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 asks whether Monte Carlo simulation can benchmark tree methods for pricing American options with discrete dividends, and how such a simulation should be built. The response explains a key difficulty: Monte Carlo simulates paths forward, while…
The document considers how to set up a finite-difference method (FDM) when the goal is to price one option at a known initial spot, rather than study the option value across many starting prices. The response recommends centering the price grid on the…
The document asks what to study beyond prominent stochastic-volatility models such as Hull–White, Heston, and SABR. It identifies incompleteness as one important issue: stochastic-volatility models may admit multiple equivalent martingale measures, so…
The document explains why futures prices can exceed forward prices when the underlying asset is positively correlated with interest rates. Daily settlement gives a futures position cash flows along the way: a long can reinvest gains at higher rates and faces…
The document asks how two representations of a one-factor Cheyette interest-rate model relate. One uses state variables for the short-rate factor and an auxiliary variance-like process, while the other expresses discounted zero-coupon bond prices using the…
This note distinguishes two related option concepts: implied volatility across strikes and vega, the sensitivity of an option’s price to a change in volatility. It explains that strike-specific implied volatility reflects market pricing and expectations that…
This note asks why a long-dated cash-or-nothing put can be worth more than a comparable call when the underlying follows a geometric Brownian motion with zero drift. It points to Black–Scholes binary option pricing, where call and put values depend on…
The document describes how to bootstrap discount factors from annual fixed-rate OIS swaps with successive maturities. Starting with the shortest swap, it sets the swap’s present value to zero and solves for its terminal discount factor. Each longer swap then…
The document raises a question about the delta-hedging step in the Black–Scholes derivation. It observes that option delta depends on both the underlying price and time, and asks why the change in a portfolio holding a delta-sized position in the asset…
The document explains how to supply a missing historical fixing when pricing floating-rate bonds in QuantLibXL. Its proposed workflow starts from a bond’s previous cash-flow date, converts that date to the relevant index fixing date, then adds a default rate…
The document explains how to price a payer swaption when the forward swap rate follows a normal, or Bachelier, model rather than a lognormal Black model. It expresses the swaption payoff as the positive part of the difference between the swap rate and…
The document discusses staircase-shaped prices from an explicit finite-difference solution of the Black–Scholes PDE for a digital option. Its central explanation is grid based: with a discontinuous terminal payoff, the computed value depends on which…
The document explains why a positive volatility skew can lower the fair value of a binary option, despite a distribution with fatter tails seeming to imply a higher chance of a far out-of-the-money call finishing in the money. The first explanation…
The document asks how European call options are valued in a Bachelier market, where the stock follows Brownian motion with constant absolute volatility. It considers the terminal payoff and conditional expected payoff before maturity, then uses the…
The discussion compares two ways to think about stock price movements: equal dollar changes across stocks or changes proportional to each stock’s price. It explains the standard modeling convention through volatility, which is expressed as a percentage.…
This explanation describes how to infer market expectations for central bank rate changes in Europe using overnight index swap meeting contracts. Each contract spans the effective dates associated with two successive policy meetings. Its fixed rate can be…
This QuantLib example compares the net present value of a fixed-rate bond with a separately calculated discounted cash-flow sum. The two calculations disagree because the zero curve starts several months before the stated valuation date. The accepted answer…
This QuantLib example explains a negative-time error encountered while valuing an interest rate swap. The accepted answer points to a likely mismatch between the curve reference date and cash-flow dates: requesting a discount factor for a date before the…
The document gives a high-level overview of how a bank may value, structure, and manage risk in an autocallable equity product. Pricing typically uses a model calibrated to market option data, with Monte Carlo simulation to estimate the product’s value…
The document distinguishes smile butterfly quotes from market butterflies, also called broker flies, in foreign exchange volatility markets. It explains that at-the-money volatility, risk reversals, and butterfly quotes together describe key features of the…
The document explains how volatility can be used to model a future stock price distribution. It distinguishes the normal distribution of the log price from the resulting lognormal distribution of the price itself. Under a simplified assumption of no…
The document distinguishes volatility quotes by both pricing framework and volatility convention. OIS volatility refers to pricing in a multiple-curve setting, while LIBOR volatility is associated with the older approach in which discounting and forwarding…
Treasury bond futures are linked to a basket of eligible bonds rather than one fixed security. The short can choose which bond to deliver, and the cheapest-to-deliver bond is identified by comparing each bond’s market price with its conversion factor. The…
This troubleshooting example addresses a failed QuantLib bootstrap built from Treasury yields. The error occurs at the one-year instrument because the curve solver cannot bracket a root. The key issue is a mismatch between the quote expected by the…