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.
12,303 documents
The document compares ways to estimate value at risk for a call option. If historical prices for the option are available, an analyst can calculate returns over the chosen horizon and estimate VaR from a tail percentile. For a current option without a usable…
The discussion compares ways to fit implied volatility skew across strikes for a single option maturity. A quadratic polynomial is raised as a simple alternative to higher-order polynomial fits, but the responses focus on parametric distribution approaches…
The document explains how to convert annualized volatility into volatility over shorter horizons using the square root of time. It initially gives an incorrect monthly conversion for a VIX reading of 15; the accepted answer corrects it to about 4.33 percent…
The answer explains a route from stochastic future volatility to strike-dependent implied volatility. It writes a vanilla option value as an expectation over possible future realized volatilities, or equivalently as an average of Black–Scholes prices…
The document describes an attempt to fit a stochastic volatility model to five-minute volume-weighted average prices for the euro–US dollar market. It outlines parameters for the long-run volatility level, persistence, current latent volatility, and…
The document asks why model-free implied volatility measures such as VIX are offered for major equity indices and only a small number of individual stocks. The accepted response adds that similar indices also exist for gold, silver, and oil, showing that the…
The document poses an apparent contradiction in the Black–Scholes model. As volatility rises without bound, the probability that a geometric Brownian motion finishes above the strike tends toward zero, which seems to imply a worthless call. Yet the…
The document examines an FX option whose payoff is settled in the currency of the underlying rather than the usual domestic currency. It first sketches a Black–Scholes setup for an exchange rate, then changes the payoff through the currency conversion and…
The discussion compares at-the-money payer swaptions with different expiry and underlying swap terms: one-year expiry on a ten-year swap and ten-year expiry on a one-year swap. It explains that expiry affects option value through volatility accumulated over…
The discussion explains why constant volatility appears in market-making models and how volatility differs from the risk that incoming trades carry adverse information. Volatility estimates the risk that an inventory position will lose value as prices move;…
The document discusses the two-dimensional term structure of lognormal implied volatility for European swaptions, varying by option expiration and underlying swap tenor. It describes a typical pattern in which volatility may rise over the shortest…
The note explains how to translate option sensitivities into approximate dollar gains or losses for specified changes in the underlying price and implied volatility. It defines delta and vega as changes in option value for unit changes in their respective…
The document distinguishes constant-volatility geometric Brownian motion from a model in which returns have time-varying conditional volatility. It explains that a GARCH model is fitted to historical returns, typically by estimating its parameters, and then…
The document derives the distribution of the time integral of a deterministic function multiplied by a Brownian motion. It uses integration by parts to rewrite the integral in terms of the Brownian value at the horizon and a stochastic integral whose…
The note explains the theoretical replication of a variance swap using out-of-the-money options across strikes. Its fair variance is expressed as an integral of put prices below the forward and call prices above it, weighted inversely by squared strike.…
The document discusses why American options on illiquid underlyings are difficult to price: when the underlying share value is poorly known, option valuation is correspondingly uncertain. One answer recommends scenario-based risk and reward analysis, similar…
The document explains that a basic geometric Brownian motion assumes constant drift and volatility, so company fundamentals are not directly represented. To include fundamental information, an analyst would need a separate model translating it into…
The document describes how a swaption trader can move from an at-the-money implied volatility surface to prices for options struck away from the money. The answer says that desk models commonly add parameters for the volatility smile and skew: these capture…
The document asks whether a LIBOR rate can be modeled like a stock price with geometric Brownian motion, then outlines concerns with that choice. One response argues that interest rates tend to exhibit stationarity, whereas Brownian motion does not, so the…
The document raises a conceptual question about combining seasonal ARIMA and GARCH models for time-series forecasting. It distinguishes the familiar SARIMA prediction of future series values from a GARCH forecast, which the author understands as producing…
The document asks whether volatility measures calculated from intraday price data can help predict close-to-close squared returns. The intended use is estimating the profit and loss of a gamma scalping strategy that trades once daily, with trading assumed to…
The document shows how to establish that two weighted combinations of log prices from correlated stochastic processes are uncorrelated. It starts with correlated geometric Brownian motions, takes logarithms, and forms a sum and difference using the assets’…
The document discusses implementing a finite difference pricing model for equity index options using local volatility derived from a fitted SVI volatility surface. The question is how to align the surface’s log-forward-moneyness coordinate with the pricing…
In a GARCH model, returns are represented as conditional volatility multiplied by an innovation. The document explains that the innovation is standardized to have zero mean and unit variance, even when its underlying distribution is non-normal. This…