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 shows how to plot fitted conditional volatility together with forecasts from a GARCH(1,1) model in R. Its example uses the fGarch package to specify and simulate a normally distributed GARCH process, fit the model, and predict future conditional…
The document explains how volatility inputs differ when an option expires before its underlying commodity forward settles. It distinguishes options on different forward contracts: a quote for a two-month option on a two-month contract should not…
The document explains why the time decay of a European call differs by time to maturity and moneyness in the Black–Scholes model. With substantial time remaining, the passage of a day generally changes exercise likelihood only modestly, so theta is…
The document asks why the instantaneous volatility of a simply compounded forward rate is defined through the quadratic variation of its logarithm rather than the rate itself. The response interprets this as percentage volatility: changes in the log of a…
The response proposes using programming and financial data skills to study market risk through equity index options. It describes an approach associated with Ian Martin: use prices from a small portfolio of European options on the S&P 500 to infer the…
The document explains why the Heston pricing framework includes a market price of volatility risk and how it relates to Monte Carlo simulation. The stock and variance processes have two Brownian drivers but only one traded risky asset, so the no-arbitrage…
The document asks for a rigorous interpretation of the functional derivative terms in Bergomi’s pricing equation for a European claim. The price is viewed as depending on spot and a family of stochastic processes indexed by future times, which raises…
The document explains why a binary call and a standard European call with matching contract inputs do not have the same delta. A vanilla call has a payoff that rises continuously with the underlying above its strike, while a cash-or-nothing binary pays a…
The document collects learning resources for someone starting with volatility modeling, especially local volatility and surface calibration. It points to a practitioner book and lectures, a thesis focused on calibrating a local volatility surface, and a…
The document considers whether varying the autocall level of an autocallable bond can reproduce the value of an issuer-callable bond priced with an optimal exercise policy. It explains that the issuer-callable bond is no more valuable than an autocallable…
The document explains the leverage effect by separating a company’s enterprise value from its financing. In a simple example, a business owns a gold asset and has fixed nominal debt. As the asset value changes, the debt claim stays fixed while the residual…
The document clarifies a proposed volatility adjusted moving average crossover for fixed income momentum. A shorter moving average of an index represents a more recent price level, while a longer moving average represents a smoothed longer term level. Their…
The document explains how to extend a Heston stochastic volatility option model with jumps in the underlying asset. It recommends first considering a jump diffusion such as Merton’s model, which uses lognormally distributed jump sizes, or Kou’s model, which…
The document asks how models can use the full open, high, low, and close record instead of relying only on closing prices. It explains that the high–low range contains information about variation within an interval and may help estimate volatility, including…
The document diagnoses a mismatch between a European option’s net present value and the model value reported by a QuantLib Heston calibration helper. The example calibrates a Heston model to implied volatilities and then prices a put with what appear to be…
The document explains an arbitrage argument linking Black–Scholes option values to total variance, expressed as volatility squared times time to expiration. For otherwise comparable options, the Black–Scholes price rises with this input. If total variance…
The document considers how to calibrate the Heston stochastic-volatility model and narrows its response to calibration from time series. Because volatility is latent, that task can be framed as nonlinear filtering. The answer points to research methods and…
The document asks for intuition behind a forward variance stochastic differential equation used in rough volatility research. The displayed dynamics depend on the forward variance level, a volatility parameter, the Hurst parameter, the time to the forward…
The document investigates why a SABR calibration using Bloomberg cap volatility figures produces a poor match across strikes. The question provides an example with caplet-related strikes and volatilities, estimates a forward from interest-rate curve inputs,…
The document describes a proposed volatility forecasting exercise using ARCH, GARCH, and EGARCH models on daily returns for two stocks. The author divides the observations into a training portion and a later testing portion, estimates model parameters on the…
This note explains why Black–Scholes vega can look large when volatility is entered as a decimal. Vega measures the option price’s sensitivity to a one-unit change in volatility, equivalent to a 100 percentage point move. The quoted S&P 500 example has vega…
The document challenges a proposed expression that would price a down-and-out call as a scaled European call with the same initial asset price, strike, volatility, rate, and expiry. The response explains that a barrier option cannot generally be represented…
The document discusses time variables used in Haug’s presentation of the Turnbull-Wakeman approximation for arithmetic-average rate options. It identifies the option’s remaining time to maturity, the original averaging-period length, the time elapsed since…
The document describes an effort to calibrate a simple stochastic volatility model with the Efficient Method of Moments (EMM), as a step toward calibrating Heston parameters from historical equity returns. The author reproduces a SAS example in Python,…