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.
26 documents
The article introduces time series analysis as a statistical way to study sequential data modeled as outcomes of an underlying stochastic process. It highlights trends, seasonal patterns, and serial dependence, including volatility clustering, as features…
This article describes a directional S&P 500 strategy that refits a return model on a rolling window, forecasts the next day, and takes a long or short position according to the forecast sign. For each window, it selects an ARMA specification by Akaike…
This article relaxes the constant volatility assumption in Black–Scholes by allowing the asset's volatility to vary over time. It models log volatility with a mean reverting Ornstein–Uhlenbeck style equation driven by a stochastic process. To represent…
This article describes using a Gaussian Hidden Markov Model (HMM) as a risk filter for a simple S&P 500 trend-following strategy. The model is trained on historical SPY adjusted returns to identify latent volatility regimes. A QSTrader risk manager then…
The article lays out a progression for learning financial econometrics, starting with probability and statistics before moving through introductory econometrics, financial data analysis, specialist time-series texts, and current research. It highlights…
The document introduces geometric Brownian motion as a model for an asset price whose proportional changes have a constant drift and volatility. It outlines the derivation of the process solution using Itô's lemma: transform the price to its logarithm,…
This tutorial uses minute-level foreign exchange prices to build return series and calculate rolling realized volatility. It defines realized volatility from squared returns over a chosen interval and applies a rolling standard deviation to represent recent…
This article introduces conditional heteroskedasticity: periods of high return variance can cluster, even when a return series’ ordinary correlogram resembles white noise. ARCH models represent changing variance using past squared shocks, while GARCH models…
This mathematical introduction explains how stochastic differential equations extend ordinary calculus to processes driven by Brownian motion. It motivates the framework with asset prices: ordinary Brownian motion can take negative values, so a later…
The article explains how ARMA(p,q) combines autoregressive effects from past observations with moving-average effects from past shocks. It introduces BIC as a more severe penalty for model complexity than AIC, and the Ljung–Box test as a check of residual…
The document outlines a developing Python options library that combines analytical pricing with Monte Carlo simulation. Closed-form methods use the normal probability density and cumulative distribution functions to price vanilla calls and puts, calculate…
The article explains how discrete Asian options use sampled prices along an asset path to determine their payoff. It distinguishes arithmetic averaging from geometric averaging and models price paths with geometric Brownian motion. Monte Carlo pricing…
The document explains implied volatility as the volatility input that makes a model option price match an observed market price. It motivates volatility quotes as a way to compare options whose premiums are affected by different underlying prices, especially…
This article describes an object-oriented framework for generating synthetic asset-price paths using Geometric Brownian Motion (GBM) and a jump-diffusion process. A shared model interface accepts a starting price, time step, and externally supplied random…
This tutorial explains how to estimate the value of a down-and-out call using Monte Carlo simulation on a GPU. A simulated price path is invalidated if it crosses the lower barrier before expiry; absent a rebate, the payoff depends on the terminal price…
This article introduces Lévy processes as alternatives to geometric Brownian motion for modelling asset prices in derivative-pricing frameworks. Under the standard Black–Scholes assumption, log returns are normally distributed; the article argues that…
The document presents closed-form pricing for floating-strike European lookback calls and puts under Black–Scholes assumptions. A call’s payoff depends on the asset’s terminal value relative to its minimum over the option’s life; a put uses the maximum. The…
The article explains how adding instantaneous random jumps to geometric Brownian motion changes the assumptions behind Black–Scholes option pricing. Jump arrivals are modeled with a Poisson process, while jump sizes are treated as random and lognormally…
This article explains how to generate correlated standard-normal draws for simulating multiple asset paths. Its motivating application is the Heston stochastic-volatility model, where the asset and variance processes are driven by Brownian motions with a…
This article introduces strict stationarity and the Akaike information criterion (AIC) before explaining autoregressive models of order p. An AR model predicts a series from its own prior values and a white-noise term, extending the random-walk idea. For an…
The document introduces the MA(q) time-series model, in which each observation depends on a finite number of current and past white-noise shocks. It explains that the autocorrelation function should cut off beyond lag q, then illustrates model identification…
The document builds standard Brownian motion from a scaled sequence of random coin tosses. Scaling each step by the square root of its time interval keeps the walk’s quadratic variation finite as the number of steps grows. In the continuous-time limit, the…
The article demonstrates fitting Gaussian hidden Markov models (HMMs) to simulated returns and S&P 500 daily returns. In the simulation, bullish and bearish periods are generated with different means and variances; a two-state model is then fitted with…
The document explains how to solve for an option’s implied volatility using Newton-Raphson iteration. The target is the volatility at which a Black-Scholes call price matches an observed market price. Each iteration updates the volatility estimate using the…