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 discusses how to design a cross-asset pricing library that supports multiple models and numerical methods while keeping products and payoffs immutable for serialization. Its central design principle is to keep a payoff focused on contract terms…
The document considers bull and bear equity performance bonds that pay periodic coupons linked to stock returns, subject to a minimum coupon. It raises a modeling ambiguity: the coupon might be a minimum plus a positive performance component, or the maximum…
The document describes a numerical failure when calculating implied volatility for American options with RQuantLib: the solver reports that it cannot bracket a root, even though the user obtains values by entering observations manually. The suggested…
The document examines whether a covered call can earn a relatively reliable profit by waiting for time decay. Its example sells calls against a large stock holding, but the response points out that the stock’s price movement dominates the small option…
The document raises a question about why the COS method presents a characteristic-function relation specifically for Lévy processes. It notes that if a log price is represented as an initial log-moneyness plus a random log-price change, the characteristic…
This note examines an apparent arbitrage in put-call parity when a stock follows a zero-drift Black-Scholes process, with no interest or dividends. For a strike equal to the current stock price, parity makes the call and put prices equal. The apparent puzzle…
The document outlines an Euler–Maruyama simulation for log asset prices under a local volatility model, using volatility that varies with time and the asset level. It asks which drift to use for option valuation versus estimating the real-world chance of an…
The document asks whether the average strike and, where relevant, average implied volatility of a set of calls can be entered into one Black-Scholes calculation to approximate the portfolio’s average delta. The scenarios hold the underlying, expiry, rates,…
The document derives lower and upper bounds for a European call using payoff dominance. A call payoff cannot exceed the underlying asset’s payoff, so its price is at most the asset price. It also dominates both zero and the payoff from holding the asset…
The discussion explains why a cash-or-nothing digital call cannot generally be replicated exactly using ordinary calls and puts at strikes spaced five dollars apart. In theory, a digital payoff can be approached by a call spread whose strike gap shrinks…
The document proposes a way to construct model inputs for year-on-year and zero-coupon inflation options when example quotes are unavailable. Comparing yields on Treasury Inflation-Protected Securities with yields on nominal Treasury securities of similar…
The document outlines a first-order and second-order method for assigning daily option profit and loss to delta and gamma. Delta contribution is estimated from delta times the underlying price change, while gamma contribution uses one half of gamma times the…
The document asks whether European options can be priced in closed form when the variance gamma model’s drift, volatility, and variance rate are random. It explains that unrestricted random coefficients generally do not yield a closed-form price:…
The document shows how to replicate a payoff that is zero below a lower strike, rises linearly between two strikes, and is capped above the higher strike. The call construction is a bull call spread: buy a call at the lower strike and sell a call at the…
The document explains why a high correlation between a call option’s price and its underlying stock does not conflict with a much smaller option delta. Correlation describes how consistently the two prices move together, while delta estimates the option’s…
The document discusses what traders mean by spot volatility and how it can be expressed through traded instruments. It presents several interpretations: volatility swaps can provide exposure linked to realized volatility; options can express implied…
The document asks whether negative state prices, which may appear when extracting risk-neutral distributions from option prices, can have an economic interpretation. It describes a state price as the current value of a claim paying one unit in a particular…
The document asks why the stated theta of an Apple put appears large when compared with its midpoint and the time remaining before expiration. The question treats the option’s value divided by theta as if it directly represented the number of days until the…
The document compares discounted cash flow intuition for stocks and bonds with derivative pricing. For an option, the future payoff is uncertain and depends on an underlying asset, so a discounted-cash-flow approach would first require a probability…
The document raises a statistical inference problem for a time series of variance risk premia derived from options and realized variance, following Carr and Wu. The author wants to assess whether the series has a statistically significant mean and considers…
The document outlines how to price American options when the underlying pays discrete dividends. Because exercise may be optimal before expiration, the problem is treated as an optimal-stopping problem. A numerical grid method, such as a recombining tree or…
The document describes how strike spacing and the availability of listed equity option series are governed by exchange rules rather than by a single formula chosen by each broker. It gives Cboe examples of standard intervals that vary with the stock price,…
The note explains the notation used for CME 10-year Treasury note option strikes. A quoted strike of 1300 represents 130.0 in futures-price terms, while 1305 represents 130.5; the decimal is implicit. It also states that the minimum strike increment is 0.5.…
The document addresses how to interpret a convertible bond whose yield is negative and how to estimate its implied credit spread. The response attributes the negative yield primarily to the embedded conversion option, which has both conversion value and time…