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 clarifies what an implied volatility function calibrated to vanilla options can and cannot establish. If the model is recalibrated to match vanilla option prices across strikes and maturities, it reproduces the risk-neutral distribution of the…
The document explains implied correlation as a measure of how closely investors expect the assets in an index or portfolio to move together. It distinguishes correlation indices, which can be calculated from index and constituent options, from correlation…
The discussion clarifies why dollar gamma is intended to measure convexity exposure rather than every change in the dollar value of delta. For a small spot move, the change in the number of delta shares is multiplied by the starting spot to express the hedge…
The discussion explains why a trading desk’s non-stationary daily P&L does not by itself prove that next year’s P&L is unpredictable. A desk’s P&L may reflect strategies and exposures that differ from the return stream of an investible asset, so…
The document asks how portfolio volatility reports might better match investors’ perception of risk. It starts from the sample standard deviation of monthly returns and notes that the estimate depends on the length of the lookback window. The questioner…
The document asks how to rigorously establish the Markov property for the Heston model’s joint stock-price and variance process, whose square-root variance dynamics do not meet the familiar Lipschitz conditions cited in many introductory SDE results. It…
The document compares absolute changes in interest rates with percentage changes when constructing historical return series for value-at-risk analysis. Its example shows how an identical change in yield can produce very different percentage returns depending…
The document frames a thesis question about established, pre-neural-network approaches to calibrating stochastic volatility models, with particular interest in Heston. It asks for research areas and papers that could support a historical overview of…
The document explains why ordinary Taylor expansion needs a correction when applied to functions driven by Brownian motion. Brownian increments have variance proportional to elapsed time, so the sum of their squared increments converges to elapsed time…
The document discusses plotting the historical minimum and maximum returns over holding periods of increasing length, alongside a central band, to visualize how observed outcomes vary by horizon. The accepted replies suggest variance ratios as a related…
The document raises whether daily historical option prices can be approximated from historical closing prices of the underlying asset. It identifies Black–Scholes as one possible pricing framework and notes that the model requires implied volatility for…
The document poses a hedging problem for a one-year payoff that activates only if a stock falls at least 20% from its initial level. If that condition is met, the holder receives the positive excess of realized volatility over a threshold; otherwise the…
The document explains how to obtain the probability that a stock price modeled by Heston will finish above a specified threshold at a future date. In options terminology, this probability is the undiscounted value of a digital call on the modeled spot…
The document derives the probability that an investment has a positive return over a chosen horizon under a geometric Brownian motion model. Starting with a price process whose drift is 15% and volatility is 10%, it applies Itô’s lemma to show that log…
The document asks why a rolling average of a compounded price series can appear to have the same variance as the underlying price levels, even as the averaging window grows. The question contrasts this observation with the familiar intuition that averaging…
The document investigates why a GARCH(1,1) fit differs from a variance model that replaces its lagged squared-return term with an external regressor. The example uses daily equity returns and compares fitted coefficients from the two specifications. The…
The document examines the moment generating function of a stochastic process formed by integrating Brownian increments against a response kernel whose argument depends on both integration time and the current time. Applying Itô’s lemma to the exponential of…
The document explains why forward Libor rates are often modeled as lognormal in Black’s framework, while clarifying that this distribution is a modeling choice rather than a requirement of no-arbitrage. By expressing a forward rate as a ratio of zero-coupon…
The question compares two ways to specify returns when modeling stock prices under the physical measure. A conventional GARCH model uses a constant conditional mean, with volatility changing through the variance process. An alternative adjusts the mean by…
The discussion surveys software and methods for testing options strategies, including multi-leg spreads. It explains why this work is harder than testing linear instruments: historical option chains are large, implied volatility histories may be unavailable,…
The document addresses a mistaken either-or choice between modeling returns with a parametric probability distribution and using an autoregressive model. These describe different parts of a model: a distribution specifies the form of uncertainty, while…
The discussion distinguishes listed options from over-the-counter foreign exchange options. Conventional option chains are associated with listed contracts. Interbank FX options are predominantly over the counter and are usually quoted in implied volatility,…
Volatility forecast evaluation depends on what quantity is forecast and what observation serves as the benchmark. Possible targets include volatility, variance, or log volatility; because true volatility is latent, evaluation may use implied volatility or a…
The document describes a numerical failure when calculating implied volatility for American options with RQuantLib: the solver reports that it cannot bracket a root, even though the user obtains values by entering observations manually. The suggested…