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.
10,263 documents
The document examines valuing a corridor variance swap partway through its life, when realized variance is known for the elapsed period but future variance remains uncertain. It explains that a standard variance swap can be replicated in theory by weighting…
The discussion classifies second-order partial differential equations as elliptic, parabolic, or hyperbolic, then connects those types to financial models. Option values derived from Itô processes generally have a first-order time derivative and second-order…
The discussion examines what “vega” should mean when an exotic option is priced with a model beyond Black–Scholes. It raises several possible bump conventions: shifting local volatility, changing stochastic volatility parameters, or bumping an implied…
The discussion derives the drift of a pricing kernel formed by multiplying a state-dependent discount factor by a function of state variables that follow Itô processes. The key point is that the accumulated integral of the discount rate has finite variation:…
The document addresses how to find risk-neutral probabilities that an asset finishes above a threshold at a later observation date, conditional on having stayed below earlier thresholds. A single-date Black–Scholes probability does not capture those multiple…
The document explains a result for American and European digital calls with the same strike and expiry, when the underlying follows Brownian motion without drift and interest rates are zero. A digital pays when its exercise condition is met. The American…
The document discusses how traders construct implied-volatility smiles and surfaces from option quotes. Its central guidance is to use liquid market instruments across strikes rather than building a curve from calls alone or puts alone. For many European…
The document outlines a calculation for pricing an at-the-money interest rate cap under the Vasicek short-rate model. It derives zero-coupon bond prices from affine term-structure functions, uses those prices to calculate quarterly simple forward rates and…
The document outlines a way to estimate a five-year UK gilt yield, and a potential futures price, when the contract is illiquid and only a few related market quotes are available. It first fits a US Treasury curve to short and longer maturity rate…
The document compares put exercise probabilities under the Black–Scholes–Merton framework. It distinguishes a probability calculated using the stock’s expected return from the risk-neutral probability derived using the risk-free rate, and asks why the…
The document asks how to evaluate a calibrated Cox-Ingersoll-Ross short-rate model against historical observations, noting that the ordinary R-squared from a linearized parameter fit may not provide a meaningful goodness-of-fit measure. The response does not…
The document asks what calibration of an option volatility surface means, how often it should occur, and what determines its timing. It starts from the familiar implied volatility smile for one expiry and asks whether a spline with anchor points can…
The document asks how stock borrow rates should enter the pricing of short-dated single-stock options. The proposed approach is to compare European and American option values, then use put-call parity relationships across strikes to estimate funding and…
The document explores why correlation between a foreign underlying asset and the exchange rate matters for a quanto option, whose payoff is fixed in the holder’s currency. The questioner compares extreme positive and negative correlation cases in a simple…
The document considers a short over-the-counter foreign exchange forward hedged with a long exchange-traded currency future when their maturities differ. It identifies counterparty exposure if the forward counterparty defaults while the futures position…
The document presents a method for analyzing whether a stochastic process is a martingale: apply Itô’s formula to obtain its differential, then inspect the coefficient of the time increment, or drift. A zero drift makes the process a local martingale under…
The document shows a QuantLib setup for pricing European call options with the analytic Black–Scholes engine. It compares outputs for several strikes with an online calculator and asks whether QuantLib supports Black ’76. The response identifies two inputs…
The document describes a static replication result for a European payoff using calls and puts across a range of strikes. For a twice continuously differentiable payoff function, the second derivative determines the weights applied to vanilla options. The…
The document derives bounds on the derivative of a call price with respect to strike. It compares calls with nearby strikes and uses the fact that, at maturity, the difference between their payoffs is bounded by zero and the negative of the strike gap.…
The document asks how to price equity quanto options with a local-stochastic volatility model, building on a proposed Heston approach that adjusts equity and variance dynamics for quanto effects. The supplied answer recommends modeling both the equity and…
The document explains how forward rates relate to the dates in an interest rate swap's floating leg. It distinguishes payment dates, accrual dates, reset or fixing dates, and rate valuation dates. The rate being estimated is associated with the period over…
The document compares Monte Carlo Value at Risk with a parametric approach. Monte Carlo methods can be useful when a portfolio contains nonlinear or path-dependent positions, such as options, mortgage-backed securities, or convertible bonds. The method…
The document asks how to price American options in QuantLib when the contract is specified by a time to maturity rather than fixed calendar dates. Its suggested approach is to choose a start date, such as today, and add a period representing the duration in…
The document discusses how to interpret exercise decisions for options with multiple exercise dates. It uses a European call to illustrate the basic rule: at expiry, exercise when doing so gives a positive payoff. For a Bermudan option, it compares immediate…