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 asks how to generate observations from a four-factor t-copula when the dependence matrix changes over time. Its setting is a series of 2,000 correlation matrices from a copula-DCC model, with one matrix intended for each time step. The accepted…
The document explains how to select interpolation schemes when bootstrapping yield curves in QuantLib-Python. It shows a dual-curve setup using deposit, forward rate agreement, and swap helpers, then constructs curves with different interpolation choices,…
The document compares two discrete approximations for estimating the volatility parameter in a mean-reverting stochastic differential equation with a deterministic time-varying mean. One approach begins from the continuous-time solution and approximates the…
The note addresses why variance minimization can help find cointegrating combinations among nonstationary series. It explains that when a cointegrating relationship exists, the coefficients can be estimated super-consistently, giving more flexibility in how…
The document shows how a bond price process can define a change of probability measure under which a shifted Brownian motion is Brownian. Starting from the bond’s risk-neutral dynamics, it forms a density process from the discounted bond price divided by its…
The document explains why a standard variance swap payoff uses a scaled sum of squared log returns without subtracting the sample mean squared. One answer distinguishes realized variance in the market convention from the statistical sample variance: the…
The document asks how to determine whether a strategy’s performance edge has weakened across time periods. It mentions comparing period means with a t-test as an approach encountered elsewhere, while expressing concern that this test may be unreliable for…
The document poses a pricing puzzle under Black–Scholes assumptions: with spot at 100, zero interest, and volatility chosen so the one-year one-standard-deviation price range is 50 to 200, the call at 200 costs more than the put at 50. It asks why strikes…
The document explains how to infer a discount curve from fixed-rate bond prices using Rateslib. It contrasts sequential bootstrapping, which solves curve values in maturity order and relies on suitable instrument and curve conditions, with Rateslib’s global…
The document examines how a power-law exponent affects the share of aggregate income received by the highest earners. It challenges an illustrative example by showing that merely doubling salaries while halving the number of earners at each level does not,…
The document asks whether the negative half-variance term in the logarithm of a geometric Brownian motion price process is related to volatility drag when converting arithmetic returns into geometric returns. It supplies the Black–Scholes stochastic…
The document considers a three-day, 99% value-at-risk estimate for a portfolio split equally between two stocks, given an annualized covariance matrix and joint Student t returns with five degrees of freedom. It asks whether portfolio returns can be combined…
The note explains that a product term in a regression represents an interaction: the association between one predictor and the outcome changes with the value of another predictor. For two predictors, including their product allows the fitted slope for one…
This note frames trading under an assumed known stochastic price model as a finite-horizon stochastic control problem. The trader’s state includes capital, current position, price, and model parameters; the model evolves price and parameters using noise. The…
This exercise asks whether a market with two assets and three states admits arbitrage, and how to bound the price of a risk-free asset. State prices assign a price to receiving a unit payoff in each state; multiplying the payoff matrix by the state-price…
The document derives the probability density of the minimum of a standard Wiener process over a fixed time interval using the reflection principle. It first observes that the minimum has the same distribution as the negative of the process maximum, since…
The document raises a mathematical question about expressing the self-financing condition for a continuously traded portfolio when gains are defined through Lebesgue–Stieltjes integration. It contrasts this setting with discrete trading, where portfolio…
The document explains how the bond price dynamics in the Vasicek short-rate model follow from the model’s closed-form bond price. That price is written as a time-dependent factor multiplied by an exponential involving the current short rate and the function…
The document considers a daily classification task: using index features to predict whether the next day's open-to-close move is up or down. The proposed workflow forms a direction label, selects and scales features, trains an SVM on a rolling window, and…
The discussion explores how discrete binomial models can help teach Itô's lemma and its correction term. One proposed illustration transforms a symmetric random walk with a convex function, such as squaring it, then compares the expected transformed value…
The document examines whether one stock divided by another remains a martingale after changing from the money-market account to a stock numeraire. It sets out two uncorrelated stock processes under the risk-neutral measure and applies a Radon–Nikodym density…
In the classical mean-variance setup, expected returns and covariances are treated as known inputs, so optimization produces deterministic portfolio weights. The weights become random when the inputs are estimated from return data: changing samples can…
The document examines a second-order approximation for the certainty equivalent of a risky payoff. Expanding utility around the payoff’s mean approximates expected utility using the utility curvature and payoff variance; a first-order expansion of utility at…
The document presents a question about applying the Capital Asset Pricing Model to a two-stock portfolio. The investor supplies portfolio weights and estimated betas, then asks how to obtain the expected return and whether a correlation inferred from the…