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 explains that common technical indicators answer different questions, so choosing among them depends on the market behavior being examined rather than assigning one a universal higher weight. Bollinger Bands use a moving average and price…
The discussion corrects the intuition that a deeply in-the-money European put might lose value as volatility rises because the underlying has little room to fall. For standard European options, put-call parity gives puts and calls the same volatility…
The document considers how to model a path-dependent payoff whose number of vanilla calls increases when the underlying exceeds a threshold on periodic observation dates. It asks whether local volatility, stochastic volatility, or another model is…
The document discusses the possible outcomes of selling an out-of-the-money European call while delta hedging with the underlying stock. It contrasts a gradual rise toward the strike, where the call may expire worthless and the hedge can gain value, with a…
The document explains the idea behind selling options to collect the variance risk premium in the S&P 500. It describes a common pattern in which implied volatility is often above subsequently realized volatility, making options appear expensive relative to…
The document compares historical simulation, variance–covariance estimation, and Monte Carlo simulation for calculating Value at Risk. Historical simulation revalues a portfolio against past market moves, avoiding an explicit return-distribution assumption,…
The document discusses practical differences between trading on smaller, less liquid exchanges and larger markets. It highlights wider slippage and potentially greater market impact, fewer liquid securities and trading opportunities, limited derivative…
This note explains why volatility measured from simple returns can imply a different growth picture from volatility measured in log returns. Its central concept is volatility drag: alternating gains and losses do not cancel when wealth compounds, even if the…
The document describes an attempt to fit hourly Bitcoin returns with asymmetric GARCH-family models. The reported fit has a portmanteau statistic of 198.4 and an estimated first ARCH and GARCH coefficient sum above one, raising concern about volatility…
The document discusses where to obtain historical daily settlement prices for individual VSTOXX futures, prompted by a comparison with freely available VIX futures data. The responses describe several possible sources: Eurex’s data shop, an institutional…
The document compares calibrating SABR models at quoted tenors and interpolating their parameters with using a stochastic volatility LIBOR Market Model. The proposed interpolation approach can produce smiles at intermediate maturities from sparse market…
The discussion offers an intuitive explanation for why a deep in-the-money European put can retain positive vega, even when the underlying stock price is near zero. Its value includes time value as well as intrinsic value, and that remaining time value can…
The discussion surveys ways to estimate intraday patterns in volatility, volume, bid–ask spreads, order activity, and correlations. For level shifts, it mentions regression with time indicators and a Kalman filter with a changing slope. For spreads, it…
The question concerns finding the underlying price at which a credit spread reaches a specified loss, using Black–Scholes option prices. The writer currently searches across underlying prices, which becomes slow when repeated across many spreads. The…
The document asks how Lie groups, differential geometry, and string theory relate to mathematical finance, but the available answer gives only a brief connection. It notes that mathematical finance often involves partial differential equations also studied…
The document explains how to infer a risk-neutral terminal-price density from call prices. By the Breeden–Litzenberger result, the density at a strike is the second strike derivative of the call price, adjusted for discounting. Since market quotes are…
The document asks how to extend a volatility skew from a set of observed strike and volatility points across a much wider strike range. The initial cubic spline approach produces negative values at distant strikes, raising concerns about overshoot and…
The document asks how to calculate a portfolio’s 99% value at risk when returns are normal conditional on volatility, but volatility itself follows a gamma distribution. It contrasts this setup with the familiar normal VaR calculation based on fixed…
The document raises a modeling question about a two-regime option-pricing setup built around a risk-neutral GARCH process. The author fits crash and normal regimes and observes that options are more expensive in the higher-volatility crash regime. The…
The document examines whether a continuously monitored Asian call can be bounded by a vanilla call with the same strike and maturity. Under zero rates and dividends, and assuming continuous asset paths, it uses the integral mean-value theorem to represent…
The document discusses how to estimate the covariance matrix needed to construct a Markowitz efficient frontier. It names maximum-likelihood estimation from historical returns as a standard approach, then describes alternatives: shrinkage of the covariance…
The document raises an input-selection problem in estimating implied correlation from bivariate option prices. The described approach trains a model on a decade of returns, prices options, and inverts Stulz's formula to infer a correlation coefficient.…
The document explains why Monte Carlo estimates of a European option price can become less precise as volatility rises. The central point is that the estimate averages simulated payoffs, and its sampling error depends on payoff variance and the number of…
The document derives the replication error that arises when a trader hedges an option with a Black–Scholes delta while the underlying asset’s realized variance differs from the constant variance assumed by the model. For a one-dimensional diffusion with the…