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
This note describes a numerical approach to pricing European and American options under Kou’s double-exponential jump-diffusion model. The implementation uses a Crank-Nicolson time scheme for the partial integro-differential equation, a nonuniform spatial…
This note outlines a transformation of the Black-Scholes option-pricing equation into a diffusion equation, then asks how to simulate the transformed PDE numerically. It gives the variable substitutions, the resulting heat-equation form, and a transformed…
The document describes how market makers can hedge index options without trading every constituent in the underlying equity basket. For options written on index futures, a single option’s delta exposure can be offset by trading the corresponding futures…
The document considers a portfolio formed from several contingent claims whose prices depend on one underlying asset. It explains why differentiating the portfolio value as a weighted sum can be misleading: the weights may change over time, but the…
The document distinguishes the mechanical effect of interest rates on a stock forward price from the broader economic effect of rates on the underlying share price. Under a no-arbitrage carry argument for a non-dividend-paying stock, the forward price is the…
The document explains why changing interest-rate or dividend-yield inputs can make an option implied-volatility smile appear unusual, especially for in-the-money options. Under Black–Scholes intuition, a higher interest rate raises a call’s modeled value; if…
The question asks whether Black–Scholes can use an expiration measured in hours after converting that duration to years, and why an option calculator returns a different value when the input changes from a day to an hour. The answer interprets the change as…
The document explains how derivative volatility relates to the volatility of its underlying asset through elasticity, also called leverage or lambda. Elasticity measures the derivative’s percentage price response to a one-percent change in the underlying,…
This document asks how to translate an earnings event volatility estimate into an implied one-day expected return using a formula from a volatility trading text. The formula combines the exponential of half the event variance with the normal cumulative…
The document frames discrete delta hedging as a tradeoff: more frequent rebalancing can reduce hedge error but raises transaction costs, while less frequent trading lowers costs and leaves greater residual risk. It argues that there is no single practice…
The document addresses how to tell whether listed call options are European or American when searching for real market data. Its key distinction is that US options on individual securities are generally American, while options on indexes are generally…
The discussion explains why an arbitrage-free call price curve should be convex in strike. A butterfly spread combines calls at neighboring strikes so that its payoff is nonnegative across terminal prices and positive over an intermediate range. If the call…
The document explains how to value a payoff equal to a forward LIBOR rate fixed and paid at the start of its accrual period by translating it into a payoff at the period's end. Under the assumed risk-neutral framework, the rate known at the start can be…
The document asks whether every twice-differentiable call-price surface across maturities and strikes can be generated by a local volatility function of time and the underlying asset price. It points to the assumption used in Dupire’s approach and seeks a…
The document explains dual delta as the sensitivity of an option’s value to its strike, distinguishing it from ordinary delta, which measures sensitivity to the underlying price. In the Black–Scholes–Merton framework, call dual delta is negative and relates…
The document derives Black–Scholes prices for two contingent claims under geometric Brownian motion. The first pays the positive part of the difference between the stock price at maturity and its price at an earlier observation date. Conditioning on the…
The document discusses how bid-ask spreads affect a minimum-variance portfolio of stock and options. It argues that transaction costs can shift the efficient frontier and change the optimal portfolio. For small trades, it offers an approximation based on the…
The document presents a Python workflow for fitting a SABR volatility smile with QuantLib. The example supplies option strikes and implied volatilities, constructs a NoArbSabrInterpolatedSmileSection, sets initial values for alpha, beta, nu, and rho, and…
The document explains the options phrase “buy back a short strike” as purchasing an option previously sold, thereby closing that short position. The example describes placing an order to buy it back for five cents per contract, with a good-till-canceled…
The document describes a local volatility pricing implementation that derives volatility from an SSVI implied volatility surface using Dupire's formula and finite differences. The author checks the implementation by repricing the vanilla options used to…
The document concerns numerical evaluation of the integral used to price a call option under the Heston stochastic volatility model. The question asks whether Simpson’s rule or Gauss–Legendre quadrature is suitable and seeks MATLAB or Scilab implementations.…
The post studies option pricing under a time-dependent Heston model in which mean reversion changes across time intervals while other listed parameters are held fixed. It compares prices from an Elice method and two Monte Carlo approaches, Milstein and…
The document outlines a proposed workflow for pricing a quanto option: estimate marginal distributions for the underlying asset and exchange rate, connect them with a copula, then calculate the expected payoff under the resulting joint distribution. Its main…
This document asks why a 15-period binomial model gives an unexpected value for an American put under specified Black–Scholes assumptions. It does not provide a corrected price or a specific diagnosis. Instead, the response offers a general debugging…