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 discussion distinguishes two research questions that can look similar but require different outcomes. To compare volatility estimators as forecasting inputs, regress a later realized-volatility measure on each estimator available at the forecast date. A…
The document asks how to apply antithetic sampling when simulating the Heston stochastic volatility model with a discretized process. The central issue is whether to reverse the random draws only for the stock price or for both the price and variance…
The document explains why counting losses beyond Value at Risk on the same sample used to estimate the quantile cannot validate a VaR model. For a historical VaR estimate based on past profit and loss observations, the proposed approach is to use a rolling…
The document estimates the chance that a stock reaches a buy limit price at least once during a waiting period. It models log prices as Brownian motion with constant volatility, uses the distribution of the running minimum to relate a price threshold to a…
The document explains how the Cox–Ross–Rubinstein binomial option-pricing recursion approaches the Black–Scholes model as the time step shrinks. It corrects the risk-neutral pricing equation, then uses first-order expansions of the up and down moves and the…
The note explains why portfolio theory commonly plots expected return against standard deviation rather than variance. Its example combines a risk-free asset with a risky asset: scaling the risky position by one half scales standard deviation by one half,…
The document examines a reported average duration of roughly 25 minutes for continuous ETH price rises or falls, measured in five-minute intervals over three months. The response recommends defining what would count as unusual and comparing the observation…
The document addresses a numerical implementation issue in the CGMY model’s characteristic function. The questioner encounters an error because the expression includes gamma functions evaluated at negative values and asks whether the formula is incorrect.…
The document compares two ways to generate paired Brownian increments with a specified negative correlation and time-step variance. One approach draws independent standard normal samples and transforms one using the target correlation; the other draws…
The document asks whether stock prices, log returns, and cumulative returns have probability density functions, cumulative distribution functions, or both, and when each representation is useful. The included answer explains that a cumulative distribution…
The document raises a time-series interpretation problem: a Hurst exponent above 0.5 is understood by the questioner as evidence of persistence, while a variance ratio test appears to indicate mean reversion. It asks which result to trust and why the two…
The note derives an unconditional-expectation form of expected shortfall from its definition as the negative conditional mean of returns in the loss tail. It uses the indicator of the event that a return falls below the VaR threshold, then applies the…
The document raises a methodological question about applying principal component analysis to financial asset series. It compares using price levels with using returns, and asks whether the selected series should be standardized before calculating covariance.…
The document distinguishes what HJM and commonly used Markovian short-rate models say about interest-rate curves. HJM specifies the current forward curve and models its evolution across maturities. A short-rate model specifies the evolution of the…
The document explains why expected value differs for holding an underlying asset and holding a call option. An underlying position is exposed to the asset’s full range of possible prices, so its expected price weights every outcome by its probability. A…
The document compares two ways to scale daily trading profit and loss: dividing by the previous day’s gross portfolio value or by the account’s initial equity. These choices describe different things. The prior-day value expresses each day’s gain relative to…
The document asks why a Black–Scholes option price differs from an expected option payoff calculated from a spreadsheet model. One response identifies a key model mismatch: Black–Scholes assumes lognormal stock prices, while the spreadsheet uses normally…
The document asks whether a proposed optimal holding for a CARA investor with normally distributed risky-asset payoffs is correct. Its setup compares expected payoff net of the risk-free investment cost with payoff variance, and suggests scaling expected…
The answer recommends calibrating interconnected interest-rate curves with a global solver instead of bootstrapping each curve in sequence. The workflow defines curves and calibration instruments, assigns each instrument its forecasting and discounting…
The discussion distinguishes forecasting the aggregate equity premium for the next month from ranking individual stocks by expected return. It points to characteristic-based cross-sectional models, using rolling Fama–MacBeth slopes and multiple firm…
The document asks how factor exposures differ from the factor returns themselves in the Fama–French three-factor model. It contrasts a Fama–MacBeth second-stage regression using estimated asset betas with a proposed regression using the factor series…
The document raises a formula discrepancy in the Yang–Zhang drift-independent volatility estimator. It compares the expression for the weighting constant k in the original paper with a different expression shown in R documentation, and asks why the two…
The document describes how a simulated short rate can be used to obtain bond prices and the term structure of interest rates. Under the risk-neutral measure, a zero-coupon bond price is the conditional expected value of discounting one unit of payment by the…
The document addresses how a technically capable beginner can move from trading infrastructure and market knowledge toward designing strategies. It describes strategy as a broad category, ranging from simple rules based on price gaps to models using…