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 discussion compares Bayesian and frequentist approaches in finance and argues that method choice should depend on the data, model, and question. Frequentist tools include least-squares estimation and hypothesis testing. Bayesian methods add prior…
The document considers an investor who spends an initial amount evenly over a fixed interval to buy shares of a stock with stochastic price dynamics. The number of shares accumulated changes over time according to the spending rate divided by the current…
The document uses a fixed-coupon bond example to ask how to interpret Macaulay duration, modified duration, and convexity. It presents the bond price as the discounted value of coupon and principal cash flows, then identifies modified duration with the…
The document examines whether non-Gaussian stock returns can be transformed into a Gaussian series. It warns that forcing observations to match a normal quantile distribution can produce a normal-looking sample while distorting the data and removing…
The document asks for references explaining the Feller condition for the Cox–Ingersoll–Ross square-root diffusion, a model often used for interest rates. It points readers to treatments in Iain Clark’s Foreign Exchange Option Pricing and Andersen and…
The document asks whether an annualized Sharpe ratio can predict how often or how long a strategy will lose money, and whether a striking record of few losing days implies a particular Sharpe ratio. The responses distinguish average excess return relative to…
The document works through a covariance involving the stochastic integral of cubed Brownian motion and the time integral of squared Brownian motion. It rewrites the latter using an Itô-integral representation plus a deterministic term. The deterministic…
The document asks whether the time integral of Brownian motion is a martingale. Although integration by parts rewrites it using a stochastic integral, the resulting integrand depends on the terminal time. The accepted answer explains that the familiar…
The document explores an empirical approach to estimating fair implied volatilities for SPX options. It proposes using a proxy for future volatility, such as VIX, to select similar historical observations, fitting a distribution to those observations, and…
The note asks how to define risk factors for scenario testing of a portfolio containing several currency pairs. It outlines a basic stress-testing workflow: identify portfolio-relevant drivers, specify scenarios, shock those drivers, and interpret the…
The document explains why applying Itô’s lemma to a function of a diffusion requires a second-order term. For a process with drift and Brownian volatility, a Taylor expansion includes the squared process increment. Ordinary time increments have negligible…
The document explains how to identify the standardized random increment in a risk-neutral trinomial asset model and connect it to a weak convergence argument for Black–Scholes. Taking logarithms of each of the three possible one-step multipliers gives three…
The document describes a discrepancy between a closed-form price for a geometric Asian call and a Monte Carlo estimate. The author uses a formula parameterized by spot, strike, maturity, volatility, interest rate, and a monitoring count, and reports that the…
The document explains how to calculate a portfolio’s logarithmic return from its value at two consecutive times. With fixed holdings represented by weights, first calculate the weighted sum of component prices at each time, then take the logarithm of the…
The document discusses why Fama–French work testing the CAPM may not cite Ross’s arbitrage pricing theory (APT) as its foundation. The answer distinguishes the frameworks: it characterizes Fama–French factors as added variables used to test whether the CAPM…
The document raises a practical concern about combinatorial purged cross-validation (CPCV) in financial backtesting. By combining separated time blocks into a training sample, the method can make observations on either side of a gap appear adjacent. That can…
The document reviews a Monte Carlo implementation for a payoff capped at an upper barrier and floored at a lower barrier at expiry. The accepted answer identifies errors in the simulation: each price update should multiply the current spot by the geometric…
The document works through the time-zero value of a claim in a one-period, two-state market. A portfolio holding the risky asset and a bond is chosen so that its terminal value matches the claim in both the up and down states. The hedge ratios are obtained…
The document asks why Laguerre polynomials are used as regression basis functions in Longstaff–Schwartz Monte Carlo pricing of American options. It cites discussion of multicollinearity among basis functions and a separate numerical comparison that found…
The document raises a preprocessing question: how to transform a time series with changing volatility before using it as a predictor in a regression model. The author reports trying several scaling methods without obtaining satisfactory stationarity, and…
The document derives the correlation between two stocks under a single-market-factor setup. Each stock’s return is decomposed into a market-driven component, scaled by its beta, and a residual component. Given the assumption that residual returns are…
The document discusses how financial pattern discovery can extend beyond traditional technical analysis. It distinguishes loosely defined chart patterns and indicator rules from approaches that state hypotheses mathematically and evaluate them with…
Antithetic sampling pairs each simulated random draw with a complementary draw, such as transforming a uniform probability by taking its complement. For normally distributed inputs, this produces paired values with equal and opposite standardized shocks.…
The document extends the Ornstein–Uhlenbeck process by allowing its mean-reversion level to vary over time. Applying an integrating factor gives a closed-form stochastic solution: the initial value decays exponentially, the drift function contributes through…