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 collects book recommendations for an algorithmic trading programmer who wants to connect basic options theory with the language and practice of volatility trading. Recommendations include introductory treatments that emphasize intuitive option…
The document explains why vanilla calls and puts can show the same asymmetric volga profile, with larger values for in-the-money calls and out-of-the-money puts. It uses the Black–Scholes expression for volga, which combines vega with a term based on d1 and…
The note discusses how to identify market periods that favor trend-following or mean-reversion strategies. One suggested approach is regime modeling with Hidden Markov Models, with two research papers offered as starting points. The answer also cautions that…
The document addresses which option maturities to use when replicating a variance swap whose observation period runs from the next day through a later end date. It says the option strip used for static replication should expire on the same date as the…
The discussion explains why adding the vegas of all options in a portfolio can misstate total volatility exposure. A simple sum assumes implied volatility moves in parallel across strikes and maturities, an assumption that may not hold when the volatility…
The document introduces raw SVI, natural SVI, and SVI Jump-Wings parameterizations for a single implied-volatility slice, using log-moneyness and total implied variance. It then asks how these choices relate to direct volatility fitting, what maturity…
The discussion considers whether triple-barrier labeling should use a flexible vertical horizon alongside volatility-scaled profit and loss barriers. One response frames the vertical barrier as a practical limit on how long a trade event can remain tied to…
The document addresses how to evaluate GARCH forecasts, which predict conditional volatility rather than the return level. It outlines an out-of-sample comparison associated with Hansen and Lunde: estimate an ARCH-family model using data through a chosen…
The document explains why portfolio managers might buy calls or take long exposure to options on a volatility-target index. Such exposure can provide gains in turbulent markets, which may help offset losses in portfolios with a long equity bias when…
The question challenges the interpretation of annualized volatility as a normal range for a stock price, especially when volatility reaches or exceeds 100%. Applying a symmetric normal distribution directly to the price can imply negative outcomes, which…
The document explains why some options markets, especially over-the-counter foreign exchange, quote implied volatility by delta rather than by strike. In these markets, available strikes are not fixed and prices may not be directly quoted. Delta provides a…
The document presents a question about annualizing volatility from a fitted GARCH(1,1) model for stock returns. The example uses daily percentage returns, fits a normal-error GARCH model with rescaling enabled, forecasts variance several days ahead, reverses…
The answer treats a future implied volatility surface as a conditional modeling problem. In the direct approach, simulate outer paths under a calibrated model; at a future state, launch an inner Monte Carlo from that state, price options across strikes and…
The document describes two ways to estimate an option volatility surface for an asset with no listed options, using a more liquid, correlated asset as a reference. A practical rule of thumb maps the reference asset’s at-the-money implied volatility through a…
The document raises questions about paired-class exchange-traded products VXUP and VXDN, which were designed to provide opposite exposures related to the VIX. The prospectus excerpts describe funds holding cash or short-dated Treasury-related assets, with…
The document asks how to adapt a payment-delay convexity adjustment used for Libor to daily compounded risk-free rates, with SOFR as the example. It describes a normal-model expression involving a discount factor between the accrual end and payment dates,…
The document examines a common tension in options practice: Black–Scholes is often treated as a way to express prices through implied volatility, even though its assumptions do not fully describe markets, while its Greeks are still used to measure portfolio…
The document considers whether volatility or correlation is more stable over one- to two-year horizons and over longer periods. Its central lesson is to analyze the two quantities separately: volatility responds to the size of returns, while correlation…
This document frames a comparison between estimating daily return volatility from daily closing prices and scaling minute-return standard deviation by the square root of the number of minutes in a day. It asks whether using daily observations discards…
The document explains delta as the sensitivity of an option’s value to a change in the underlying asset’s value. A quoted 50 delta corresponds approximately to a 0.5 change in option value for a one-unit change in the underlying, making delta useful for…
The document answers whether to use an underlying asset's volatility or each option's implied volatility when calculating delta or vega across strikes. It recommends using the implied volatility associated with the option's strike and expiry, reflecting the…
The document surveys empirical ways to estimate implied volatility across option strikes. It describes spline or piecewise polynomial fits, parabolic parameterizations, and Edgeworth expansions. A typical workflow selects reliable market volatilities,…
The exchange investigates an unevenly choppy implied volatility smile produced by Monte Carlo pricing of swaptions under SABR with beta below one. It describes simulating forward rates and volatility with Euler steps, estimating option prices across strikes,…
The document sets up a ratio between a geometric Brownian motion with time-varying volatility and a Brownian bridge, then asks how to derive its stochastic differential. The bridge has a drift that pulls its value toward a fixed endpoint as the terminal time…