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 document explains a rule of thumb that relates an option's bid-ask spread to its vega. Vega measures how much the option price changes when implied volatility changes. Because of that sensitivity, a volatility bid-ask interval can be translated into a…
The document discusses ways to estimate a reference implied volatility (IV) for options at different moneyness levels, with the aim of identifying contracts whose market IV appears mispriced. For forward-looking average volatility, it points to variance swap…
The document explains why a portfolio of stock and a money market account is chosen to match a derivative’s payoff in a one-period, two-outcome binomial model. The derivative has specified payoffs for the up and down outcomes, and the investor selects the…
The document discusses how to obtain the two risk-free rates used in the CBOE VIX calculation for its near and next expirations. The cited methodology uses U.S. Treasury Constant Maturity Treasury yields and applies a cubic spline to estimate yields at the…
The document explains why a long put can sometimes have positive theta, meaning its value can rise as time passes. The sign depends on the relationship among the option price, intrinsic value, interest rates, and remaining maturity; it is not determined…
The document considers a ten-day, 99 percent value-at-risk estimate for a portfolio of options on the USD/GBP exchange rate. It presents a delta-equivalent position and a daily-volatility-based calculation that scales daily risk by the square root of the…
The discussion asks whether Asian option prices reveal information about a stock’s stochastic process beyond what can be inferred from European options. In an idealized setting, a full set of European call prices across strikes can be differentiated with…
The document examines how to specify cross-correlations among Brownian drivers for two equity spots and their volatility processes. The question challenges an assumed cross-correlation between the first spot driver and the second volatility driver, proposing…
The document considers pricing a payoff that combines an upside payoff on one random variable with a downside payoff on another. It asks whether the joint expected value can be recovered from limited observations of individual cross-payoffs and marginal…
The document examines a proposed cash-and-stock replication of a call under the Black–Scholes model. It uses a Taylor expansion in the stock price to argue that the option’s convexity makes its value rise more than the local delta hedge when the stock moves,…
The document describes an attempt to model intraday price changes in SPX options that expire the same day. The goal is educational: to explore how option values respond to movements in the underlying index and volatility, especially near expiration, rather…
The document explains how time to maturity enters the Black–Scholes option pricing formula and why calculators often request days until expiration. The input unit itself is flexible: time must be expressed consistently with the units used for the risk-free…
The document derives how premium-adjusted Greeks differ from Black–Scholes Greeks when an option is settled in a currency different from the underlying’s currency. In the example, the option value in the settlement currency is the value in the underlying…
The document addresses whether market makers’ dynamic hedging pushes an underlying asset toward options “max pain.” Its answer distinguishes the effect of dealers’ net option positions. Dealers who are long options tend to sell as the market rises and buy as…
The document discusses why an implied volatility computed with a European Black-Scholes model may differ from a quoted estimate for Microsoft options. The response points out that these options are American style, so they can be exercised before expiration,…
The document explains why implied volatility and historical realized volatility can move in opposite directions when a scheduled event occurs. Before the event, implied volatility for a fixed expiry can reflect uncertainty from that event as well as other…
The document concerns the wild card option embedded in Treasury futures and asks how to interpret an equation for the expected payoff from exercising early after a significant price move versus waiting to earn another day of gross. The responses point toward…
The document explains how a dealer can handle a client’s request to reduce the notional of an existing SPX variance swap before maturity. It treats variance as additive over time: the position’s value at the unwind date can be viewed as realized cash profit…
The document clarifies the distinction between an option’s expected value and the instantaneous volatility of its price. Under constant rates, the conditional expected future option value is described as the current value grown at the risk-free rate;…
The document explains common desk terminology for locating swaptions on a volatility grid. The grid is organized by option expiry and underlying swap tenor: short expiries are often treated as gamma exposures, while longer expiries are associated with vega.…
The document analyzes a capped S&P 500 protection note with a fixed minimum payment, upside participation above the initial index level, and a maximum payout. It represents the payoff as a zero-coupon bond plus a call spread: long a call at the initial index…
The document considers a workflow for pricing a European call: fit a SABR volatility smile to market implied volatilities across strikes, use the fitted model to obtain volatility for the target strike, and insert that volatility into the Black–Scholes…
The document asks how to obtain the initial instantaneous forward variance curve used to calibrate variance curve models. Given market variance swap quotes, it describes a common procedure: interpolate total variance, calculated as maturity times quoted…
The document derives the sensitivity to the initial asset value of a down-and-out call whose barrier is set equal to its strike, interpreted here as a debt level. It rewrites the option value as a vanilla Black–Scholes call minus a scaled call on a…