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
This discussion examines the commonly used SABR at-the-money volatility approximation that keeps only the leading term, alpha divided by the forward price raised to one minus beta. The fuller Hagan expression includes correction terms involving expiry, the…
The document asks whether extensions to the SABR stochastic-volatility model, often motivated by rates that can become negative, offer benefits for options on non-negative underlyings such as equities and foreign exchange. The response argues against using…
The note asks how to size option positions so a strategy reaches a chosen long-run daily volatility. It considers strangles and risk reversals, and compares sizing from the historical P&L volatility of one unit, from implied-volatility and vega estimates, or…
The note clarifies what volatility implied by VIX options represents. VIX itself reflects an estimate of S&P 500 volatility over a forward 30-day period, but a VIX option does not simply measure the future volatility of today’s spot VIX. VIX options expire…
The document raises research design questions for comparing two sentiment datasets as predictors of volatility. It considers whether to include both GARCH and HAR models to broaden the analysis, and how to use sentiment measured continuously when the HAR…
The document clarifies that implied volatility is a Black–Scholes-equivalent volatility inferred from a European vanilla option price for a given strike and maturity. A smile implied by a different pricing model is constructed in two steps: fix that model’s…
The document examines a stock model with continuous Black–Scholes movement and a jump at a specified time, restricted initially to two possible proportional jump sizes. It asks whether option prices can reveal the probabilities of those jump outcomes and…
The document presents an attempted out-of-sample volatility forecast for a stock using a GARCH model fitted to percentage returns. It forecasts across a multi-day horizon and compares the output with annualized rolling standard deviation calculated from…
The document describes a route from a commodity’s historically observed return distribution to an implied volatility smile. Rather than relying on a Cornish–Fisher expansion, the accepted answer proposes fitting a distribution to returns over the option’s…
The document presents a SABR calibration problem in which an optimizer minimizes the difference between model and market volatilities across many strikes. The data are converted before fitting, and a differential evolution routine searches within parameter…
The document clarifies that increasing option maturity means moving toward longer time to expiry. It explains how a volatility surface table can show a flatter implied-volatility smile at longer maturities: the relevant comparison is the wings' implied…
The document discusses model features that can better represent equity-market behavior than a basic constant-volatility diffusion. It proposes a flexible stochastic-volatility framework in which log prices follow Brownian motion, volatility varies over time…
The document explains how to calculate sample variance from consecutive close-to-close log returns while accounting for their estimated drift. The question begins with a sum of squared log returns and asks how the drift adjustment appears in an alternative…
The document presents a dual digital option whose payoff depends on two foreign exchange rates crossing specified thresholds at maturity. Because the payoff requires both conditions to hold, its value is sensitive to the correlation between the rates. The…
The document describes calibrating a geometric Brownian motion model from daily prices. It gives formulas for estimating diffusion from the variance of daily returns and drift from their mean, adjusted by half the estimated variance. The questioner then asks…
The document asks whether multiple risk estimators can be considered together, including whether their divergence might be summarized with a ratio or whether their correlation makes this redundant. The response suggests using GARCH and Value-at-Risk (VaR) in…
The discussion considers why Monte Carlo estimates of a call price under the SABR stochastic volatility model may disagree with prices obtained using the commonly cited SABR implied volatility formula. One answer points to discretization bias: a basic Euler…
The document examines proposed ways to adjust option vega for time to expiry and asks whether such adjustments can be justified by dividing vega by the square root of time. It explains that ordinary vega is already a meaningful sensitivity for a particular…
The document distinguishes an option’s implied volatility (IV) from its vega. IV is an input to an option pricing model, while vega measures how much the modeled option price changes when IV changes. A larger vega for one option therefore does not show that…
The document raises the practical problem of calibrating local-stochastic volatility models when an FX volatility surface has only a few quoted strikes per maturity. It notes that standard FX quotes may be expressed through at-the-money straddles and…
The document asks how to obtain a binary option value from the change in call prices across nearby strikes. With implied volatility held constant, the limiting price difference corresponds to the negative strike derivative of the call price, which is the…
The document asks how to build a consistent historical swaption volatility series when market conventions change. It distinguishes normal from Black volatility and quotes referencing IBOR or OIS discount curves, and asks whether backtests should use only…
The document explains how a risk-neutral probability density for the underlying at expiration can be recovered from the second strike derivative of call prices, under a constant interest-rate assumption. Once recovered, the density can be integrated against…
The document concerns fitting a Libor Market Model volatility function to market observations by minimizing a nonlinear least-squares objective over five parameters. The calibration has positivity conditions, including a combined constraint on two…