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 considers whether options can reveal the market’s expected volatility from one close to the following open. It explains that an option’s implied variance over its life represents variance accumulated across the full interval to expiry. A quoted…
The document considers feature choice for a multilayer perceptron that classifies financial price moves as buy, hold, or sell. The proposed inputs concatenate recent returns and transaction volumes, and the question is whether a vector containing more than…
The document discusses the consumption-based asset pricing equation and why an asset’s payoff covariance with consumption matters for its price. In the model, an investor chooses asset holdings to maximize current and expected future utility, yielding a…
The document explains why a global minimum variance portfolio has the same covariance with any fully invested asset or portfolio. Its algebra starts with the GMV portfolio weights, proportional to the inverse covariance matrix applied to a vector of ones.…
The document asks whether daily trading strategy returns have a reasonable upper bound as a way to detect faulty backtests. One answer frames the issue through information coefficient, the correlation between forecasts and subsequent returns. Under perfect…
The document clarifies how tick imbalance bars are formed from transaction data. Each tick receives a direction of plus or minus one based on the change from the prior trade price; unchanged prices inherit the previous direction. The running sum of these…
The note asks how to estimate whether options trades were initiated by buyers or sellers, ideally for individual strikes and maturities. It identifies two approaches. A specialized exchange dataset used in published research classified daily call and put…
This post asks whether a proposed Average Directional Index calculator produces plausible values across several example price sequences. The examples include steadily rising and falling prices, an accelerating rise, a constant series, and a repeating…
The response offers several theoretical research areas for someone seeking mathematical finance problems grounded in analysis, probability, and optimization rather than statistical modeling. It suggests investigating convergence questions in simulation-based…
The document explains a common return on invested capital calculation: after-tax operating profit divided by invested capital, with invested capital defined as equity plus debt minus cash. It uses quarterly financial statement fields to illustrate the…
The discussion addresses portfolio analysis when stocks have different listing dates and incomplete monthly return histories. It warns that interpolating irregular observations to create an even time series, often by linear interpolation, can introduce…
The document compares several ways to annualize returns from a bet costing one unit today, with an equal chance of receiving either two units after one year or half a unit after two years. It contrasts averaging the two annualized outcomes, using an average…
The document explains that differencing and detrending address different sources of nonstationarity, so the appropriate choice depends on the data-generating process. A trend-stationary series has a deterministic time trend around a stationary error…
The document considers the expected maximum drawdown of a Brownian motion with constant drift and volatility over a fixed horizon. Drawdown is defined as the gap between the running peak and the process value, and the maximum drawdown is the largest such gap…
The note explains why multiplying the Vasicek short-rate SDE by the deterministic factor e^{at} produces the differential d(e^{at}r_t). Using the Itô product rule for e^{at} and r_t, the differential is the sum of e^{at}dr_t and r_t d(e^{at}). Since the…
This discussion examines a negative yield returned by QuantLib for a fixed-rate bond when the user expected a small positive yield. The replies identify several input and convention issues to check: the coupon is divided by 100 after already being described…
The document asks how to price a long-maturity fixed-for-floating interest rate swap when the available LIBOR curve quotes extend only to short maturities. Its answer is to use quoted market swap rates beyond the end of the Eurodollar futures strip,…
The document works through the normalized gains process for a stock paying continuous dividends, using a bank account as numeraire. It starts with geometric Brownian motion under the real-world measure, applies a change of measure, and identifies the…
The document explains how interest rate derivatives use historical index fixings for dates already observed and projection curves to estimate future fixings. It then considers valuing a derivative at a simulated future date, when the fixing history available…
The document examines why the Schöbel–Zhu stochastic volatility model can be treated as affine when deriving the stock price characteristic function. It describes augmenting the state with squared volatility and applies Itô’s lemma to obtain the dynamics of…
The document explains how to interpret realized variance formed by summing squared returns over a chosen sampling window. A sum of 5-minute squared returns covering two hours is a two-hour realized variance; annualization requires scaling by the number of…
The document compares two definitions of arbitrage in a single-period market with a risk-free asset. One requires a zero-cost portfolio whose payoff is nonnegative in every state and positive in at least one. The other states the condition using discounted…
The document presents a validation question for a machine-learning portfolio strategy evaluated out of time against a strong benchmark. Its custom rolling metric reflects portfolio value and additional state variables such as inventory and time. The observed…
The document explains why changes in accounts receivable, accounts payable, and inventory appear in the operating cash flow reconciliation even though they are balance-sheet accounts. The cash flow statement bridges accrual-based net income and actual cash…