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 discussion addresses volatility forecasting for financial stocks observed at five-minute intervals and notes that standard ARCH and GARCH approaches may not work as well at this frequency. One response reports that, in a thesis and related literature,…
The document separates three tasks that are easy to conflate when constructing an option volatility term structure. Implied volatility is inferred by finding the volatility input at which an option-pricing model, such as Black–Scholes, matches the traded…
The document asks how to derive the two risk-free rates used in VIX calculations from a table of Treasury yields when the near-term and next-term SPX option series expire on different days. It describes linear interpolation between the 30-day and 60-day…
The document asks which barrier options can have negative gamma after the questioner finds positive gamma in the knock-in and knock-out options they examined. One response gives a nearby example rather than a barrier structure: a digital call near its…
The note considers why volatility can show long memory and why its measured persistence may vary across periods. It describes an analysis of daily realized volatility for multiple assets, comparing autocorrelations before and after the global financial…
The document derives the probability that a zero-strike spread put finishes in the money. Its payoff is positive when the second asset’s terminal forward price exceeds the first asset’s. Assuming both forwards are lognormally distributed, their log-price…
The document examines Monte Carlo estimation of a European call’s delta under the Heston stochastic-volatility model. Its central correction is that the Malliavin weight should use the Brownian component driving the stock that is orthogonal to the…
The document proposes simulating equity prices under a constant elasticity of variance model, then pricing European and American options across strikes and maturities. It asks whether implied volatilities inferred from those prices would form the same…
The document asks whether pairs trading can be applied to related options or to an option and its underlying asset. The proposed idea is to trade a stationary linear combination over short horizons, where changes in delta and time decay may have less…
The document examines a multi-asset delta-hedging P&L decomposition and asks why a pricing function should satisfy a condition involving a positive break-even covariance matrix. Taylor expansion and delta hedging remove the first-order asset-price terms; the…
The document asks whether a Black-Scholes equation with an issuer credit spread is suitable for pricing an autocallable structured product, and how to examine its Delta, Vega, and hedge. The response advises against using Black-Scholes as the pricing model…
The document discusses which volatility convention to use when deriving forward volatilities from cap prices. Its central point is that the appropriate model depends on the currency and rate environment. For currencies such as EUR or CHF, negative rates and…
The document discusses the familiar claim that higher volatility raises the value of standard American calls and puts, and considers why a formal reference may be hard to find. The response suggests reasoning from the relationship between American and…
The document asks for a rigorous basis for a proposed decay-time relationship between diffusion volatility and the effect of lognormally sized Poisson jumps on the final return distribution. It focuses on a claim from a volatility text that relates the…
The document raises a comparison between a Fourier-based estimator of realized variance and covariance and the conventional sum of squared returns. The author applies the estimator to one day of ultra-high-frequency observations, samples the data at…
The document explains a simple way to estimate an option’s future value across a range of underlying prices for a platform-style P&L chart. The proposed baseline is to reprice with Black–Scholes using the remaining time to expiry and a chosen volatility,…
The question considers how a call’s value might change when stock returns have fatter tails than a log-normal model. It gives a numerical setup with zero interest rate, specified volatility and maturity, and an initial stock price equal to the strike. The…
This discussion explains how option quotes on a less liquid stock can reflect both the difficulty of hedging in the underlying and the flow of customer orders. Market makers account for hedge liquidity in their bid–ask spreads and implied volatility, so…
The document asks how selecting an iron condor’s short strikes by option delta relates to changes in implied volatility. The central question is whether choosing a target delta makes the spread width adjust as volatility changes, even though the distance…
The document considers the reciprocal of a stock price modeled by geometric Brownian motion (GBM). It gives the standard GBM solution and uses the moment-generating identity for a Gaussian variable to derive the reciprocal’s mean. For initial price S₀, drift…
The document examines whether a basic Kalman update can estimate both the evolving mean and the variability of a price series. It presents a recursive mean update using the Kalman gain, with a filtered state variance that shrinks when the gain is below one.…
The document asks which implied volatility surface should serve as the target when calibrating the leverage function in a stochastic-local volatility model. It describes a two-stage setup: first calibrate pure Heston parameters, then fit the leverage…
The document explains an apparent asymmetry in simulated currency prices generated from a GARCH model. The model is fitted to log returns, which may have a symmetric innovation distribution, but the simulation is transformed back into price levels by…
The document asks how quickly simulated asset paths converge under a Milstein discretization of the Heston stochastic volatility model. It gives the coupled stochastic differential equations for the asset price and variance, including mean reversion in…