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 asks whether factor volatilities in the multi-factor Heath–Jarrow–Morton framework may be negative. It notes that the drift expression uses products of volatility functions, then reports a reference that explicitly assumes these functions are…
The document considers how to track changing dependence between two time series when a changing regression slope may reflect shifting variances rather than a stronger relationship. It raises similar interpretive concerns about time-varying quantile…
The document asks how to price structured products that depend on three-month EURIBOR, including constant-maturity swap spreads, range accruals, and target redemption notes, when discounting uses €STR. It proposes modeling the €STR short rate with a…
The document explains why the Black–Scholes delta hedge can have gains or losses when volatility changes, despite the model’s claim of a riskless hedge. The key distinction is that the theoretical result assumes geometric Brownian motion and continuous…
The document addresses which implied volatility to use when converting a quoted option delta into a strike. Its guidance is to use the volatility associated with that particular delta, together with the other inputs required by the option-pricing…
The document explains the intuition behind buying an option when its implied volatility appears lower than a forecast of realized volatility. A long option position has positive gamma: as the underlying rises, its delta increases and a trader can sell some…
The document asks what parameter restrictions apply when estimating EGARCH and GJR-GARCH volatility models, contrasting them with the familiar positivity and stationarity conditions for standard GARCH. It presents the two asymmetric model specifications but…
Financial prices often behave as nonstationary series: their statistical properties can depend on the price level and past observations. Returns, calculated as percentage changes or differences in log prices, are more often treated as stationary. That makes…
The document distinguishes implied-volatility skew across option strikes from skewness in the underlying asset’s return distribution. It presents model-free implied skewness as a measure connected to realized skewness, and describes research finding a…
The response suggests comparing a volatility forecast from a non-normal GARCH model with the volatility implied by option prices. If the options appear inexpensive relative to the forecast, the proposed position is to buy calls and puts; if the implied…
The document discusses how market participants price American options on Eurodollar futures and when a European-option approximation may be adequate. It contrasts tree-based models that represent early exercise with the simpler European treatment often used…
The discussion explains why equity volatility and credit default swap spreads may move together, focusing on structural models of a firm’s capital structure. In the basic Merton framework, equity behaves like a call option on firm assets, with debt repayment…
This exchange addresses how to retrieve the long-run variance component from a component GARCH model fitted with the rugarch package in R. The questioner can obtain conditional volatility with the package’s standard accessor but needs the time-varying…
The note explains why hedging skew exposure in a forward-starting option differs from hedging an ordinary option. A forward-starting put may be analytically short skew, yet during the forward period its strike resets in proportion to the underlying price.…
The note explains why stock price models often require the volatility process to be square integrable so that its stochastic integral with Brownian motion is well defined in the standard Itô framework. It distinguishes the condition that the expected…
The document compares three representations of option market information: implied volatility by strike and maturity, raw call or put premiums, and the risk-neutral return distribution. It argues that these are equivalent views of the same information and can…
The document asks how to select the mean-reversion parameter in a one-factor Hull–White model when pricing Bermudan swaptions. It describes a calibration approach based on the ratio of standard deviations of two forward rates with a shared expiry and…
The document distinguishes the average return conditional on a loss from the unconditional contribution of losses to expected return. For a zero-mean normal return with volatility parameter sigma, it identifies the requested conditional quantity as the…
The document derives the distribution of a scalar geometric Brownian motion when its drift and volatility are deterministic functions of time. Applying Itô’s lemma to the logarithm converts the process into an integral of a deterministic drift term and a…
The document maps views about forecast return distributions to simple option positions. A belief that expected returns are understated or overstated is associated with buying a call or put, respectively. Views on dispersion are paired with long or short…
The document studies a payoff that delivers the stock’s terminal price only when its return relative to an index clears a threshold. It first sketches Monte Carlo simulation using geometric Brownian motion, then gives a risk-neutral derivation. The…
The document explains how QuantLib’s BlackVarianceCurve distributes variance through time according to its day-count convention. Because the curve interpolates linearly in variance, using Business/252 produces a constant variance increment per business day…
The document discusses using SABR to price EUR inflation caplets when strikes can be negative, a setting where standard Black and unshifted SABR formulations are not directly applicable. One response recommends reconsidering the model: inflation option…
The document asks whether option prices can reveal a likely rise followed by a later decline in a security. The answer explains that a sufficiently broad set of European option strikes for two expirations can be used to infer a risk-neutral price…