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 questions whether a bank’s coded option pricing function can sensibly be used to calculate the profit and loss of a short option position. It presents a one-period P&L expression that combines the change in the option’s model price, interest on…
The document explains that an incomplete market generally has multiple equivalent martingale measures rather than a unique risk-neutral measure. For a nonreplicable claim, expected discounted payoffs under these measures yield a range of arbitrage-free…
The document explains how counterparties manage exposure on OTC variance swaps when initial or maintenance margin is not posted. It says that many OTC swaps are governed by a credit support annex, but arrangements vary; without margin, counterparties rely…
The document addresses why nearby option strikes can show sharply different open interest. Its proposed explanation is a preference for round-number strikes: traders may concentrate positions at salient levels such as 7,400, leaving a nearby strike like…
The note explains why the effect of implied volatility on a vertical credit spread depends on the net Greeks of its two option legs. A credit spread sells one option and buys another with the same expiration but a different strike, receiving a net premium at…
The discussion examines why replacing a vanilla option at one strike with a strip of options across nearby strikes can reduce the sharp gamma concentration near expiry. It offers two related explanations: a strip distributes exposure across strikes, and as…
The document uses a one-period, two-outcome stock model to show how stock and call positions can produce a payoff that is the same in either market outcome. With the stock ending above or below the strike, the call’s payoff differs across states. Choosing a…
The document considers how to define carry for a USD payer swaption with a six-month expiry and a ten-year underlying swap. It questions a simple calculation based on subtracting a short-term LIBOR fixing from a ten-year yield, and whether that spread alone…
The note explains the CBOE Put Protection Index as a tail-protection strategy: it holds exposure to the S&P 500 and buys a monthly put struck out of the money. The put premium reduces returns in ordinary markets, while the option can cushion losses when the…
The document challenges the idea that fitting a convex curve in strike-implied-volatility space guarantees an arbitrage-free option surface. Implied volatility need not itself be convex for market prices to be free of arbitrage, and convexity of implied…
The document presents two ways to price a forward-start call whose payoff depends on the asset price at the start date as well as at expiry. One approach conditions on the information at the forward start date and rewrites the value using the price of an…
At expiration, a call with a zero strike pays the stock price when the stock price is nonnegative. The discussion asks whether this means the option should be worth the stock itself before expiration, and whether shareholder rights or counterparty risk…
The question describes an energy option that runs across several months. For each month, its strike resets to that month’s first-of-month index, and daily settlements below that level generate a payoff based on the difference. The question asks how to value…
The document addresses why the Black–Scholes call formula contains different volatility adjustments in d1 and d2 under risk-neutral pricing. It outlines a derivation route: solve the stock price process with its drift set to the risk-free rate, then express…
In a binomial model, the risk-neutral probability is chosen so that the stock’s expected return under that pricing measure equals the risk-free rate. The document explains why a stock’s CAPM expected return is not substituted: option valuation uses…
The document examines the Black–Scholes prices of digital calls and puts as volatility approaches infinity, assuming a zero interest rate. From the model’s formulas, it identifies limiting prices of zero for the call and one for the put, independent of…
The document raises a conceptual question about volatility skew: options at different strikes imply different volatilities, even though implied volatility is often treated as a measure of expected future risk. It asks whether those differences represent…
The discussion explains how Black-Scholes is used in over-the-counter FX vanilla options. Market quotes commonly express implied volatility in delta space; traders convert those quotes into prices using the relevant market inputs, such as spot, rates, and…
The document asks whether a flat implied-volatility skew implies a normal risk-neutral distribution when option prices are converted into a density using the Breeden–Litzenberger relationship. It notes that the density inferred from its stated formula…
The document seeks to interpret a paper's implied-gamma method for fitting option prices across strikes. In the described approach, gamma is a modeler-selected parameter defining a return uncertainty set. For each in-sample strike, the parameter is…
The document sets up a Heston stochastic volatility model for log price and variance, then states an exponential-affine conditional moment-generating function in the terminal log price and variance. It also presents a known expression for an unconditional…
The document asks whether the CBOE SKEW index can serve as the shape parameter of a skew-normal distribution alongside VIX. It explains the index conversion to a skewness measure and notes that the shown skew-normal parameter is constrained to a bounded…
The document discusses pricing and risk analysis for derivatives on dividends paid by constituents of equity indices, with particular interest in dividend futures. One response distinguishes futures from options: dividend futures are linked directly to…
The document concerns a Monte Carlo estimate of a European call option price compared with the Black–Scholes analytical value. The implementation uses antithetic normal draws: each simulated stock path is paired with one generated from the opposite shock,…