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 contrasts how corporate and public pension plans account for liabilities and asks whether public plans need tail-risk protection. Under the simplified description, corporate plans discount liabilities using market interest rates, so rate changes…
The document compares fitting local or stochastic volatility models, such as Heston, to option prices versus to Black–Scholes implied volatilities. In an idealized Black–Scholes setting, price and implied volatility map one-to-one, so either representation…
The document asks how to infer a local volatility function from a surface of American option prices. It considers a stock model with diffusion driven by a state- and time-dependent volatility, with the aim of reproducing the observed prices across strikes…
The document examines why implied volatility in election-related stocks did not uniformly fall after the Georgia Senate runoff was called. The question expected an event-driven volatility crush, yet one renewable-energy stock rose while its volatility stayed…
The answer describes estimating weak convergence for an Euler discretization of a stochastic differential equation by tracking how an expected payoff changes as the time step is refined. Under regularity conditions on the drift, diffusion, and payoff, it…
The document raises a practical problem in recovering a stock’s risk-neutral distribution from option prices. The author first derives implied volatilities and constructs densities, but observes that the plotted right tail becomes less complete for longer…
This discussion considers buying calls to limit the cost of covering a short stock position during a squeeze. A call sets an exercise price for the potential cover, whereas a stop buy order can become a market order with an uncertain fill price. The option…
This explanation derives the first and second derivatives of an option value after changing variables from the underlying price S to its logarithm ξ = log(S). It represents the value as a discounted function of the transformed variable, then applies the…
The document explains how a known cash dividend affects a binomial stock-price tree used to price a European put. The question concerns a dividend paid between the two steps: the stock price drops to its ex-dividend level on the payment date, then follows up…
The document addresses whether a reverse convertible coupon should exceed the sum of a risk-free rate and the premium from a short put because the put premium could earn interest after inception. The answer emphasizes that a buyer purchases a packaged…
The document describes calibrating a parametric implied volatility smile from foreign exchange option quotes. The market supplies at-the-money volatility, a delta-based market strangle quote, and a risk reversal. The calibration seeks parameters that pass…
The document raises the problem of estimating a stock price probability distribution from call option prices using a procedure attributed to Interactive Brokers. The described approach solves a pair of linear equations at each strike, but the resulting…
The document examines why least-squares Monte Carlo (LSMC) regression often uses only in-the-money paths when valuing American options, and how to adapt path selection to callable convertible bonds. The explanation frames this filter as a way to omit paths…
The note explains how exchanges maintain a set of upcoming monthly expirations for listed stock options. Under the described cycle system, each underlying is assigned a quarterly sequence beginning in one of three possible months. As an expiration passes,…
The note proposes a way to value backward-looking compounded risk-free-rate caplets when a liquid volatility surface is available for forward-looking LIBOR options. It separates the problem into estimating the relationship between LIBOR and RFR volatility,…
The document asks whether an American put must have Gamma at least as large as the Gamma of a matching European put when early exercise is not optimal. The response challenges that proposed ordering by appealing to continuity across the American option’s…
The document considers how to use broker-provided bid and ask implied volatilities and Greeks when building an option volatility surface. It asks whether to take the midpoint, how to handle a missing side, and whether implied volatility values above one…
The document raises a valuation question about a cleared cancellable interest rate swap with Bermudan-style early termination rights. The term sheet does not identify which party owns the termination option, and the questioner asks whether the option holder…
The document clarifies why a binomial stock model can use different probabilities for the same up and down outcomes. The random variable’s possible values, represented by the up and down factors, remain fixed when moving between probability measures. What…
The document reviews a one-period binomial replication for a put and diagnoses an error in the cash position. The stock holding is calculated from the difference between the option payoffs in the up and down states. The cash amount must then be chosen so…
The document explains how to transform the Black–Scholes partial derivatives after changing variables from stock price and calendar time to log moneyness and scaled time. It focuses on the second derivative with respect to the stock price, building from the…
The document distinguishes an option's exercise date from its expiration date. Exercising means using the option right on a permitted date and receiving the payoff associated with that date. For an American option, the holder may choose an exercise date…
The document considers a call option on a foreign equity with its strike denominated in the foreign currency, while the payoff is valued in domestic currency. At expiration, the domestic payoff is the exchange rate multiplied by the positive difference…
The question examines the BlackCallableFixedRateBondEngine in QuantLib using a zero-coupon callable bond with a call price well below the bond's expected value, a nearly zero volatility, and a flat interest-rate curve. The author expects the bond's value to…