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 answer explains that an MA model represents a series using current and past shocks, rather than past observed values. It suggests comparing simulated AR(1) and ARMA(1,1) series with the same errors to see how the moving-average coefficient changes their…
The document asks how to set internal concentration limits for a retail credit portfolio and whether the Herfindahl-Hirschman Index (HHI) is suitable. It defines HHI as the sum of squared exposure weights and notes that its range depends on the number of…
The document examines how correlation can affect best-of and worst-of options and discusses confusion arising from the payoff definition. The questioner's Monte Carlo example simulates correlated terminal prices for two assets and reports that the price of a…
The document distinguishes two conventions for compounded overnight-rate swap coupons. In a lookback without an observation period shift, each daily rate observation is moved earlier by a set number of business days, while the accrual weights remain tied to…
The document explains that the right bond comparison measure depends on the task. For an indicative price on an illiquid bond, it describes interpolating between observable bonds that mature earlier and later. For amortizing bonds, weighted average life may…
The document investigates why a simulated call price comes out as zero when the Black–Scholes calculation gives a positive value. Its proposed remedy is to simulate the underlying under the risk-neutral geometric Brownian motion process, using the risk-free…
The document answers whether local volatility can be estimated using only the spot price at a particular time. It explains that Dupire’s approach derives local variance as a function of option maturity and strike from a surface of call prices, rather than…
The document outlines a Monte Carlo approach for valuing performance share units whose payout depends on a company’s share-price performance relative to a peer group. It estimates daily log-return means, volatilities, and correlations from historical prices,…
The document explains how to aggregate ordinary monthly returns into quarterly returns. For each quarter, add one to every monthly return, multiply those gross returns together, and subtract one. This captures the effect of sequential returns; simply summing…
The document gives an approximation for the probability that a stock touches a short strangle’s higher strike without touching its lower strike. It defines events for touching each side and expresses the desired probability as the probability of touching the…
For normally distributed asset returns with known means and covariance, the document relates portfolio VaR optimization to familiar portfolio objectives. When VaR is defined as a return quantile centered on the portfolio mean, maximizing it is equivalent to…
The document examines why a finite-step Taylor expansion for an option price can include the squared asset-price increment, while a continuous-time Itô calculation uses quadratic variation. It distinguishes two ways to express a change in a smooth function:…
The document considers how to specify the mean equation when forecasting stock index return volatility with a GARCH model. One workflow first selects AR and MA terms for the mean using an ARIMA procedure, estimates that equation by least squares, and checks…
The document proposes a heatmap for showing how often obligors remain in each credit rating class from one period to the next. Ratings occupy one axis and time intervals the other; color represents the proportion that kept the same rating. This puts many…
The document distinguishes martingale assumptions used in derivative pricing from assumptions used in trading and risk management. For pricing, it describes a risk-neutral probability measure under which an underlying asset is a martingale, linking that…
The document asks how to apply stratified sampling, a variance reduction technique, when pricing Asian options by Monte Carlo simulation. It contrasts stratifying the terminal Brownian motion value for a European option with stratifying the average of…
The document concerns estimating parameters for a stochastic volatility model in which variance follows a Cox–Ingersoll–Ross (CIR) square-root process. The question asks for estimation from time-series data rather than option prices, with quasi-maximum…
The document examines how to simulate multiple geometric Brownian motion price paths with a specified correlation structure. The attempted R approach draws independent normal shocks, applies a Cholesky factor of the input correlation matrix, and uses the…
The document explains free cash flow as operating cash flow after capital expenditures. Operating cash flow reflects cash generated through business operations, while capital expenditures are spending on long-lived operating assets. It distinguishes free…
The document considers how to calculate returns from one-minute price bars when a trading session begins after a long market closure. The first observed price of a session and the prior session’s final price produce a return spanning far more than one…
The document distinguishes a stock’s return over an individual year from its annualized return across multiple years. It describes an example with an initial investment, a change in year-end price, and no purchases or sales during the holding period. The…
The document notes that market depth has no single official quantitative definition and proposes measuring it through the cost of immediately buying and selling a specified quantity, given the order book at a particular time. This cost varies with both the…
The document explains translation invariance for a risk measure: adding a constant amount to a profit-and-loss position reduces its VaR by that amount. For a continuous P&L distribution, VaR is expressed as the negative of a lower-tail quantile, so shifting…
Realized variance is an estimate of intraday variation, not by itself a model for forecasting volatility across days. To forecast future volatility, a model must specify how information from realized measures relates over time. The document describes…