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 describes a volatility surface calibrated with singular value decomposition, comparing current implied volatilities with a previous surface. For maturities without market quotes, the author extrapolates at-the-money volatility using forward…
The document describes fitting a one-factor Vasicek short-rate model to at-the-money cap volatilities across several maturities. It reports the input volatility term structure and the fitted mean-reversion speed, long-run rate, volatility, and starting rate,…
The document questions whether linear correlation is sufficient when studying relationships among financial variables and combining volatility forecasts. It describes a proposed comparison of GARCH, support vector regression, and fractionally differenced…
The document asks for the probability distribution of a European call option's price at an intermediate time under the risk-neutral measure. The response starts from the Black–Scholes pricing function, which maps the underlying asset price and time to…
The document clarifies how researchers estimate univariate heterogeneous autoregressive models for realized variance across multiple stocks. The cited study does not pool all stocks into one long dataset to estimate a single common set of coefficients.…
The document asks why a volatility model should calibrate the S&P 500 index and VIX together, and whether an underlying asset’s model should use implied or realized volatility. Its answer links the indices through VIX’s construction: VIX is derived from a…
The document surveys ways to simplify Black–Scholes calculations, with a particularly compact approximation for short-dated, at-the-money options. Expanding the normal distribution function around zero gives an option value proportional to spot, volatility,…
The document discusses why an equity index and its implied volatility index can move in opposite directions intraday. It presents dealer hedging as one explanation: demand for protective puts and call writing can leave dealers exposed to volatility,…
The document examines a concern in deriving a continuous-time asset model from discrete steps. Each step multiplies the current price by a random factor involving drift and a normally distributed shock. Taking logarithms turns the product of step factors…
The document explains why volatility estimated from every transaction price can be overstated at high frequency. It models observed prices as a latent price that evolves with market uncertainty plus a separate component reflecting whether a trade occurs at…
The document derives the one-period volatility formula for a two-outcome binomial asset model. With equal probabilities, it defines each outcome’s return as the log of the price ratio, computes the average log return, and shows that the two outcomes’…
The discussion considers whether GARCH-MIDAS, commonly applied to daily returns, can model one-minute returns while incorporating daily exogenous variables. It suggests adapting the model to include an intraday volatility component, with a multiplicative…
The document addresses why percentage Value-at-Risk can grow sharply when a daily volatility estimate is scaled to a long holding period using the square root of time. Under a simple normal-return assumption, scaling daily standard deviation by the square…
The document asks whether a price model driven by Brownian motion evaluated at a random time can be represented as a stochastic volatility model. It proposes identifying the random clock with integrated variance, so that instantaneous volatility accumulates…
The document explains why the stochastic differential equation for a geometric Brownian motion cannot be solved by treating its two sides like ordinary differentials and directly integrating the relative change. In the proposed direct approach, the unknown…
The document explains how to obtain the quadratic variation of a process defined as an exponential function of Brownian motion. Applying Itô’s lemma gives the price process a drift term and a Brownian shock term. In the quadratic variation, the drift…
The document asks whether the Heston model’s characteristic function can give the conditional distribution of a future asset price when the current price is known but the current variance is not. It explains that, when both current price and variance are…
The document asks how to simulate implied volatility (IV) together with stock prices in a Monte Carlo option analysis. The author generates stock paths with Geometric Brownian Motion using estimated daily return mean and standard deviation, then values…
The document gives a brief overview of models commonly used to price exotic options across asset classes. For equity and foreign exchange products, it identifies local stochastic volatility models as a widely used family. It says individual firms may…
The document explains why options with less than a week to maturity may be excluded from implied volatility analysis. As expiry approaches, an option’s price becomes less sensitive to implied volatility, especially near the money. Consequently, small bid–ask…
This indicator measures the close’s distance from a movement-weighted mean and scales that distance by an ATR-based range width. The resulting oscillator is centered around zero, with reference levels at plus and minus one hundred. Its parameters set the…
This indicator tracks volatility measures across several maturities, from very short-dated VIX through one-year VIX, and plots them as a term-structure curve. It classifies the curve as contango when most adjacent maturity slopes are positive, backwardation…
Market EKG is a price-only oscillator intended to show how a recent candle’s open, high, low, and close compare with earlier bars. It takes the prior bar’s OHLC values, compares them with averages of the two bars before that, and plots four resulting…
This indicator proposes representing candle geometry in coordinates scaled by estimated volatility, so price movement and bar time can be compared on a normalized basis. It uses a rolling volatility estimate and logarithmic price transformation, then treats…