selling bonds at shorter and longer maturities. It illustrates the…
The document explains why a cash flow in one currency may be discounted using the overnight rate associated with the collateral currency. Under a USD collateral agreement remunerated at USD OIS, the foreign-currency cash flow is converted through the…