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 poses a pricing question for an American put on a non-dividend-paying stock. Its strike declines over time at the risk-free rate, and the stock is assumed to have constant volatility. This setup makes the contract different from a standard…
The document asks whether option implied volatility can reveal the probability that a stock will exceed a specified return threshold by a given expiry. It frames the question with an at-the-money option example and asks whether out-of-the-money options or…
The document explains why traders may consider calendar spreads when implied volatility is low. It emphasizes that option combinations should be understood through their Greeks. A calendar can combine positive vega exposure with negative gamma exposure, so a…
The document considers how to estimate portfolio risk when short call positions have only a brief pricing history, alongside bonds, currencies, and stocks. Its central recommendation is to model the risks that drive option values rather than extrapolating a…
The document asks why an option’s sensitivity to total variance includes a factor of time. It defines total variance as volatility squared times time and refers to a Black–Scholes option value expressed as a function of spot price, strike, and total…
The document presents an R implementation of a normal-innovation NGARCH(1,1) model intended for five-minute stock returns. The conditional variance updates from a constant, a lagged variance term, and a squared lagged standardized shock shifted by an…
The document distinguishes volatility inputs for option Greeks according to the purpose of the calculation. Implied volatility is recommended when estimating the Greeks reflected in current market option prices, which are the market-implied Greeks traders…
The document explains the effect of remaining time on option value through uncertainty in the underlying price at expiry. For at-the-money and out-of-the-money options, more time can increase value because a larger range of outcomes creates more opportunity…
This exchange clarifies why volatility estimated from past returns can be called conditional. In ARCH terminology, conditional variance is variance given information available from the process’s history. That history matters when volatility clusters: recent…
The discussion explains how the dynamics of instantaneous variance follow from a family of forward variance claims. Since instantaneous variance at time t equals the forward variance maturing at t, its change can be split into the change in a nearby forward…
The document considers whether to fit an options implied-volatility smile using delta or moneyness as the independent variable. Its answer points to research modeling volatility with a quadratic polynomial in both moneyness and maturity. This produces a…
The document compares option quote data with executed transactions as sources of information about implied volatility. Quotes show prices and volatility levels at which participants are willing to trade, including times when no opposing order arrives. Trades…
The document raises a practical problem in measuring historical volatility when an instrument’s prices fluctuate around zero and may be negative. Log returns are undefined for nonpositive prices, while simple percentage changes can become extremely large…
The document asks whether MATLAB’s `garchset` and `garchfit` interfaces allow dummy or explanatory variables in the conditional variance equation, analogous to regressors in the mean equation. It seeks a way to specify such a model, rather than only adding…
The discussion asks whether warrants carry higher implied volatility than comparable exchange-traded options, whether the difference can be exploited, and whether warrant volatility can help analyze structured products. The answers explain that an apparent…
The discussion presents four idealized ways an implied-volatility surface may respond when spot moves: sticky delta, sticky strike, sticky local volatility, and jumpy volatility. Each implies a different relationship between spot and implied volatility.…
The discussion examines how to interpret the effective window of an exponentially weighted moving average (EWMA), especially when the input uses two-day rather than daily returns. For an infinite geometric weighting scheme, a tolerance threshold and decay…
The document asks whether alternative component weighting schemes can improve a volatility index’s forecasts of realized volatility. The question describes a simple trade-weighted emerging-market index that was highly correlated with the VIX over a stated…
The document compares rolling and expanding estimation windows for GARCH volatility forecasts. A rolling window emphasizes recent observations, which may help when volatility shifts between regimes. An expanding window keeps the full history and may capture…
This brief exchange asks which volatility to use when pricing and hedging a European option, given conflicting daily and annual volatility figures. It mentions that Black–Scholes conventionally uses annualized volatility and asks whether a different measure…
The document asks why historical volatility is commonly estimated over a rolling window, such as a short run of daily observations, and then annualized. It contrasts this practice with annualized historical return, which the author understands as being…
The document asks how an option’s time decay relates to gamma, focusing on the gain from delta-hedged exposure to small underlying price moves. It describes the intuition that, when realized volatility matches the volatility implied in the option price, the…
The answer clarifies why option pricing models are often calibrated against a market implied-volatility surface that has a smile or skew, rather than against a flat surface. A correctly specified model's own volatility structure may be flat where its…
The answer presents an empirical framework for comparing realized volatility measures when the latent true volatility is unobservable. It recommends specifying data cleaning, sampling frequency, candidate measures, a volatility proxy, and ranking and…