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 examines the moment generating function of a stochastic process formed by integrating Brownian increments against a response kernel whose argument depends on both integration time and the current time. Applying Itô’s lemma to the exponential of…
The question compares two ways to specify returns when modeling stock prices under the physical measure. A conventional GARCH model uses a constant conditional mean, with volatility changing through the variance process. An alternative adjusts the mean by…
The discussion examines whether the risk-neutral measure, used to price securities, should also be used to forecast real-world returns. It argues for comparing predictive performance empirically rather than relying only on theoretical objections or strong…
The discussion distinguishes elicitation from backtesting. Expected Shortfall (ES) lacks a scoring function that uniquely elicits it as a point forecast, but that limitation does not by itself make ES impossible to backtest. The document cites work proposing…
The document addresses a mistaken either-or choice between modeling returns with a parametric probability distribution and using an autoregressive model. These describe different parts of a model: a distribution specifies the form of uncertainty, while…
The document discusses the Corwin–Schultz estimator, which infers bid-ask spreads from high and low prices over consecutive days. Its derivation relies on a geometric Brownian motion assumption and a relationship between one-day and two-day variance,…
The discussion asks whether variance is a convex risk measure and tests the question by expanding the variance of a weighted combination of two random variables. The key method is to bound covariance by its maximum possible value, attained when the variables…
The document explains how a Gaussian short-rate model with a multivariate Ornstein–Uhlenbeck state process produces a yield curve. Its derivation includes a maturity-dependent covariance adjustment; omitting that term gives the familiar Nelson–Siegel curve…
The discussion addresses frequent Value at Risk exceedances in backtests of portfolios whose VaR was estimated with historical simulation using rolling samples of 250 or 500 daily returns. It frames the issue as potential underestimation of risk and mentions…
Volatility forecast evaluation depends on what quantity is forecast and what observation serves as the benchmark. Possible targets include volatility, variance, or log volatility; because true volatility is latent, evaluation may use implied volatility or a…
The document asks how to approximate a portfolio’s loss distribution with a single-factor Vasicek model when individual loans have different default probabilities and correlations to the risk factor. The stated goal is to match the aggregate expected loss…
The document describes a numerical failure when calculating implied volatility for American options with RQuantLib: the solver reports that it cannot bracket a root, even though the user obtains values by entering observations manually. The suggested…
The document connects portfolio theory, CAPM, factor models, and the Sharpe ratio to the problem of analyzing short-term loan repayment data. It explains that loan portfolios are often assessed through loss distributions, since losses are a central driver of…
The document derives a linear state-space representation for estimating parameters in a futures price model with two latent factors. The state variables follow continuous-time stochastic processes: one mean-reverts, while the other accumulates shocks.…
The document asks whether potential pairs can be screened faster than testing every stock pair across every tick. It describes a theoretical approach based on fast matrix multiplication, which can reduce the asymptotic cost of computing a correlation matrix.…
The document addresses how to prove subadditivity for an entropic risk measure, after monotonicity, positive homogeneity, and translation invariance have been established. The response introduces an auxiliary function of a random variable and a positive…
The document asks how to choose a function when applying Itô’s lemma to solve a stochastic differential equation, using the logarithm of a geometric Brownian motion process as an example. It seeks a systematic way to identify a useful transformation rather…
The document raises a modeling question about whether the short rate is Markov in the Heath–Jarrow–Morton framework. It presents an expression for the instantaneous forward rate and a derived spot-rate dynamics expression that includes a stochastic integral…
The document contrasts two approaches to generating alpha: forecasting future prices or returns, and estimating an asset’s intrinsic value. Valuation methods such as discounted cash flow and peer comparisons can identify a gap between estimated value and…
The document addresses a question about why portfolio weights from a mean variance optimization may not sum to one when short selling is allowed. It presents the Lagrange multiplier setup for minimizing portfolio variance subject to a budget constraint and a…
The document explains the popularity of GARCH(1,1) as a volatility model. Its simple structure, connection to established time series methods, and ability to represent volatility clustering and heavy tailed returns help explain its use. The discussion cites…
The document asks how to annualize a Sharpe ratio for an intraday strategy evaluated with prices sampled every ten seconds. The trader describes computing each interval return, summing those returns to form a daily result, and then applying the usual…
The document raises a question about why the COS method presents a characteristic-function relation specifically for Lévy processes. It notes that if a log price is represented as an initial log-moneyness plus a random log-price change, the characteristic…
The document explains why rolling multi-day returns are statistically dependent and how that dependence affects covariance. It expands the covariance of two overlapping two-day return series into same-day covariance terms and cross-time covariance terms.…