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 considers how to price European calls and puts on an underlying that can jump, fluctuates with short-term supply and demand, and tends to lose value over longer horizons. It also raises practical questions about physical delivery and indivisible…
The document asks whether sharp foreign exchange price moves around short binary option expiries reflect trades or misleading posted bids, and where traders can inspect FX order depth. The answer attributes many such moves to market makers hedging binary…
The document explains why implied volatility calculated from in-the-money (ITM) and out-of-the-money (OTM) equity calls may appear higher for ITM strikes. For calls, ITM contracts have strikes below spot, while OTM contracts have strikes above spot; the…
The document presents a question about extracting a risk-neutral density from SPY weekly options using the R package RND. The author fits a three-lognormal mixture to American option prices and plots the resulting density over strikes around spot, but finds…
The document asks for the maximum price of a European call butterfly with strikes at 103, 106, and 108, assuming no fees and a zero interest rate, without specifying a distribution for the underlying. The accepted reply gives a maximum theoretical value of…
The document describes the collateral choice option as an expectation involving the time integral of the maximum among several spread processes, typically modeled as Gaussian. It notes that this expectation is difficult to calculate and that a cited…
The document asks how to compare a numerical European call price from an explicit finite-difference scheme with the analytical Black–Scholes value at an intermediate time step. The model uses spatial grid points corresponding to underlying asset prices, and…
The document considers a four-option position consisting of a long put below the middle strike, two short options at the middle strike, and a long call above it. The questioner calculates one region of the payoff and finds a negative amount, which appears…
The document explains the probability meanings of the two normal cumulative terms in the Black–Scholes call price. The probability associated with the strike indicator in the discounted payoff is computed under the risk-neutral measure, while the…
The document examines whether the sum of squared log returns is an unbiased estimate of variance under geometric Brownian motion. At finite sampling intervals, the estimate can reflect drift as well as volatility. The response explains why this convention…
This explanation examines the shift parameter in a lognormal model for forward interest rates. It writes a caplet payoff in terms of the shifted rate and strike, assumes the shifted forward follows a lognormal process under the appropriate forward measure,…
The note describes two ways to estimate implied volatility skew. One approach prices calls and puts across strikes, converts their prices to Black–Scholes implied volatilities, and estimates the smile’s slope. Another uses a call and a digital call at a…
The note explains that the Black model does not depend on the standard spot-to-forward relationship in which the forward price equals spot grown at the risk-free rate. Currency futures are given as an example where borrowing and lending in the two currencies…
The document explains why structured-product dealers may sell dividend exposure when equity markets fall. Products such as autocallable notes can leave dealers holding long-dated downside options or other exposures whose value and expected duration change…
The document examines why vega may give a misleading picture of volatility risk for options whose gamma changes sign, using a binary option as its example. Under Black–Scholes, it differentiates the discounted probability-based binary price with respect to…
The document considers replacing a diversified stock portfolio with long-dated calls on the same companies, keeping the same percentage allocation across names. It asks whether diversification carries over and what additional risks the options introduce. The…
The document asks how to choose a drift for simulating trading volume when pricing an option whose payoff depends on volume. The proposed model treats volume as geometric Brownian motion, and the author recognizes that option pricing calls for risk-neutral…
The document asks whether a quanto put can have a nonzero foreign-exchange delta, despite the common impression that quanto options are insensitive to FX. The question describes a case where the put’s calculated FX delta is positive and attributes this…
The document addresses how to calculate the kurtosis of a straddle payoff formed by combining call and put outcomes. The response corrects an attempted combination rule: even if cross co-kurtosis terms are assumed to vanish, the weighted sum of the…
The document answers a request for accessible study resources on Monte Carlo simulation for pricing derivatives at roughly master’s level. It names a course text associated with a master’s degree and recommends Paul Glasserman’s book as another source on…
The document explains how volatility inputs differ when an option expires before its underlying commodity forward settles. It distinguishes options on different forward contracts: a quote for a two-month option on a two-month contract should not…
The document explains why the time decay of a European call differs by time to maturity and moneyness in the Black–Scholes model. With substantial time remaining, the passage of a day generally changes exercise likelihood only modestly, so theta is…
The document asks whether a trader can sell an instrument other than an option to collect premium and fund a long equity call, while avoiding options tied to the same or a correlated underlying. The answer explains that options generally provide time…
The response proposes using programming and financial data skills to study market risk through equity index options. It describes an approach associated with Ian Martin: use prices from a small portfolio of European options on the S&P 500 to infer the…