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 simulate two positively correlated time series when one is a stock modeled with geometric Brownian motion (GBM). It describes estimating GBM inputs from historical stock data and reports a Pearson correlation of 0.5 between the two…
The document explains how factor models can reduce the complexity of modelling returns and covariance across many assets. It represents each asset’s return as exposures to a smaller set of common factors plus an idiosyncratic component. When the factor count…
The document poses a question about whether a discounted stock price that is a martingale under a risk-neutral measure must fail to be a martingale under the actual or physical measure. It frames the issue in a Black–Scholes setting, with a geometric…
The document asks whether the probability law of a Brownian motion with constant drift is the same as a measure under which that drifted process becomes standard Brownian motion. It correctly distinguishes the process’s original law from the changed measure:…
The document works through the conditional expectation of the squared value of a Brownian motion at a later time, given its filtration at an earlier time. It expands the later value into the known earlier value plus an independent increment, then asks why…
The document asks which probability measure should be used to calculate the expected discounted payoff of a replicable claim that lies below a possibly nonreplicable contingent claim. It presents an equality between a supremum over such replicable claims and…
The document contrasts two approaches to pairs trading. One estimates a hedge ratio between nonstationary price levels so their linear combination is stationary, then models that spread as autoregressive or mean reverting. The other combines asset returns,…
The document defines a credit spread from the prices of defaultable and risk-free zero-coupon bonds, then relates default risk to a hazard rate and survival probability. It also introduces a structural company valuation in which equity resembles a call…
The document asks for books that help quantitatively trained readers connect mathematical finance models with real-world practice. The responses offer a range of references across investments, portfolio theory, corporate finance, financial econometrics,…
The document asks how to verify the Euler–Maruyama method’s stated mean-square convergence order numerically. It proposes estimating the root mean square error across simulated paths at each time point, taking the maximum over the grid, and comparing results…
The document sets up a Heston stochastic volatility model for log price and variance, then states an exponential-affine conditional moment-generating function in the terminal log price and variance. It also presents a known expression for an unconditional…
The document addresses whether differentiating an accumulated stochastic integral requires adding an Itō correction term. For an integral whose integrand is the smooth function g of a process S, the differential of the integral is simply its current…
The document explains how to derive a theoretical 1.5-year Treasury spot rate from the price and cash flows of a semiannual coupon bond, using shorter-maturity Treasury bill yields as earlier spot rates. Each bond payment is valued using the spot rate for…
The document asks whether the CBOE SKEW index can serve as the shape parameter of a skew-normal distribution alongside VIX. It explains the index conversion to a skewness measure and notes that the shown skew-normal parameter is constrained to a bounded…
This question describes a QuantLib issue that occurs when a pricing workflow changes the evaluation date to an earlier date after calibrating a hazard curve with UpfrontCdsHelper objects. The reported runtime error says the cash settlement date falls before…
The document concerns a Monte Carlo estimate of a European call option price compared with the Black–Scholes analytical value. The implementation uses antithetic normal draws: each simulated stock path is paired with one generated from the opposite shock,…
The document describes a Liar’s Poker approach that uses the serial numbers on a player’s own bills to inform bids, then asks whether that aggressive escalation is optimal. The answers connect the game to liar’s dice, where players make claims about a hidden…
The document compares using an interest-rate level, a log change, a simple percentage change, or a first difference as a regressor alongside stock returns. One answer recommends beginning with the untransformed rate because it is itself a rate, while another…
The document examines the annualized effective rate for borrowing over a period using backward-looking overnight rates. It presents a formula that compounds each observed annual rate over its applicable day count using simple interest for that accrual…
The document presents a curve-building setup intended to help benchmark a spreadsheet model for float-float cross-currency swaps. The question describes importing GBP, USD, and EUR par rates and cross-currency basis quotes, interpolating rates, bootstrapping…
The discussion asks whether portfolio returns can be compared using semi-standard deviation, which focuses on downside variation, instead of ordinary standard deviation. The answer frames the Sharpe ratio more generally as excess return divided by a chosen…
The discussion explains why cointegration test p-values can change sharply when the start and end dates change. If the underlying data-generating process is stable, using the longest available sample can improve a test’s statistical power. If the process…
The document considers the square of a geometric Brownian motion and asks how to derive its stochastic differential and quadratic variation. Applying Itô’s lemma to the function that squares the price adds a drift adjustment from the second derivative, while…
The answer explains the distinction between averaging periodic simple returns and calculating a compounded return over multiple periods. Because wealth evolves multiplicatively, the geometric average gives the constant per-period return equivalent to the…