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 outlines a basic Monte Carlo check of Black–Scholes pricing. Simulate the underlying under risk-neutral geometric Brownian motion for the option’s life, evaluate the chosen payoff at expiry, average the simulated payoffs, and discount that…
The document explains why a spot at-the-money call can have a Black–Scholes delta above one-half, and distinguishes delta from the risk-adjusted probability of expiring in the money. Delta measures the option’s sensitivity to the underlying and the shares…
The document discusses why an implied volatility smile can curve downward, with at-the-money volatility above that of out-of-the-money puts and calls. Suggested explanations include negative excess kurtosis, which corresponds to thinner tails than a…
The document points to a paper describing how to test claims about Bernie Madoff’s reported steady monthly gains by reconstructing a simplified version of the associated strike-conversion strategy. The referenced work presents backtesting as a way to examine…
The document clarifies an angle-bracket notation appearing in a stochastic-volatility discussion. Although angle brackets often denote quadratic variation or quadratic covariation in stochastic calculus, the same symbols can represent an average in other…
The document raises a valuation problem involving a derivative whose underlying share price is modeled with geometric Brownian motion while its strike changes with company EBITDA. The author questions whether the absence of a traded EBITDA instrument…
Quanto option pricing depends on the underlying asset’s volatility, the exchange rate’s volatility, and their correlation. When liquid quanto instruments are available, their prices can imply the combined correlation and volatility adjustment directly;…
The note explains why delta, gamma, and vega describe an option’s local sensitivity rather than its response to a large underlying-price move. It gives a second-order Taylor approximation for estimating a price change from delta and gamma, and relates gamma…
The document discusses how to estimate an equity ETF’s forward price and implied dividend yield when building an implied volatility surface. The questioner derives a synthetic forward from call and put prices near the spot price, then combines it with spot…
The document asks how to estimate implied volatility for a stock that has no traded vanilla options, when options are available on an index containing that stock. The questioner proposes estimating the stock’s beta to the index, potentially with a Kalman…
The document considers how weekends should affect historical volatility estimates used in Black–Scholes pricing when option market prices are unavailable. It describes a distinction between calendar time used for discounting and effective volatility time…
The question asks how much capital might be required to influence a stock price and raises options activity, short availability, ownership, and company characteristics as possible factors. It distinguishes this broad price impact question from claims about…
The document explains a limiting relationship between risk-neutral probabilities in a finite-step binomial model and those in the Black–Scholes framework. For a given event, the risk-neutral probability generally differs between the two models when the…
A trader describes trying to sell out-of-the-money puts in an illiquid options market with a wide bid-ask spread. After placing a limit order inside the spread, they observed other sell orders move to the same price when they changed their own quote. The…
The document considers fitting the SVI volatility model to swaption implied volatilities when forward swap rates can be negative. Standard SVI formulations use log-moneyness, based on the ratio of strike to forward, which is undefined when those rates are…
The document explains Taleb’s “soft” American option idea through foreign exchange options. Unlike a simple stock call or put, an FX option combines exposure to two currencies, so early exercise depends on the relative domestic and foreign interest rates as…
The document collects recommendations for rigorous study of martingale theory, stochastic calculus, and arbitrage pricing. Suggested books include works by Karatzas and Shreve, Shreve’s two-volume finance series, and Musiela and Rutkowski. The answers…
The document considers how to parameterize an implied volatility smile for cryptocurrency options using observed bid and offer prices. The author’s starting point is a simple power relationship between volatility, strike, and the underlying price, but finds…
The discussion seeks a European call value when the underlying follows arithmetic Brownian motion, with zero interest rates. The questioner changes measure to remove the drift and tries to use the probability of finishing above the strike to derive the…
This post describes a challenge in constructing an FX local volatility surface for use with a stochastic local volatility model in QuantLib. FX option quotes are commonly specified by delta, so their strikes vary with maturity and market conventions. That…
The document raises a foundational question about hedging volatility risk when an asset is modeled with stochastic volatility. It starts from the option-pricing assumption that a second traded asset can hedge changes in the volatility of the underlying, then…
The document explains how interest rates and dividends affect the carry associated with equity options, and how a long call combined with a short put replicates a forward. It emphasizes that carry belongs to the underlying financing and dividend economics:…
The document examines whether a portfolio of options can capture a relative implied-volatility opportunity while remaining immune to changes in the underlying price throughout its holding period. The author constructs a four-option position with initial…
The document asks why greater correlation might lower the forward value of a basket used in a rainbow option, where the basket payoff weights stocks according to their ranking. It presents two proposed effects: correlation may raise basket volatility and…