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 compares distributional choices for modeling interest rates, beginning with a proposed sequence of nonnegative independent observations. Responses caution that this assumption misses persistence and changing volatility: rates tend to cluster…
The document asks how a paper’s infinite-product representation of a pricing kernel relates to the familiar one-period stochastic discount factor and the change of measure from historical probabilities to risk-neutral probabilities. It outlines an affine…
The document explains how Greeks for swaptions, caps, floors, and other interest rate options are defined and calculated. They measure sensitivity of a derivative’s value to pricing inputs. Because interest rate pricing depends on an entire curve, the…
The document explains the drift in the extended Vasicek, or Hull–White, short-rate model. Under the risk-neutral measure, the short rate follows a mean-reverting process with a time-dependent drift term and volatility. The drift is not itself the riskless…
The document examines whether adding a swap payment period changes the value of American and Bermudan swaptions in a predictable order. It defines co-terminal and co-initial swap structures, their exercise schedules, and the proposed comparisons between…
The document asks why a bank may incur a cost when it holds a positive derivative value as a receivable before cash settlement. It distinguishes the economic profit implied by a future payment from cash already available to the bank, and considers whether…
The document asks how to price a zero-coupon bond from a short-rate model, starting with the risk-neutral conditional expectation of the exponential of the negative accumulated short rate. It names several model families and asks how simulated rates,…
The document explains how floating-rate notes linked to overnight benchmarks accrue interest over a coupon period. It frames the calculations as adaptations of overnight indexed swap compounding and distinguishes simple averaging from compounding. It also…
The document discusses which market instruments can provide data for constructing yield curves during the transition from LIBOR to SOFR. It describes the familiar LIBOR approach, which uses forward rate agreements, futures, and swaps referencing the relevant…
The document considers a bond with a call and a put exercisable on the same date, using different strikes to illustrate how the embedded options affect value. Under its stated assumptions—a forward bond price of 100 and no discounting—the example values the…
The document describes using a normal, or Gaussian, model to price caplets and floorlets when rates can be negative. Under the stated setup, the forward rate evolves as a Gaussian martingale with constant absolute volatility, so its value at expiry has a…
The document addresses how a T-forward measure can be used when a directly observed zero-coupon bond for the required maturity is unavailable. It explains that market curves are built from instruments spanning different horizons: spot borrowing rates anchor…
The document explains why standard CDS settlement after a credit event does not generally depend on the trade’s original coupon or upfront payment. Those amounts reflect the trade’s earlier mark-to-market and are treated as historical once the event occurs.…
The document presents ways to explain bond P&L in a format resembling swap curve attribution. One method maps each bond’s risk to maturity buckets, such as splitting a bond between adjacent swap tenors, then estimates bucket moves by minimizing the…
The document considers how to hedge a 30-year bond when the most liquid bonds extend only to 10 years. As the bond ages, its maturity eventually enters the liquid part of the curve, where a 10-year bond may provide a closer hedge. The difficult period is the…
The document explains why the term duration can refer to different bond measures and how compounding conventions affect their relationship. Macaulay duration is described as a time-weighted measure of fixed cash flows, while modified duration measures the…
This note outlines ways a Europe-based investor can hedge the currency exposure of a USD bond. One approach is to align a cross-currency swap with the bond’s payment schedule, paying USD fixed to match the bond coupons and receiving either fixed or floating…
The document evaluates a calculation that uses a mean-reverting short-rate process to explain a particular future long-term Treasury yield. It confirms that the displayed closed-form solution applies to a Vasicek process with a constant long-run mean. It…
The document explains how a LIBOR market model can be used to estimate the future value-at-risk of a portfolio of interest rate swaps. The proposed workflow starts by choosing a time grid and collecting current market rates, then bootstrapping or…
Bootstrapping a yield curve from market instruments produces discount factors or zero rates at the instruments’ maturities. These observed maturities are curve nodes; they do not by themselves specify values at every date. An interpolation method fills in…
The document asks how to price an Arrow security that pays one unit if a specified event occurs at a future date. It frames the question through the stochastic discount factor: the current value is expressed as the expected product of that factor and the…
The document asks how to select a yield curve for discounting cash flows when pricing bonds, swaps, swaptions, equity options, FX forwards, and FX options. It distinguishes government, swap, overnight-indexed, and reference-rate curves, and asks whether the…
The document clarifies terminology and pricing relationships in the agency mortgage-backed securities market. A TBA contract lets the short party choose a mortgage pool from a set meeting agreed criteria, such as coupon, origination period, and geographic…
The discussion considers how to obtain a nine-month LIBOR fixing when that tenor is unavailable. It emphasizes that interpolation depends on the intended use. In a loan whose contract required a nine-month rate, the parties agreed to create a synthetic…