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 the survival probability of a default time relates to its hazard rate, and why a conditional survival probability has a shifted hazard integral. It presents the standard unconditional relation as an exponential of the negative…
The document explains how to convert fractional betting odds into implied probabilities. For odds stated as a to b, it gives the conversion b divided by the sum of a and b. Applying that formula to the quoted odds yields implied chances of 0.652 for remain…
The document asks when Monte Carlo discretization is needed in financial modeling, given that geometric Brownian motion can be simulated exactly at selected dates. The responses name the LIBOR market model, Heston stochastic volatility, and local volatility…
The document explains why rates and discount factors derived from a QuantLib zero-coupon curve may differ from input deposit yields. The example builds a curve from deposit rate helpers and compares calculated forward rates and discount factors with quoted…
The document asks how to value a one-period payoff equal to the higher of two stock prices and whether stochastic calculus is necessary. For jointly normal prices, the accepted answer rewrites the maximum as one stock plus a call-like payoff on the…
The document considers ways to assemble a spreadsheet comparing selected public companies across fields such as headquarters, market capitalization, earnings, revenue, free cash flow, debt, and cash. It describes a programmatic route using a finance data API…
The document discusses ways to reduce sampling noise when simulating a Cox–Ingersoll–Ross interest rate process for option valuation. It recommends quasi-random sequences, with Niederreiter sequences given as an example, and control variates, suggesting a…
The document explains how least-squares Monte Carlo (LSM) values an American option and identifies when exercising is preferable to continuing to hold it. Working backward from terminal payoff, the method estimates each time step’s discounted continuation…
The document discusses a worked example from research on price impact, where market sells consume bid depth and limit bid additions replenish it. The response interprets the sequence in ticks: selling 15 shares against depth of 5 removes three levels, while…
For a stock modeled by geometric Brownian motion, the document explains how to find the chance that its future price falls below a specified threshold. The logarithm of the price is normally distributed, with a mean adjusted for the volatility term and…
The document asks how to define a stock that fades through the day in a way that can be measured. An open-to-close decline alone may miss a rise earlier in the session followed by a sharp late drop. The questioner suggests requiring an early high of day that…
The document surveys approaches to estimating time-varying dependence with copulas in R. It points to vine copulas with evolving parameters as one research direction and mentions the CDVine package and related materials for statistical inference. It also…
The document raises two questions about reproducing a hidden Markov model study of factor investing across market regimes. First, it asks whether the reported regime labels and their return and volatility summaries use future observations to classify past…
The document explains why differentiating a Black–Scholes option price with respect to time does not include a derivative of the stock price. The option pricing formula treats time and spot price as separate arguments: a partial derivative with respect to…
The document asks how to connect risk-neutral moments of simple gross returns to moments of log returns under a Black–Scholes model. It applies Itô’s lemma to obtain the stock’s terminal value, then uses the moment-generating function of a normal variable to…
The document resolves an apparent paradox: an American put’s value is at least its immediate exercise payoff, yet early exercise can still be optimal. The option value is the greater of immediate exercise value and the best expected discounted payoff from…
The document discusses reducing Monte Carlo pricing variance for a European put under a stochastic volatility simulation. The questioner uses the terminal stock price as a control variate and reports a modest reduction in the estimated standard error after…
The document considers how to fill gaps in cumulative default probability data across maturities and credit ratings. One proposed framework is to choose a probability matrix that stays close to a target, such as a calibrated estimate or a smoothness…
Yield curve PCA needs observations on a consistent tenor grid, but some markets have quotes at only a few maturities. The note compares running PCA on the sparse observed points with interpolating or extrapolating rates to create a fuller grid. The choice of…
The document asks how to obtain a conditional variance-covariance matrix from an estimated MGARCH-BEKK model fitted to spot and futures price series. It presents a two-asset BEKK-style recursion built from a constant matrix, lagged return residuals, and the…
The document addresses how traders might identify market conditions associated with changes in algorithmic strategy performance. It proposes structural-break analysis as one avenue, naming CUSUM tests on recursive residuals or levels and explosiveness tests…
The answer considers whether market betas and rolling-window beta estimates should be normally distributed when asset and market returns are assumed normal. It distinguishes beta estimated from raw returns from beta estimated using log returns, and argues…
The document asks how a biased random walk converges to a process with nonzero drift as its time step shrinks. It starts from the expected displacement after repeated up-or-down steps, then considers steps of size proportional to the square root of the time…
The document explains the origin and limits of a simple approximation that relates implied variance at a strike and maturity to local variance near the initial spot and the strike at expiry. It places this shortcut alongside short-maturity results: the…