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 discusses why absolute or squared returns often show positive autocorrelation even when raw returns do not. It compares a synthetic example with a single period of elevated volatility to empirical return behavior, then considers whether…
The document explains the relationship between standard Brownian motion and a Brownian process with drift and scale. Standard Brownian motion starts at zero, and its increments over an interval of length t are normally distributed with mean zero and variance…
This note raises a modeling question about entropy pooling, a method that adjusts a prior distribution to satisfy views while staying close to that prior according to relative entropy. The author observes that imposing a higher expected return, without an…
This document is a curated reading list spanning factor investing, trading and execution, volatility estimation, derivatives pricing, and commodity futures. It names influential papers and briefly describes their contributions, including multifactor asset…
This exchange concerns how to construct an equal risk contribution portfolio when the investor also wants a specified total volatility. It defines portfolio volatility from the covariance matrix and weights, and frames the allocation as minimizing squared…
The document presents Fourier integral representations for European vanilla call pricing under the Heston stochastic-volatility model. One representation expresses the call through two probability terms whose characteristic functions depend on the current…
The document addresses how stochastic volatility affects pricing of exotic options, including barrier and Asian contracts, and points to numerical methods as the central practical challenge. It identifies Monte Carlo simulation as a common approach: simulate…
The document explains why the premium of an at-the-money straddle is not generally equal to the dollar amount of a one-standard-deviation move. At expiry, a straddle pays the absolute distance between the underlying price and the strike. With the strike at…
The document asks how to choose mean and variance orders efficiently for a time series with both autocorrelation and changing volatility. It contrasts selecting an ARMA model first and then choosing GARCH orders with a joint search over all ARMA-GARCH…
The question describes a path-dependent contract with one payoff if the underlying stays above a barrier and a different payoff if it crosses below it. It asks how to balance the component instruments to give the contract zero initial value and how to solve…
The document raises a question about how volatility affects the value of an in-the-money European call when the underlying return distribution is negatively skewed. The author observes that, under a variance-gamma pricing formula, increasing the volatility…
The note explains how to select strikes for a costless collar using gold options. A collar pairs a long put with a short call whose premium offsets the put’s cost. There is an unlimited set of such strike pairs: for each positive put strike, a call strike…
The note considers why a stock can have high market sensitivity and high total volatility while showing low specific volatility, even when it does not appear to use unusually high debt. The example is Aptiv, whose risk model estimates a beta of 2 using three…
The document presents Black-76 formulas for European payer and receiver swaptions, scaling the option payoff by the present value of the underlying swap’s fixed-leg annuity. It defines the forward swap rate, strike, expiry, volatility, compounding frequency,…
The document considers whether futures options volatility behaves as sticky strike or sticky delta, and why intraday tick data can make the distinction difficult. Options and futures quotes may update at different times, while illiquid markets may not…
The document considers whether two call options can hedge a short call so that the resulting portfolio is both gamma-neutral and vega-neutral. It expresses the hedge as a two-equation linear system, with the other options’ vegas and gammas forming a…
This exchange examines whether implied volatility can be used to estimate the range of future stock prices. The question raises three concerns: log returns may be modeled as normal while prices are lognormal, the expected return affects longer-horizon…
The question asks how to model daily SPX implied volatilities across several maturities and moneyness levels, preserving their correlations and incorporating jumps linked to recurring events such as economic releases and dividends. The proposed goal is to…
The document considers filling missing market-maker bid and ask values across strikes and maturities when historical option prices are available for all liquid contracts and fair quotes exist for only some. It covers both European options, for which the…
The document asks whether hourly or multi-hour realized variance can be used in a realized variance GARCH model. The author has minute-bar foreign exchange data and notes that the usual setup pairs daily returns with a daily realized volatility measure. With…
The document examines parameter estimation for a stochastic differential equation driven by fractional Brownian motion. It describes an Euler approximation in which each process increment combines a drift term with a scaled fractional Brownian increment,…
The document asks how to derive a stock price at a future time from a geometric Brownian motion and why several familiar expressions differ. It compares direct integration of the proportional price change, the exponential solution with a volatility…
The document investigates an apparent increase in call-option gamma when a Black-Scholes routine is used to represent options on futures. The setup discounts the futures price before passing it as the underlying, then compares options with the same spot and…
The document discusses a question about Gatheral’s derivation connecting local variance to the conditional expectation of instantaneous variance. The central issue is why a stochastic differential term involving the underlying price and a strike disappears,…