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 concerns noisy, incomplete one-minute price and volume data for several stocks, with the goal of forecasting volatility for the month after the sample ends and investigating whether volatility is related to liquidity. The response recommends an…
The document distinguishes implied volatility from historical volatility. Implied volatility is the volatility parameter that makes an option pricing model reproduce the market price of an option; it is inferred from current prices rather than calculated…
The explanation links negative correlation between an asset’s spot price and its instantaneous volatility to a downward implied-volatility skew. It contrasts the result with the standard Black–Scholes assumption of constant volatility, under which…
The document presents several uses of the term microstructure noise. In high-frequency econometrics, it can mean disturbances that make estimates such as realized volatility unstable. In market microstructure, it can refer to observed price deviations from…
The document recommends a practical scenario approach for pricing down-and-in puts when vanilla option prices and implied volatilities are available. Apply a spot shift and test a small set of implied volatility shifts, using the existing volatility surface…
The document discusses estimating a Heston stochastic volatility model with an Unscented Kalman Filter. The response recommends expressing the system in log prices or returns rather than raw prices, then discretizing the price and variance dynamics as a…
The document considers how to price options with maturities as long as several decades when market quotes for those maturities are unavailable or illiquid. It raises three possible inputs: calibrating to the liquid portion of the volatility surface, using…
The document asks why derivatives traders use stochastic-volatility models when pricing and hedging products such as digital options. It frames the issue through approximate static replication: a digital payoff can be approximated with a narrow put spread,…
The discussion explains how Fourier transforms and characteristic functions can price European options when the underlying log-price density is difficult to obtain directly. It starts from the discounted expected payoff, expresses that expectation as an…
The document asks whether persistent realized volatility reflects slowly changing latent volatility or whether observed volatility shocks cause future latent volatility to rise. It presents the latter as closer to the usual market consensus, then describes…
The document asks how to model stock returns whose estimated left and right tail exponents differ, noting that a skewed Student-t distribution uses a shared tail exponent. It describes an analysis of daily prices for 250 stocks beginning in 1972, with tail…
The document uses a delta-hedged option approximation to estimate the underlying price move needed to offset one day of time decay. Setting the approximate gamma gain equal to theta decay gives a break-even move proportional to the square root of twice the…
The document challenges the claim that demand is generally greater for out-of-the-money and in-the-money options than for at-the-money options. The responses distinguish trading volume from volatility-smile explanations: near-the-money options are described…
The document examines whether gross exposure divided by capital is a useful definition of portfolio leverage. It points out that this measure omits cash and can overstate risk when offsetting holdings are highly correlated, then derives a risk-based…
The document examines a common first-order approximation for the premium of an FX risk reversal: multiply at-the-money option vega by the risk reversal in volatility points. It explains that the approximation should compare the market-priced call and put…
The document considers how to infer a second asset’s covariance structure from that of a first asset and a relationship between their returns. One answer models the second asset’s return as a constant beta times the first asset’s return plus a small…
The document considers whether ordinary least squares can estimate the parameters of a GARCH model, which are commonly fitted using quasi-maximum likelihood. It summarizes a reference describing explicit OLS estimation for ARCH models through an…
The document explains why barrier-option Greeks cannot be represented by one general curve. Their shapes depend on spot, strike, barrier placement, volatility, and time to expiry. In a knock-out call, a rising spot can increase the call’s payoff potential…
The document shows how to estimate the real-world probability that a stock will finish within a specified price interval using a geometric Brownian motion model. It treats the stated required annual return as the drift and, for illustration, uses implied…
Vega and gamma often have the same sign for a single option under standard assumptions, but a calendar spread can produce opposite exposures. The example pairs a long near-dated at-the-money option with a short longer-dated at-the-money option, yielding long…
The document considers pricing a European option when the underlying asset’s daily return is constrained to a fixed interval. It proposes replacing the usual return density with a two-sided truncated normal risk-neutral density, then valuing the option by…
This question asks how SABR is used in practical option workflows. It contrasts fitting or interpolating a volatility surface with SABR to obtain Black implied volatilities, then managing positions with Black Greeks, against measuring and managing risk…
This troubleshooting note concerns an error raised by the rugarch package while running a rolling GARCH forecast with ugarchroll. The reported setup estimates an sGARCH model with an ARMA mean specification, then forecasts one step ahead over a rolling…
The document asks for a more accessible derivation of the semi-closed-form price of a European call under the Heston stochastic-volatility model. It does not derive the pricing formula itself; instead, the replies point readers toward a paper with a…