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 describes how to recover an option’s implied volatility when its price must be estimated by Monte Carlo simulation. Independent random draws at each volatility can make estimated prices jump around, obscuring the price-versus-volatility…
The document explains why the Fama–French model represents size and value effects with portfolio returns such as SMB and HML instead of using firm characteristics directly. In the asset-pricing framework discussed, expected returns are linked to covariance…
The document clarifies how to obtain the stochastic differential for a process defined as the sum of an ordinary time integral and an Itô integral. Rather than differentiating with respect to the stochastic state or Brownian motion, it treats the integral…
The document derives the expected asset price under geometric Brownian motion. Starting from the exponential solution of the price process, it factors out the deterministic terms and evaluates the expectation of the exponential of a normally distributed…
The document explains why an Itô integral driven by Brownian motion is a martingale. It splits the integral at the current time: the part up to that time is already known, while the later part has conditional expectation zero under the usual assumptions.…
The document raises a measurement question for a volatility risk premium strategy using options on a futures contract. The underlying future expires annually, while options are available at quarterly expiries. The proposed measure is to compare the implied…
The document examines a mathematical issue in deriving the expected value of the Cox–Ingersoll–Ross short-rate process. Applying Itô’s lemma to an exponentially scaled rate gives a drift term that leads to the familiar expected-rate expression, provided the…
The document explains how to estimate pre-settlement risk, or potential future exposure (PFE), for a five-year interest rate swap. Although its question asks whether payments from the counterparty should be constant, the answer clarifies that exposure is the…
The document considers whether a continuously traded energy market can be modeled with diffusion and an auction-based market with occasional jumps. The proposed approach is to build a separate jump-diffusion process for each market, allowing the auction…
The document explains why a swap-based reference curve can be suitable for pricing USD interest-rate instruments, while emphasizing that the spread measure often matters more than the curve choice. It distinguishes the I-spread, which compares a bond’s yield…
The document compares two portfolio optimization objectives: expected return penalized by variance, and expected return penalized by standard deviation. It derives a parameter mapping, δ = η divided by the portfolio’s standard deviation, that makes their…
The discussion compares two ways to estimate annual return skewness and kurtosis from a long series of daily continuously compounded returns. One approach is to aggregate daily returns into annual returns and calculate the statistics from those annual…
The document discusses unstable coefficient estimates when returns-based style analysis uses many correlated indices or factors. Suggested tools include ridge and lasso regression, which add penalties to coefficient estimates; lasso can also encourage factor…
The document distinguishes return measures according to their use. To summarize a monthly portfolio series as an annual growth rate, it recommends compounding the simple monthly returns and converting that compounded growth into an annualized simple return.…
The document considers whether two observed option-implied distributions, at an early expiry and a later expiry, can reveal the return distribution over the interval between them. It expresses the total log return as the sum of an early-period return and a…
The document examines whether pairwise dependence measures such as correlation, Kendall’s tau, or tail dependence can replace covariance in a quadratic portfolio risk calculation. Covariance has a specific justification: for portfolio returns, the quadratic…
The document derives the time-t value of a cash-or-nothing call that pays one unit when the stock finishes above the strike. Under the risk-neutral Black–Scholes model, the payoff indicator is not independent of current information because the terminal stock…
The document examines how a stock split appears in historical price data, using Apple’s seven-for-one split in June 2014 as its example. It contrasts a reported pre-split closing price near $645 with a finance site’s historical table showing a price around…
The document raises a backtesting question: how to report annual performance for a strategy evaluated on hourly open, high, low, and close data. The author has code that replays different portions of the historical series and calculates total return and…
The document gathers suggestions for quantitative investigation of suspicious stock trading, including spoofing and possible information asymmetry. One proposed method builds behavioral attributes for each trader, such as trading frequency and volume, then…
The document asks how to estimate the chance that one company’s credit rating will be upgraded or downgraded over time. The reply describes two perspectives: rating agencies use industry-specific scorecards combining company and broader economic factors,…
The document asks how to calculate the beta of a call payoff relative to its underlying at expiry under the risk-neutral measure. This covariance ratio is the hedge coefficient that minimizes the variance of the terminal option payoff minus a fixed holding…
The document discusses a log-log regression method for estimating the Hurst exponent from a price series. For each lag, it calculates differences between log prices separated by that lag, measures their variance or a related dispersion statistic, and fits a…
The document clarifies why two calculations on a rising price series produce very different values: one measures dispersion of price levels around their mean, while the other uses changes in log prices. These are different data series and have different…