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 introduces volatility dispersion trading through a position that sells at-the-money straddles on an equity index and buys straddles on its component stocks. It asks how the payoff of this combination relates mathematically to implied correlation…
The document gives an intuition for why averaging can reduce the volatility exposure of an Asian call option with an average-strike payoff. It uses the fact that the time average of standard Brownian motion over a fixed horizon has standard deviation…
The document explains the intuition for modeling financial price paths as cadlag: right-continuous with left limits. Under this convention, a jump is observed as having happened at a particular time, while the path immediately before that time has a…
The question concerns pricing a US three-month Libor cap under euro collateral, where the discounting and forward curves reflect the collateral agreement. It asks whether the volatility quoted for a US-collateralized cap can be reused, given that the pricing…
The document explains why a same-strike FX call and put do not generally have offsetting deltas, so their straddle is not automatically delta neutral. Put-call parity links call and put deltas through the discounted forward, and a delta-neutral straddle…
The document describes an attempt to estimate an option premium by replicating a strategy using futures order-book snapshots. The data consist of daily observations at noon over one month for futures with different delivery periods. The central question is…
The document asks how machine-learning methods such as random forests, support vector regression, gradient boosting, and nearest neighbors compare with GARCH when forecasting volatility beyond a single step. It also asks whether these models use lagged…
The document examines the expected value and variance of gamma P&L under different delta-hedging intervals. The question assumes normally distributed underlying returns, constant implied volatility, no transaction costs, and a constant dollar gamma exposure.…
The question asks how to price a European call when the underlying follows mean-reverting arithmetic dynamics with constant absolute volatility. The answer frames option valuation through a change to a risk-neutral process: in a complete market with…
This exchange examines why realized volatility can support profits from a long gamma position and why volatility alone does not determine the result. The questioner understands that scalping requires buying after a decline and selling after a rise, and asks…
The document considers how to set up a finite-difference method (FDM) when the goal is to price one option at a known initial spot, rather than study the option value across many starting prices. The response recommends centering the price grid on the…
The document asks what to study beyond prominent stochastic-volatility models such as Hull–White, Heston, and SABR. It identifies incompleteness as one important issue: stochastic-volatility models may admit multiple equivalent martingale measures, so…
The document asks how two representations of a one-factor Cheyette interest-rate model relate. One uses state variables for the short-rate factor and an auxiliary variance-like process, while the other expresses discounted zero-coupon bond prices using the…
This note distinguishes two related option concepts: implied volatility across strikes and vega, the sensitivity of an option’s price to a change in volatility. It explains that strike-specific implied volatility reflects market pricing and expectations that…
The document explains how to price a payer swaption when the forward swap rate follows a normal, or Bachelier, model rather than a lognormal Black model. It expresses the swaption payoff as the positive part of the difference between the swap rate and…
The document explains why a positive volatility skew can lower the fair value of a binary option, despite a distribution with fatter tails seeming to imply a higher chance of a far out-of-the-money call finishing in the money. The first explanation…
The discussion compares two ways to think about stock price movements: equal dollar changes across stocks or changes proportional to each stock’s price. It explains the standard modeling convention through volatility, which is expressed as a percentage.…
The document gives a high-level overview of how a bank may value, structure, and manage risk in an autocallable equity product. Pricing typically uses a model calibrated to market option data, with Monte Carlo simulation to estimate the product’s value…
The document distinguishes smile butterfly quotes from market butterflies, also called broker flies, in foreign exchange volatility markets. It explains that at-the-money volatility, risk reversals, and butterfly quotes together describe key features of the…
The document explains how volatility can be used to model a future stock price distribution. It distinguishes the normal distribution of the log price from the resulting lognormal distribution of the price itself. Under a simplified assumption of no…
The document distinguishes volatility quotes by both pricing framework and volatility convention. OIS volatility refers to pricing in a multiple-curve setting, while LIBOR volatility is associated with the older approach in which discounting and forwarding…
The document asks how to estimate historical at-the-money S&P 500 option prices using public data, including VIX or another implied-volatility index, and whether modestly out-of-the-money strikes could also be considered. The answer points to a published…
The discussion clarifies which degrees-of-freedom estimate belongs in a one-day Value at Risk calculation under a Student-t GARCH model. It distinguishes conditional residuals, which scale with the time-varying volatility, from standardized innovations,…
The document considers whether option open interest and trading volume can help predict next-day stock direction. It identifies candidate features such as call-put imbalances, changes in open interest, volume relative to open interest, activity by moneyness,…