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 explains why the intercept in a standard GARCH(1,1) conditional variance equation is usually constrained to be strictly positive, even when the lagged squared return and lagged variance terms are nonnegative. The accepted answer distinguishes…
The document asks how to express time-sensitive inputs when using a closed-form option pricing approximation, specifically the Bjerksund–Stensland model. The question lists the risk-free rate, volatility, time to expiration, and cost of carry, and asks…
The document describes a workflow for pricing interest-rate caps at multiple valuation dates with QuantLib. It builds yield curves from dated market data, interpolates cap volatilities across maturities, then creates Euribor-linked cap instruments and prices…
The document develops a definition of realized gamma from the second-order term in an option’s price change. It defines gamma dollars as one half of spot squared times option gamma, then uses the diffusion component of spot’s change to show that the option’s…
The document examines whether non-Gaussian stock returns can be transformed into a Gaussian series. It warns that forcing observations to match a normal quantile distribution can produce a normal-looking sample while distorting the data and removing…
The document explores an empirical approach to estimating fair implied volatilities for SPX options. It proposes using a proxy for future volatility, such as VIX, to select similar historical observations, fitting a distribution to those observations, and…
The document explains why applying Itô’s lemma to a function of a diffusion requires a second-order term. For a process with drift and Brownian volatility, a Taylor expansion includes the squared process increment. Ordinary time increments have negligible…
The document explains how to turn a Dupire local volatility model into a European option price. Its example starts with an implied volatility surface, constructs a Black–Scholes–Merton process that uses the surface, and sets up a vanilla call. It then…
The document considers how to derive a pricing PDE for a derivative under the Heston–Hull–White model, where the stock, stochastic variance, and short rate are correlated. It identifies a problem with applying the usual discounting transformation directly:…
The document examines how to calculate vega sensitivity under the Basel Fundamental Review of the Trading Book standardized approach. The question contrasts multiplying Black–Scholes vega by implied volatility expressed as a decimal with an example using a…
The document discusses two interest-rate products that pay based on absolute changes in future rate volatility. One references successive six-month LIBOR changes; the other references changes in a long-dated forward-start swap rate and includes capital…
The document raises a preprocessing question: how to transform a time series with changing volatility before using it as a predictor in a regression model. The author reports trying several scaling methods without obtaining satisfactory stationarity, and…
The document asks how to implement Rebonato’s approximation for swaption volatility in C++. The formula combines swap weights, forward rates, correlations, and the integrated products of forward-rate volatilities. With piecewise-constant volatilities, each…
The document extends the Ornstein–Uhlenbeck process by allowing its mean-reversion level to vary over time. Applying an integrating factor gives a closed-form stochastic solution: the initial value decays exponentially, the drift function contributes through…
The discussion asks whether a binary option always has a Black–Scholes implied volatility and presents several competing answers. A binary call price can rise and then fall as volatility increases, so an observed price may correspond to two volatility…
The document asks how to sample a Wiener process with specified starting and ending values as well as a prescribed maximum and minimum, extending the usual Brownian bridge setup. A response outlines an approximate construction for a fixed maximum: simulate a…
The document examines valuing a corridor variance swap partway through its life, when realized variance is known for the elapsed period but future variance remains uncertain. It explains that a standard variance swap can be replicated in theory by weighting…
The discussion examines what “vega” should mean when an exotic option is priced with a model beyond Black–Scholes. It raises several possible bump conventions: shifting local volatility, changing stochastic volatility parameters, or bumping an implied…
The document reviews evidence on whether high-frequency trading changes market quality in ordinary conditions and during stress. It points to research concluding that greater low-latency activity improves short-term volatility, spreads, and displayed…
The document raises a modeling question about applying the heterogeneous autoregressive realized volatility model to forecast one-minute realized volatility in an active Bitcoin market. The proposed regressors are realized volatility measured over recent…
The question asks why residuals from a GARCH model might appear less Gaussian than raw returns, despite the expectation that volatility adjustment should remove some non-normality. The answer argues that seeing this outcome challenges the assumed model, then…
The document discusses how traders construct implied-volatility smiles and surfaces from option quotes. Its central guidance is to use liquid market instruments across strikes rather than building a curve from calls alone or puts alone. For many European…
The document considers whether combining a strategy with 20% annualized volatility and one with 15% volatility, when their returns have zero correlation, can produce a portfolio with volatility below 15%. The accepted response uses the portfolio variance…
The document asks what calibration of an option volatility surface means, how often it should occur, and what determines its timing. It starts from the familiar implied volatility smile for one expiry and asks whether a spline with anchor points can…