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.
8,116 documents
The discussion explains why the relationship between an underlying asset’s spot price and its implied volatility skew can vary across markets and regimes. Downside option demand may remain strong even as a stock rallies when credit protection is unavailable,…
The question derives a call-price expression from Black-Scholes delta and rho, and asks whether two Greeks can really determine the option price. The accepted response explains that, with the underlying price, strike, time, and the model assumptions already…
The document outlines a framework from Brian Johnson’s book on earnings volatility and asks whether its Excel calculations can be recreated in Python. The described workflow estimates the earnings volatility embedded in option prices, compares historical…
The note explains how to represent liquidity in options using the bid–ask spread. A wider spread indicates lower liquidity, while a narrower spread indicates higher liquidity. The spread can be measured in price units or converted into implied volatility…
The document explains how corporate actions affect single-stock futures and options. It distinguishes stock splits, which are handled through contract adjustments, from dividends, which can change the market value of the underlying shares and therefore the…
The discussion asks why volatility swaps require modeling volatility of volatility, how a variance-swap strike relates to a volatility-swap strike, and how to estimate the convexity adjustment. One answer frames the issue through asset pricing: stochastic…
The document discusses estimating the chance that a short call or put expires worthless. It presents option delta, with the sign adjusted for puts, as a rough first-order proxy for the probability of finishing in the money; subtracting that estimate from one…
A futures option gives its holder the choice to enter a specified futures contract at the option’s strike price. Exercising creates a futures position with that contract price; it does not mean paying the strike amount upfront as though buying the underlying…
The document explains how option delta can be approximated from the two successor-node option values in a binomial tree. Delta is the derivative of option value with respect to the underlying price, so the relevant Taylor approximation is in the underlying…
The document examines whether an asset could have returns that are equally likely across a bounded range, including small and extreme outcomes. One response argues that trading toward expected value would make such a distribution unlikely in an efficient…
The document considers whether the cost of a pre-earnings straddle predicts the size or direction of the stock’s move after results are released, and whether options hedging explains that behavior. The response points to post-earnings-announcement drift:…
The document explains why a cash account belongs in a replicating portfolio used to derive the Black–Scholes equation. The stock position offsets the option’s sensitivity to price changes, but rebalancing that position requires financing. A cash deposit or…
The document asks why plotted call-option implied-volatility smiles appear steeper for shorter expiries and why scaling log-moneyness by the square root of time can make smiles look more comparable. One response points to work on smiles in…
The document addresses how to derive an implied volatility for an interest rate cap after calibrating SABR to caplet quotes. Caplets are options on forward rates, and separate strike and maturity quotes can be used to fit SABR parameters and produce caplet…
The note investigates why an implicit finite-difference solution of the Black-Scholes PDE and a Monte Carlo estimate produce different plots for a sawtooth-shaped terminal payoff. The response focuses on behavior near zero spot: the payoff should approach…
The note explains how violations of European put-call parity can indicate an arbitrage opportunity. When the call is priced below the value implied by the put, stock, and discounted strike, the suggested position is to buy the call, sell the put, short one…
The document establishes that the value of an American put is convex as a function of its strike. One proof starts from the convexity of the discounted payoff in strike for each possible exercise time. Taking expectations preserves the inequality, and taking…
The note considers how to describe the instantaneous mark-to-market change of a variance swap and asks whether it is simply realized variance minus implied variance, multiplied by elapsed time. One response says a variance swap is defined through a set of…
The document assesses whether QuantLib can price a Bermudan-callable EUR/USD cross-currency interest rate swap using two Hull-White rate models, an FX process, correlations, and Longstaff-Schwartz Monte Carlo. Its answer is that QuantLib offers many relevant…
The document decodes two abbreviations used in swaption quotes. The year labels identify the option’s start date and the tenor of the underlying swap; the response focuses on the suffixes WC and WS, clarifying that they describe option structures rather than…
The document concerns estimating discrete dividends from American option prices, using paired call and put implied volatilities around the forward as a proposed calibration signal. The question describes refining dividend estimates by expiry and adjusting…
The discussion describes how to obtain local volatility from an implied volatility surface using a Dupire-style relationship. It expresses the result in terms of derivatives of total implied variance with respect to maturity and log moneyness. In the…
The discussion asks whether the Black–Scholes option value is the limiting value of a binomial tree as the number of time steps grows, and whether implied volatility can be used in that convergence. The replies point to a study comparing the models and…
The document asks how to convert quoted lognormal swaption volatilities into prices using the Black swaption formula. It outlines how option tenor and swap tenor identify the exercise date and underlying swap period, while the strike is set by adjusting the…