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 distinguishes implied-volatility skew across option strikes from skewness in the underlying asset’s return distribution. It presents model-free implied skewness as a measure connected to realized skewness, and describes research finding a…
The response suggests comparing a volatility forecast from a non-normal GARCH model with the volatility implied by option prices. If the options appear inexpensive relative to the forecast, the proposed position is to buy calls and puts; if the implied…
This explanation shows how the product rule in Itô calculus creates the discounting term when differentiating an option value divided by a bank account. Set the two factors to the option price and the inverse bank account, then apply the rule, including the…
The document discusses how market participants price American options on Eurodollar futures and when a European-option approximation may be adequate. It contrasts tree-based models that represent early exercise with the simpler European treatment often used…
The note clarifies how a replicating portfolio can also function as a hedge. Under risk-neutral pricing, a European option can be offset by a portfolio whose value reproduces the option’s payoff and whose combined position with the option evolves at the…
The note explains why hedging skew exposure in a forward-starting option differs from hedging an ordinary option. A forward-starting put may be analytically short skew, yet during the forward period its strike resets in proportion to the underlying price.…
This question frames a market-microstructure research problem: whether intraday adverse selection on a futures or options contract changes systematically as that contract approaches expiry. The focus is the instrument itself, rather than adverse selection in…
The note explains how to replicate a zero-coupon structured note that returns its principal at maturity plus an oil-linked payment. The extra payment rises in proportion to oil prices above 25, but is capped at 2,550. The proposed replication combines a…
The document compares three representations of option market information: implied volatility by strike and maturity, raw call or put premiums, and the risk-neutral return distribution. It argues that these are equivalent views of the same information and can…
The document concerns evaluating density forecasts derived from GBP/USD options. The author has estimated a time series of risk-neutral densities nonparametrically and wants to apply the unconditional test described by Christoffersen and Mazzotta. The…
The document addresses how to distinguish cap and floor claims in broker-provided spread option data organized by strike. It cautions against classifying the instrument solely from the sign of an absolute strike or by comparing that strike with a forward…
The document compares two expressions for a Black 1976 caplet price. One discounts the option payoff using the discount factor to the payment date; the other uses the discount factor to the rate period's start date and divides by one plus the forward rate…
The document responds to a request for accessible examples of probability theory in finance. It names papers and articles spanning probability distributions, option-implied distributions, continuous-time random walks, and heavy-tailed sums in insurance and…
The document maps views about forecast return distributions to simple option positions. A belief that expected returns are understated or overstated is associated with buying a call or put, respectively. Views on dispersion are paired with long or short…
The document studies a payoff that delivers the stock’s terminal price only when its return relative to an index clears a threshold. It first sketches Monte Carlo simulation using geometric Brownian motion, then gives a risk-neutral derivation. The…
The document explains how QuantLib’s BlackVarianceCurve distributes variance through time according to its day-count convention. Because the curve interpolates linearly in variance, using Business/252 produces a constant variance increment per business day…
The document discusses using SABR to price EUR inflation caplets when strikes can be negative, a setting where standard Black and unshifted SABR formulations are not directly applicable. One response recommends reconsidering the model: inflation option…
The document asks whether option prices can reveal a likely rise followed by a later decline in a security. The answer explains that a sufficiently broad set of European option strikes for two expirations can be used to infer a risk-neutral price…
The document defines two expressions used in options and trading conversations. Saying volatility is well bid describes strong buying interest in options that are particularly sensitive to implied volatility, with longer-dated options given as an example…
The document clarifies when the holder of a midcurve payer swaption must decide whether to enter the underlying forward-starting swap. The answer says the decision occurs at the option’s expiry, using the example of a one-year option on a five-year swap…
The document asks what to call the overlapping strike prices in ordered lists of call and put options. Its answer uses the underlying spot price to explain the standard moneyness categories: calls with strikes below spot and puts with strikes above spot are…
The document discusses when to roll a six-month call option into a longer-dated option, such as one expiring in nine or twelve months. Its main suggestion is to consider rolling when implied volatility in the existing LEAP is elevated and fewer than six…
The exchange explains the role of delta hedging in the Black–Scholes framework. A portfolio short the option and long the underlying in proportion to the option's sensitivity to the underlying cancels the shared stochastic price movement in the idealized…
The document explains the intuition behind representing a variance swap hedge as a weighted portfolio of vanilla options across strikes. The integral represents a continuous strip: at each strike, the portfolio holds an amount determined by a weighting…