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 asks how to choose a quote for a binary contract with a stated probability of paying a fixed amount. Its expected value supplies a simple upper bound for a buyer seeking positive expected profit, but does not by itself determine a precise bid or…
The document compares liquid over-the-counter options with exchange-traded index options for systematic trading. It identifies market depth and trading costs as potential advantages of OTC markets, and notes that swaptions are generally traded OTC because…
The document discusses pricing and hedging an option to exchange two correlated risky assets when no bank account is available. With one asset as numéraire, the other asset’s ratio can be modeled as a driftless process under a corresponding measure, and the…
The document asks for the probability that a Brownian motion with constant drift and volatility touches a lower barrier by a fixed horizon, conditional on its ending at a known value. It gives an unconditional barrier-touching formula as background, then…
The document examines a one-day call option on a stock priced at 100, with possible next-day prices of 110 or 90, and zero interest rates. It shows how to replicate the call payoff by combining the option sale proceeds with a position of one-half share.…
The document addresses why a European call’s value rises with volatility even when it is already in the money. The questioner focuses on the increased chance of finishing out of the money, which seems to imply a lower price. The answers explain that this…
The discussion asks why a Barndorff-Nielsen–Shephard style model uses the square root of a variance process as the diffusion coefficient for log price, instead of using the variance process directly. The proposed alternative is motivated by algebraic…
The document is a short reading list for exploring deep reinforcement learning and related machine-learning methods in quantitative finance. It points readers toward work on optimal execution, foreign-exchange trading, price formation, options pricing, and…
The document explains two ways to represent a stock’s price when it pays cash dividends. In the first, the price equals a hypothetical no-dividend stock value minus the capitalized value of dividends already paid. This formulation starts with the observed…
The document compares an explicit finite difference implementation for a cash-or-nothing call with its Black–Scholes closed-form value. Using stated spot, strike, rate, maturity, volatility, and grid settings, the original implementation returns a price near…
The document asks why static arbitrage checks for an eSSVI volatility parametrization focus on butterfly and calendar spreads, and whether vertical spreads require a separate condition. Its accepted answer says the relevant limit for a vertical bull spread…
The document asks how to recover European vanilla option prices from a local volatility surface without relying on Monte Carlo simulation or solving a pricing PDE. It explains the links among call prices, risk neutral densities, local volatility, and the…
The document asks whether option prices should incorporate trading volume, especially when an option position is large but the underlying moves on little volume. It suggests that a volume-weighted underlying price near expiration might better capture…
The document presents the one-factor Hull–White short-rate model as a mean-reverting, normally distributed model used for pricing interest-rate products. Its tractability supports closed-form prices for zero-coupon bonds and bond options, including caps and…
The document sets up a portfolio of long and short European calls and puts on one underlying, with a common expiry and different strikes. It calculates initial cost by multiplying each option position by its quoted price and summing across contracts. A…
The document explains how prices of nearby-strike European options can approximate the risk-neutral probability that the underlying finishes on one side of a strike. A put price is expressed as a discounted integral of its payoff over the risk-neutral…
The document works through a Black–Merton–Scholes example with zero interest, unit volatility, and an option payoff based on the squared log price. Under the risk-neutral model, the log stock price can be rewritten using Brownian motion, reducing the…
The document asks when a European option pricing problem based on the Black–Scholes equation cannot be solved analytically. The response explains that the standard model has one source of uncertainty, while extensions can introduce additional risk factors,…
The document asks which option has higher implied volatility under a volatility skew: an at-the-money put with spot and strike at one price level, or an at-the-money call with spot and strike at a higher level. It provides no skew direction, market,…
The document asks why dynamic hedging an out-of-the-money option might lose money when the stock moves in one direction and finishes at the strike, even if realized volatility is assumed to equal implied volatility. The answer identifies an inconsistency…
The document explains how to apply the cash-or-nothing call formula at the valuation date. The option pays a fixed cash amount if the underlying finishes above the strike, and its value is the discounted payout multiplied by the risk-neutral probability of…
The document describes an FX option combining an American up-and-out call feature with a European down-and-in put feature. It asks why a market pricer uses a default Vanna–Volga adjustment for this path-dependent structure and whether Monte Carlo is more…
The document presents a question about an alternative derivation of the Black–Scholes model in Robert Merton’s rational option pricing work. It describes a setup in which a European warrant’s value depends on the stock price, riskless bond price, and time to…
The question asks whether the average time for an underlying to touch either short strike in a strangle can be estimated, and whether that average would be consistent enough to guide trading. It raises historical data and Monte Carlo simulation as possible…