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 distinguishes two meanings of volatility in bond option analysis. Price volatility can mean implied volatility from a Black-style option pricing model using the bond price as the underlying. Yield volatility instead treats bond yield as the…
The document asks how to price a quanto option when both the underlying asset and the exchange rate follow calibrated Heston stochastic-volatility models. It specifically questions how to use a constant-volatility quanto formula when volatility varies over…
The note asks why an out-of-the-money natural gas call can have a larger absolute delta than a put whose strike is at a similar percentage distance from the underlying, even though the put has higher implied volatility. It gives example quotes and reports an…
The document asks how to fit a seasonal ARIMA model with GARCH errors in R. It notes that the rugarch specification shown supports an ARMA mean with a GARCH variance model, but does not directly provide the requested SARIMA-GARCH combination. The suggested…
The document poses a two-day value-at-risk problem for a long position whose returns follow an autoregressive conditional heteroskedastic model. The conditional variance depends on the previous shock, while the return also depends on the previous return. The…
The document considers whether a market-timing model can identify both favorable regimes and conditions where its forecasts should be distrusted. It suggests that variables with weak direct forecasting power may still help distinguish regimes, using VIX as…
The document asks where to obtain historical implied volatility rank or percentile data for US equities. The questioner distinguishes those measures from an options data feed that provides implied volatility alongside historical realized volatility, and…
The document asks how to estimate the CEV model’s parameters, which determine the scale and price dependence of stock volatility, for simulations of CPPI and OBPI portfolio strategies. The answer recommends calibrating the model to vanilla equity or index…
The discussion compares position sizing in proportion to inverse volatility with sizing in proportion to inverse variance. In a simple portfolio of normally distributed assets, inverse volatility sizing is associated with risk parity: it treats assets as…
The document presents an attempt to forecast VIX using a constant-mean GARCH(1,1) model fitted to daily log changes in the VIX. It shows a historical sample, a training cutoff, a multi-step forecast, and forecasted conditional variances across dates and…
The document introduces the skew stickiness ratio (SSR) as a way to describe how at-the-money-forward implied volatility responds when the underlying asset moves. It uses this measure to distinguish two common smile-dynamics assumptions. Under sticky strike,…
The document surveys ways to estimate how an option’s implied volatility may respond to a hypothetical market move, with portfolio risk simulation as the motivation. It describes modeling the joint behavior of forward at-the-money volatility and the first…
The document reviews an R workflow for fitting an ARMA mean and a GARCH(1,1) volatility model with a skewed Student distribution, then calculating value at risk for two return series. Its response clarifies that the quantile of fitted model results…
The document asks how to extend a concave shape in bid implied volatility data to strikes beyond those observed. It also asks whether bid volatility should approach zero as the strike approaches zero or infinity. These are posed as questions; the document…
The document considers how to classify mutual funds into low, medium, and high volatility groups without choosing fixed volatility thresholds in advance. The answer proposes unsupervised clustering with k-means: provide the funds’ volatility measurements and…
The document examines a proposed strategy that combines a three-times inverse equity ETF with the underlying index to create a nominally hedged position. The questioner argues that, assuming zero volatility, the inverse fund’s interest-rate-related growth…
The document examines a SABR calibration on Ethereum option data where the fitted alpha parameter changes substantially when strikes and the forward are expressed at a different scale, even though the implied volatilities are unchanged. The questioner…
The document clarifies how to approach an implicit finite-difference exercise for a European call when volatility varies over time. The stated example uses a linear volatility function, while the exercise also provides a Black–Scholes approximation that…
The document explains the Carr–Madan formula as a way to represent a sufficiently smooth payoff as a linear position in the underlying, a cash amount, and integrals of European put and call payoffs across strikes. The decomposition expands the payoff around…
The document discusses extracting implied volatility from American option prices using a Cox–Ross–Rubinstein binomial tree. The tree prices the option by working backward from terminal payoffs, comparing continuation value with early exercise value at each…
The document presents two parametric ways to describe equity implied volatility across strikes and maturities. One uses ATM forward volatility plus linear skew and quadratic curvature on a log-moneyness scale normalized by volatility and the square root of…
The document shows how to solve a stochastic differential equation whose process has zero drift and a time-varying adapted volatility coefficient. It applies Itô's lemma to the logarithm of the process, turning the multiplicative equation into an additive…
The document asks whether vanilla options on two assets, together with the assets themselves, can create insurance that costs money when correlation is high and pays when correlation falls. The motivation is to hedge a strategy that benefits from the assets…
The document raises a methodology question about selecting near- and next-term options when calculating intraday CBOE VIX values under the post-2014 maturity rules. It describes the eligible terms as more than 23 and fewer than 37 days to expiration. As time…