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 discussion considers how to interpret a negative volume entry in a daily market-data file when blanks represent unavailable values. The replies agree that traded volume is not ordinarily negative, while zero volume can occur in some circumstances. One…
The discussion considers whether Markov chain Monte Carlo is useful for Bayesian inference in quantitative finance. It describes potential applications to estimating hidden-process parameters, including stochastic volatility models, and to inference for…
The document compares annualized return and volatility calculations based on logarithmic returns and simple returns. For monthly log returns, it describes scaling the mean by the number of periods in a year and scaling standard deviation by the square root…
The document considers two equivalent ways to represent a complete market: state-contingent Arrow-Debreu securities and a set of complex securities whose payoff vectors span all possible states. It asks how to express the equilibrium price of each complex…
The document asks how to read Johansen cointegration test output for two stocks and whether cointegration implies a mean-reverting pair. It presents an initial result indicating one rejected rank hypothesis, followed by a detailed trace-test output where…
The document explains how to simulate two correlated asset paths under geometric Brownian motion. It starts with a covariance matrix encoding each asset's volatility and their correlation, then factors that matrix with a Cholesky decomposition. Multiplying a…
The document considers whether predicting an asset's current price from other assets has practical value when the market already reports that price. The responses identify data alignment and missing observations as possible uses. A model could estimate…
The document asks how to define a spread for pairs trading after estimating a linear relationship between two asset prices. It compares subtracting the fitted intercept and scaling one price by the estimated gradient with omitting the intercept or simply…
The discussion distinguishes smoothing a price series from forecasting future values. It gives a recursive exponential-smoothing forecast in which the next estimate updates the current forecast in proportion to the latest observation's forecasting error.…
The discussion asks whether Bitcoin has a quantifiable fair value and how mispricing might be recognized. The answers describe its traded price as an outcome of supply and demand once the market is sufficiently liquid, while emphasizing that speculation is…
The document asks when the expectation of a function of a random variable equals the function evaluated at that variable’s expectation. It considers a convex function and whether equality at a particular parameter value implies that the function is locally…
The document explains how to derive the Black–Scholes pricing equation from a risk-neutral valuation formula. It assumes the underlying follows a geometric Brownian motion under the risk-neutral measure, with deterministic interest rates and constant…
The document collects suggested references for learning exotic option pricing and implementing pricing methods. The original question concerns volatility and variance swaps, jump diffusion, and explicit or implicit finite-difference methods, with particular…
The document describes a workflow for obtaining ISIN identifiers for listed equities. It starts with a downloadable spreadsheet of exchange tickers, then uses Bloomberg's Excel API to query the ISIN associated with each ticker. This offers a practical way to…
The document solves for the expectation and conditional expectation of an exponential built from Brownian motion at two different times. It first combines the correlated Brownian values by expressing the later value as the earlier value plus an independent…
The document examines a simulation of stock prices under geometric Brownian motion with zero drift. Although each simulated price at a fixed horizon has a lognormal distribution, the author finds that taking the median across all time steps produces a value…
The document explains how to estimate option Vega by bumping volatility and repricing, with examples involving multi-leg baskets and calendar spreads. Vega is a local sensitivity, so a one percentage point volatility move is a finite shock rather than a…
The document studies the random integral of an exponential weight times Brownian increments over a finite interval. A change of variables uses the stationarity of Brownian increments to express it in terms of a Brownian motion starting at zero, with an…
The discussion explains that Value at Risk (VaR) is defined for a stated time horizon and confidence level; without a horizon, a VaR figure is incomplete. It outlines a common parametric approach: estimate portfolio return volatility from historical data, an…
The document derives the expected stock growth factor over one time interval, restricted to cases where that factor falls below a threshold. Under geometric Brownian motion, the growth factor is lognormally distributed, so its truncated expectation can be…
The document asks why volatility forecasts from an ARMA(1,1)-GARCH(1,1) model decline slightly over a multi-step forecast horizon. The displayed output shows the standard deviation estimates decreasing across successive forecast steps, while the questioner…
The document considers a GARCH(1,1) model fitted to the spread between two correlated assets. Although the reported coefficient estimates appear unremarkable, the standardized residuals show a bimodal distribution, prompting the question of whether such a…
The example considers a riskless asset and one risky asset whose dynamics are driven by two Brownian motions, while the information available to traders is generated by both. Although the asset equation can be rewritten using their scaled sum, that sum alone…
The document presents a closed-form expression for a zero-coupon bond price under an extended Hull-White short-rate model with time-varying drift, mean-reversion, and volatility parameters. The bond price is exponential-affine in the current short rate: one…