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.
10,263 documents
The document considers how to select a floating-rate fixing for a short initial accrual period in a USD interest rate swap. The accrual dates run from the end of April to the end of July, while the three-month LIBOR fixing convention gives a value period…
The document examines a one-period market with three assets and states, asking whether a European call can be priced by replicating its payoff when the market admits arbitrage. The stated replication produces a cost of 0.5, but solving for state prices…
The document examines a potential domain issue in a paper on utility maximization in finite probability spaces. It describes a conjugate function defined for strictly positive arguments, then questions a later expression that evaluates the function at a…
The document derives an expression for the expected log return over a time interval under a local volatility stochastic differential equation. Applying Itô’s lemma gives a drift contribution and a negative half-variance contribution; the expected stochastic…
The document asks how to calculate the variance of a discounted European call or put payoff under the Black–Scholes assumptions. Its answer outlines a second-moment approach: variance equals the expected squared payoff minus the square of its expected value.…
The document frames interest rate modeling as a historical progression, listing equilibrium models such as Vasicek and CIR, no-arbitrage models such as Ho–Lee and Hull–White, multifactor models, the HJM framework, the Libor Market Model, and the Forward…
The document asks how to infer market expectations for a future central bank decision from overnight indexed swaps or short-term interest rate futures. It introduces an OIS relationship that equates the fixed leg’s accumulation with compounded daily…
The document investigates why zero rates bootstrapped from USD overnight indexed swap quotes in QuantLib differ from Bloomberg values. It presents a curve-building example and identifies several convention mismatches that can explain the discrepancy: the OIS…
The note considers which call strike to use when a trader expects realized volatility to exceed implied volatility and plans to delta hedge, aiming for gamma gains to outweigh option decay. It explains that the approximate gamma contribution to daily profit…
The document considers whether option pricing should distinguish upward from downward volatility. One response frames asymmetric volatility as a choice of a different underlying model, with risk-neutral pricing still used to value options. It suggests…
The document asks what implied-volatility fitting error is acceptable for an equity-index surface calibrated with stochastic-volatility models such as Heston or SABR. The replies do not establish a universal tolerance. One practical suggestion is to compare…
The document asks whether a QuantLib term structure can use one interpolation style for the short end and another beyond a chosen maturity. The example is an overnight-indexed swap curve with flat, stepwise behavior around central-bank meeting dates,…
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 asks how to adapt a closed-form implied volatility estimator from a call option to a put. It presents an equation attributed to Hallerbach (2004) for estimating volatility from a call price, spot price, strike, and time to expiry. This makes the…
The document tests whether the process formed by multiplying one standard normal random variable by the square root of time is Brownian motion. Although each value has a normal distribution with mean zero and variance equal to time, those marginal…
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 asks how to identify the most likely value associated with a call option when the underlying price is lognormally distributed. It starts from the discounted expected call payoff and distinguishes the mode of the underlying price distribution…
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 addresses two points about an example of VaR manipulation: a likely sign error in an inequality and how a put strategy changes reported risk and profit. The answer says the displayed ordering is consistent if the intended condition is that both…
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…