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 note examines a MATLAB implementation of the log-likelihood for a GARCH model whose standardized innovations follow Hansen’s skew-t distribution. It asks whether a normalization parameter should be square-rooted and why the likelihood includes a term…
The document raises a practical issue in constructing an implied volatility curve for ETF options during high-frequency intraday trading. Its premise is that option quotes may update faster than the ETF cash price, so calculating implied volatility from the…
The document considers whether recent historical bond-price volatility is suitable as the volatility input for pricing a bond option with the Black 76 model. The preferred input, when available, is implied volatility: the value that reproduces the option’s…
For sparse, illiquid index option chains, the response recommends cleaning and fitting prices or total variance rather than removing implied-volatility outliers and interpolating the remaining points. In option-price space, useful restrictions are clearer:…
The document presents a replication problem involving the conversion of an implied volatility surface into a local volatility surface using Dupire’s formula. The author builds a smooth implied surface by parameterizing total implied variance against time and…
The document describes how option pricing is used in practice, emphasizing that model choice depends on the contract and market. It notes that standard Black-Scholes-Merton pricing can be sufficient for European-style listed index options, while…
The document asks whether an option model can represent volatility as a deterministic function of strike alone. It distinguishes this idea from local volatility, which the author understands as deriving a volatility surface from market prices with dependence…
The document reviews a commonly cited set of empirical regularities in asset returns, including heavy tails, volatility clustering, slow decay in the autocorrelation of absolute returns, leverage effects, and relationships between volume and volatility. It…
The document describes a problem generating Monte Carlo paths from a QuantLib Black variance surface. The surface is interpolated and extrapolated from market data, with checks for decreasing total variance across maturities and butterfly irregularities, yet…
The discussion considers estimating implied volatility at each intraday option tick when end-of-day implied volatility and Greeks are available alongside tick-level option and underlying prices. One shortcut estimates volatility changes from option price…
The document raises a modeling question about computing option theta from the Black-Scholes partial differential equation when market implied volatility varies across strikes. It compares three approaches: standard Black-Scholes Greeks with implied…
The discussion explains three common criticisms of the Heston stochastic volatility model: limited flexibility when fitting observed option volatility surfaces, unusual behavior in its forward volatility skews, and limited usefulness for some exotic pricing…
Brownian motion with drift, X_t = μt + σW_t, is normally distributed with mean μt and variance σ²t. Exponentiating a normally distributed variable gives a lognormal distribution, so the stated exponential process has lognormal levels; its logarithm has mean…
The document asks whether American option prices must increase with volatility whenever European option prices do, and seeks intuition for proving the result in more general models. The answer states that a standard American option under Black–Scholes is…
The document presents a European call pricing comparison under the Heston stochastic volatility model. It gives a characteristic-function integral for the closed-form price and a Milstein-style discretization for simulating variance and log spot, then…
The document considers how to estimate annualized daily volatility from portfolio balances recorded after trades at uneven intervals. It presents a simple estimator under a zero-drift Wiener model: square each log return, divide by the elapsed time between…
The document raises a model-calibration question: whether parameters in the Heston–Nandi GARCH option-pricing model can be estimated by fitting model prices to observed option prices instead of using maximum likelihood. The proposed approach is to choose a…
The document compares using historical index returns directly in Monte Carlo option pricing with fitting a return distribution or a dynamic stochastic-volatility model. Its central pricing point is that option values are expectations under a risk-neutral…
A Lévy process is characterized by a drift vector, a diffusion matrix, and a Lévy measure, which together describe its continuous variation and jumps. The document distinguishes finite-dimensional estimation of drift and diffusion parameters from the…
The discussion explains why the magnitude of a short-interval return can serve as a rough estimate of volatility over that interval. Under a diffusion model for proportional price changes, the return contains both drift and a random shock. At daily…
This discussion considers how a shift from a currency peg toward a freer float could affect over-the-counter FX option prices, using the Moroccan dirham’s EUR and USD relationships as context. It notes that a regime change may bring a spot jump together with…
The question asks why a butterfly spread’s value might be expressed using the probability that the terminal asset price falls between the outer strikes, multiplied by half the spacing between adjacent strikes. The answer frames pricing under the risk-neutral…
The document distinguishes GARCH forecasts from realized volatility (RV) measures. GARCH models use discrete observations, commonly squared returns, to estimate conditional variance and forecast volatility. RV instead aggregates high-frequency observations…
The document discusses using ARCH or GARCH models to describe time-varying volatility in a financial series, prompted by a researcher studying copper prices. These models relate current conditional variance to past observations or shocks. The proposed…