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
The document considers why a stock price can move repeatedly even when company news does not arrive at the same pace. It presents price as a noisy proxy for underlying value: after news, market participants may take time to interpret its implications and…
The document compares two ways to forecast daily variance with a GARCH(1,1) model when five-minute returns are available. In the first approach, the model is fit or applied at the daily horizon, using a realized-variance estimate and a prior daily variance…
The document poses a terminal-value PDE in two variables with second derivatives in each variable, a mixed derivative, and a source term proportional to one state variable. It asks how to solve the equation when reducing the two-dimensional dependence…
The document explains how to simulate a geometric Brownian motion after changing from the physical measure, where the drift is the expected return, to the risk-neutral measure, where the drift is the risk-free rate. It derives the change in Brownian motion…
The document considers how to simulate correlated asset returns for Monte Carlo mean-variance portfolio optimization. A common approach starts with independent standardized draws and multiplies them by a matrix factor of the target covariance matrix,…
The document distinguishes utility representations under certainty from expected utility under uncertainty. Under certainty, any increasing transformation of a utility function preserves the ranking of preferences. With lotteries, preferences are represented…
The question asks how long it takes a stock’s historical price to reach a chosen level. The answer explains that there is no model-free estimate: the waiting-time distribution depends on assumptions about how prices evolve. Under an arithmetic Brownian…
The document asks why fitting an autoregressive model of order one to stock prices can yield a high test-set R-squared while fitting the same form to returns can yield a negative score. An AR(1) regression predicts the current observation from its lag, but…
The note gives an econometric rationale for adding lagged versions of predictors to a recession classification model. Its example is the yield curve: an inversion may precede a downturn by many months, so the curve observed earlier can be relevant to whether…
The document shows how Brownian motion's quadratic variation leads to the identity for the Itô integral of Brownian motion against itself. Applying the finite-increment expansion of one half of the squared Brownian level separates the expression into a sum…
The note explains why drift is often neglected when modeling asset prices at very short time intervals. For geometric Brownian motion with constant drift and volatility, it compares how each component scales as the interval shrinks: drift scales linearly…
The document considers whether Monte Carlo simulation can be applied directly to discrete stock percentage changes rather than to stock prices. The response highlights a key distinction between simple returns and the log returns used in geometric Brownian…
The document distinguishes estimating volatility with a GARCH model from forecasting future volatility. It also considers realized volatility calculated from high-frequency price observations as another way to quantify volatility. Its central point is that…
The document asks how to predict whether bank customers will remain active, using their account movements, and points toward customer activity or churn analysis as the problem area. It recommends multinomial logit and probit models as statistical methods to…
At expiration, a call with a zero strike pays the stock price when the stock price is nonnegative. The discussion asks whether this means the option should be worth the stock itself before expiration, and whether shareholder rights or counterparty risk…
The discussion responds to a request for learning materials on stock-price forecasting with artificial neural networks, LSTMs, regression, and other predictive methods. It recommends two practical books: one covering modern forecasting models, including…
A backtest that selects stocks using today’s market capitalization can exclude companies that later failed or fell out of the universe, while favoring firms that grew into it. This survivorship bias can make historical performance look too strong. The…
The document defines an affine term structure model through the relationship between bond yields and model state variables. In the simplest formulation, a zero-coupon bond price is exponential in a maturity-dependent constant and the short rate; taking its…
The document addresses why the Black–Scholes call formula contains different volatility adjustments in d1 and d2 under risk-neutral pricing. It outlines a derivation route: solve the stock price process with its drift set to the risk-free rate, then express…
The document explains how factor models can help identify risks and return patterns in an equity portfolio. It contrasts return-based analysis, which regresses portfolio returns on candidate factors, with holdings-based analysis, which aggregates exposures…
The document outlines checks for evaluating an ARMA-GARCH model fit. Before using GARCH, test whether the data show ARCH effects; without conditional heteroskedasticity, a GARCH model may not be needed. After fitting, inspect standardized residuals for…
The document asks how to select the optimal bandwidth for a realized-kernel volatility estimate when the desired output uses one-minute bins. It gives the bandwidth formula from the cited reference and notes that its noise-to-signal input uses integrated…
The document asks whether a flat implied-volatility skew implies a normal risk-neutral distribution when option prices are converted into a density using the Breeden–Litzenberger relationship. It notes that the density inferred from its stated formula…
The document seeks to interpret a paper's implied-gamma method for fitting option prices across strikes. In the described approach, gamma is a modeler-selected parameter defining a return uncertainty set. For each in-sample strike, the parameter is…