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 discusses maximum-likelihood estimation for a linear Gaussian two-factor state-space model of commodity prices, using the Schwartz-Smith framework. The observed log price is modeled as the sum of two latent state components plus measurement…
The document considers how to measure the fit of a portfolio or linear combination of assets intended to reproduce another asset’s returns. It notes a weakness of relative error: dividing by the target return becomes unstable when that return is near zero.…
The document discusses using the difference between five-year and two-year Treasury Inflation-Protected Securities yields as an indicator of inflation expectations. The answer’s proposed intuition is that longer-term yields may rise more than shorter-term…
The document asks how to approximate a down-and-out call price when the underlying follows the Heston stochastic-volatility model. It states the option payoff with a barrier condition, contrasts the problem with a Black–Scholes closed-form expression, and…
The document explains why balance sheet and income statement items do not always appear in the same categories across companies. It uses Goldman Sachs to illustrate that financial firms may present liabilities by type and maturity without a single…
The document asks how to examine whether changes in the PCE index help explain daily stock return changes over time. The proposed approach is rolling Granger causality: repeatedly apply a two-variable Granger causality test to a moving window of…
The document asks how to choose the lag length when applying the Johansen cointegration test to two time series. It notes that test conclusions can vary with the lag specification: some choices may lead to rejection of the null hypothesis while others do…
The document raises a distinction among probability measures used in quantitative finance. It describes risk-neutral probability as the framework used to price derivatives under no-arbitrage conditions, while identifying physical probability as the relevant…
The document discusses using importance sampling to estimate prices for far out-of-the-money barrier options under local volatility. It describes changing the distribution of simulated inputs from the original density to a shifted normal density, then…
The document poses a statistical question about annualized Sharpe ratios. It starts from the convention of multiplying a daily Sharpe ratio by the square root of the number of trading days in a year, under certain assumptions, and asks whether that scaling…
The document describes a simulation question about the Heath–Jarrow–Morton interest-rate framework. The author simulates forward rates with constant volatility and antithetic normal draws, then compares averages of simulated rates with corresponding values…
The document explains why stock positions remain open overnight even when some day traders prefer to close before the market shuts. Long-horizon investors and institutions—including mutual funds, private individuals, and bank portfolios—may hold shares as…
The discussion examines when at-the-money (ATM) implied volatility can approximate the risk-neutral expectation of average integrated variance. For very short maturities, it motivates the approximation by noting that instantaneous volatility near the start…
The discussion asks whether implied volatility (IV) produces better option prices than historical volatility (HV), noting that the common forward-looking argument for IV is not enough by itself to establish better pricing performance. It cites an experiment…
The Longstaff–Schwartz method prices American options by simulating possible asset paths and using regression to estimate continuation values. The discussion notes that simulation can accommodate options whose value depends on multiple factors, so the method…
The document explains how an out-of-the-money put affects variance-covariance Value at Risk for a portfolio of stocks, bonds, an ETF, and an option. The method begins with market-factor volatilities and correlations, then combines factor sensitivities with…
The document compares two ways of combining the annualized returns of a two-asset portfolio. Weighting each asset’s annualized return assumes the portfolio weights are maintained over time through rebalancing. Weighting the assets’ cumulative returns instead…
The document surveys the trade-offs involved in selecting an optimizer for portfolio allocation problems with multiple assets or risk factors, varied objectives, constraints, and simulation noise. It describes numerical search as a balance between…
The document distinguishes the CAPM relation for expected returns from a single-index model for realized returns. It asks whether CAPM alone can support the familiar division between systematic and diversifiable risk, since an expected-return equation does…
The document explains how a portfolio can have lower variance than either of its component assets, even when one asset has higher standalone volatility. It uses a fully invested two-asset portfolio and derives the minimum-variance weight from the assets’…
The document explains why daily volatility is commonly scaled by the square root of the number of trading days in a year. Under constant daily variance and uncorrelated returns, variances add across trading days, so annual volatility equals daily volatility…
The document examines a density that appears when expressing forward implied variance as an average of local variance. It derives the weighting from the risk-neutral distribution of the underlying and a factor involving spot squared and Black-Scholes gamma.…
The document considers whether high and low prices can improve correlation estimates from OHLC bars. Its central point is that open and close observations have known timing, while the relative timing of each asset’s high and low is unknown. A joint estimator…
The document asks how to reproduce a chart showing each percentile group's contribution to an asset class's compound returns. The proposed approach is to calculate log returns for bottom, middle, and top groups, sum each group's returns, then divide those…