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
This discussion explains why the constant-volatility assumption in Black-Scholes can be restrictive and outlines broader ways to extend the model. Stochastic-volatility models make volatility vary over time, with model dynamics linked to quantities such as…
This exchange discusses whether Stata can estimate a BEKK-GARCH model and clarifies when that model is appropriate. One answer says it is not aware of a Stata implementation and points to R software that can fit a BEKK(1,1) model, while noting that…
The document raises a question about very negative AUDJPY market strangle volatility quotes at long maturities. It gives examples for 25-delta and 10-delta strangles, alongside an at-the-money-forward volatility level, and asks whether the resulting concave…
The document addresses an apparent tension between the stationarity assumptions used in GARCH models and their purpose of modeling changing volatility. Its answer distinguishes unconditional stationarity from conditional volatility: a stationary process can…
The document asks whether Novikov’s condition holds for a proposed Girsanov kernel in the Heston model. The stock’s market price of risk leads to an exponential-integrability requirement involving the time integral of the reciprocal variance. The variance…
The note describes several reasons to trade a risk reversal, which combines a put and a call to express a view on implied-volatility skew. A delta-hedged risk reversal can be viewed as a wager on realized spot–volatility covariance relative to the covariance…
The document proposes extending the Heston stochastic volatility model by making its long-run variance level itself a mean-reverting stochastic process. The spot variance mean-reverts toward that changing level, while the asset price follows a diffusion with…
The document asks how to estimate an autoregressive model with a GARCH volatility process in R. Its practical suggestion uses the fGarch package, specifying an AR(1) mean structure and a GARCH(1,1) conditional variance structure, then reviewing the fitted…
This question compares a perpetual American put’s exercise threshold under Black–Scholes assumptions with the value of waiting for a finite period. The author argues that, from a price above the perpetual threshold, there should be some horizon for which…
This note diagnoses a warning from a rolling GARCH estimation in R. The example computes returns from SPY closing prices with `ROC`, then passes them to `ugarchroll` for repeated model estimation. The key issue is that the first return is missing because a…
The document explains why a parallel shift in a forward curve does not necessarily produce the same change in a forward swap rate. The effect depends on how the shift is defined: the answer defines it through overnight rates implied by discount factors, then…
The document examines the limits of replicating variance exposure with a weighted strip of out-of-the-money calls and puts, a construction associated with log-contract replication and the VIX calculation. The cited explanation says the continuous static…
The document examines whether a calendar spread can provide a stable way to trade changes in implied volatility while remaining delta- and gamma-neutral. The responses explain that neutrality holds only under particular market conditions and can deteriorate…
The document asks how to estimate covariance when optimizing a minimum-variance portfolio over weekly or fortnightly cumulative returns. It contrasts calculating covariance directly from returns sampled at the target frequency with scaling a daily covariance…
The post compares statistics for log returns and simple returns, using normally distributed simulated log returns and converting them to simple returns. Its central clarification is that exponentiating the sample mean of log returns does not produce the mean…
The document discusses how to estimate risk inputs for an option on the difference between two futures. It presents three approaches to spread volatility: calculate it from historical spread returns, combine the futures’ implied volatilities with a…
This discussion explains how to retrieve estimated volatility summaries from an R model fit with the stochvol package. The questioner compares a plot produced by the package’s plotting function with median values computed from the latent simulation draws and…
This note examines how Bloomberg’s swaption volatility quotes relate to Black-model prices, focusing on a EUR cash-settled payer swaption. It defines the normal cumulative distribution and Black formula, then distinguishes the physical-settlement annuity…
The document describes difficulties in deriving pseudo-European implied volatility slices from American option prices through de-Americanization. The method may produce different European implied volatilities at the same strike when both calls and puts are…
The document asks why a stock-price diffusion changes when a model includes correlation between interest rates and stock returns. In the uncorrelated case, the stock diffusion coefficient is constant; in the correlated case described, it is scaled by the…
The document raises whether annualized volatility estimated from monthly returns is typically lower than estimates based on daily returns. The questioner considers using daily observations to increase the sample size, while worrying that the measured…
The document distinguishes pricing models used for equity options from parametric fits used to store and retrieve implied volatility data. It identifies Black–Scholes, including time-dependent versions, and local volatility as common industry choices, with…
The document explains how a delta-neutral position with long call options can generate gains through repeated stock rebalancing. In its example, the trader starts long calls and short shares; a price decline reduces call delta, so buying shares to restore…
This discussion considers whether VIX-style volatility indices could be created for individual S&P 500 industries. Since the VIX is derived from index option prices, the proposed analogue would likewise depend on an adequate market in options on the relevant…