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.
21,023 documents
This note clarifies how to set up valuation equations for an asset whose dividends follow a Markov process. Its central distinction is between cum-dividend value, which includes a payment made today, and ex-dividend price, which excludes it. The investor’s…
The document explains how to generate multivariate Gaussian returns with a target covariance structure. Starting with a vector of independent standard normal draws, apply a matrix square root of the desired covariance matrix. A Cholesky factor is one such…
The document explores representing Brazilian DI1 interest rate futures with rateslib for curve calibration and sensitivity analysis. It proposes a zero-coupon swap representation and distinguishes the futures’ annualized compounded internal rate of return…
The document examines a proposed monthly regression of year-over-year stock index returns on lagged returns and macroeconomic variables, including credit spreads, inflation, and industrial production. It describes a forecasting setup that uses ARIMA…
The document explains why quasi-Monte Carlo methods use low-discrepancy sequences: these points fill a space more evenly than random samples, reducing large gaps. It defines discrepancy as a measure of how closely the fraction of points in a region matches…
The document addresses why a stock’s cumulative return can fall below the risk-free return, even when investors expect equities to earn a premium over time. Its explanation is that risky assets can have poor outcomes over particular periods. The equity…
This exchange diagnoses a dimensional error in a one-step geometric Brownian motion simulation. The closed-form process uses a drift term of (μ − σ²/2)T and a random term of σ√T multiplied by a standard normal shock. The code in the question instead…
The document compares the classical LIBOR Market Model (LMM) with a stochastic-volatility extension called SABR-LMM. LMM models a family of forward rates jointly, allowing their correlation structure to inform the pricing of products that depend nonlinearly…
The document explains how to assess completeness in a one-step trinomial stock model with a risk-free bond. An equivalent martingale measure assigns positive probabilities to all terminal states and makes the discounted stock price a martingale. The stock…
The document explains why the mean of a Black–Scholes log return is (μ − ½σ²)Δt rather than μΔt. Starting from geometric Brownian motion for the asset price, Itô’s lemma yields a log price whose drift includes the negative half variance term. Brownian…
The document asks how to express the value of a European call at an intermediate node of a Cox–Ross–Rubinstein binomial tree. It defines the node by the time step and the number of upward moves, and describes a backward-induction recurrence that discounts…
The document explains why differentiating the closed-form geometric Brownian motion solution as if it were an ordinary deterministic exponential gives the wrong drift. Because the exponent includes Brownian motion, the appropriate tool is Itô’s lemma, which…
The question asks whether a bank’s internal probability of default can be calculated from a single set of liquidity, profitability, debt-service, and solvency ratios. The answer says these figures alone are insufficient to produce a calibrated probability. A…
The document examines a spreadsheet that models portfolio wealth with a lognormal distribution derived from expected return and risk, then scales the log-return distribution across multiple years. The resulting wealth distributions spread out over time,…
The document asks whether a proposed grocery store meets an accounting profitability hurdle, given its purchase cost, annual revenue and expenses, a ten-year operating period, and full depreciation of the property over that period. The answer focuses on the…
The document asks whether information criteria or divergence measures can guide SABR calibration. The response describes a common rates-market workflow: preset beta, solve alpha to match the at-the-money volatility, then optimize rho and nu against smile…
The document examines why a bisection-style search for Black–Scholes implied volatility can fail for a put even when it works for a call. The key diagnosis is that the put price in the example is above the greatest value a European put can reach under the…
The note explains how Treasury issuance and secondary-market trading contribute to observed bond prices and derived yield curves. New issues can trade in the when-issued market before auction, where investors quote yields. At auction, the Treasury sets a…
The note distinguishes a portfolio’s Sharpe ratio from its alpha estimated against the Fama–French factors. Sharpe measures excess return relative to total return variability and can help compare portfolios. Alpha is benchmark-relative, so comparisons are…
This document explains ways to calculate Macaulay and modified duration when a bond’s remaining maturity is not a whole number of years. One approach uses a bond analytics library to construct a fixed-rate bond with a maturity specified in days, then…
This document asks whether a minimum-variance portfolio is more likely than a maximum-Sharpe, or tangency, portfolio to deliver out-of-sample performance close to its in-sample estimate. It defines disappointment as the gap between predicted in-sample…
This document poses a sequential elimination game between two teams of four gladiators. In each round, Alice chooses a fighter first and Bob responds with a matchup; each duel has no tie, and the stronger fighter’s advantage is expressed as a probability…
The document asks about geometric Brownian motion models whose drift or volatility depends on the stock’s past path, rather than only its current value and time. It gives examples of drift built from an accumulated function of earlier prices or from the…
The document proposes measuring how much a stock price moves within a day by summing absolute changes between selected observations, rounding each change down in units of a chosen price increment, and normalizing the total by the day’s range. It asks whether…