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 post describes an implementation problem in a bivariate tree used to price American options under the Heston stochastic-volatility model. The author reports getting a negative probability for the middle stock-price move while following a published tree…
The document discusses implementation options for smoothing an implied volatility surface while enforcing arbitrage-free conditions. One response characterizes this as a difficult task and suggests that ready-made implementations may be uncommon outside…
The document presents a C++ implementation of a Leisen-Reimer binomial tree for pricing American options and describes cases where its output becomes NaN. The example computes transformed probabilities from two standardized option inputs, then uses those…
The document clarifies that Itô’s formula is a mathematical tool for analyzing a process, rather than a pricing method on its own. For a European option, it describes the value as a conditional expectation of the terminal payoff given the current state.…
The document works through an algebraic attempt to derive equation 8 in Derman and Kani’s implied binomial tree for local volatility. Starting from an earlier call-price relation, the answer substitutes the risk-neutral probability, rearranges terms to…
The document explains why a pricing partial differential equation can be useful for deriving the relationship between option vega and gamma even when volatility is constant. In the Black–Scholes setting, volatility is a parameter of the differential…
The discussion examines whether a long call butterfly must have a strictly positive premium under no-arbitrage. A butterfly’s strike-price second difference is nonnegative when call prices are convex in strike. In a smooth model, this difference approximates…
The question asks why the Black–Scholes quantities involving the stock price and the normal density at d1 equal the discounted strike multiplied by the normal density at d2. The accepted derivation substitutes the standard normal density, uses the relation…
This document collects suggested online lectures, conference talks, courses, and notes related to quantitative finance. The topics range from financial mathematics, risk-neutral pricing, delta hedging, and option strategies to volatility, interest rate and…
The document asks whether forward-looking volatility estimates can improve an estimate of an asset’s CAPM beta for the coming month. The proposed approach replaces historical market variance with VIX-implied volatility and historical asset volatility with…
The document asks how to use a Python-defined local volatility function with QuantLib’s Black–Scholes process. It clarifies that a local volatility term structure handle cannot simply be constructed from an arbitrary Python function in the shown way; the…
The document explains how to translate annualized implied volatility into a one-period price move. Under the Black–Scholes interpretation, volatility is the standard deviation of log returns, so a sigma-scaled move is expressed by multiplying the current…
The document considers whether single precision is adequate for option pricing and related calculations, including Black–Scholes pricing, implied volatility solved by Newton–Raphson, and volatility smile fitting with Levenberg–Marquardt. It frames the…
The document considers whether a call option's quoted price can determine the price of a put with a different strike, when both share the same underlying, expiry, and volatility assumptions. In the stated zero-rate example, the call has spot 20, strike 25,…
The document asks how to obtain a reliable benchmark for American option values under the Heston stochastic-volatility model, with the goal of assessing bias in least-squares Monte Carlo (LSM). It considers a stochastic-volatility binomial model but asks for…
The document surveys how option theory can represent real assets and corporate financing decisions. Models may combine the option to invest in growth, debt and equity issuance, and an endogenously chosen default threshold. This framework extends the…
The document examines a perceived failure of self-financing in a two-period binomial model. The question computes the portfolio value before and after rebalancing and obtains a nonzero difference, using this as evidence that the strategy may require outside…
The document outlines end-of-day analysis for options market-making desks. Beyond explaining profit and loss through option sensitivities, it describes monitoring the book’s opening and closing positions, market-driven changes, newly executed trades, and…
The document explains why a derivative’s discounted value can be a martingale under a risk-neutral measure even though an arbitrary function of a martingale need not be one. In a Black–Scholes setting, it represents the derivative through a self-financing…
The document considers replacing random scenario generation with equally spaced probability points when estimating a terminal payoff distribution, using a European call as an example. In a single-variable setting, mapping quantiles through a payoff can be…
The document examines the stochastic process of a dividend-paying stock and a delivery contract that represents receiving the stock at a future date. It focuses on applying Ito's lemma to the contract value, defined as the stock price adjusted for dividends…
This discussion explains why delta alone cannot uniquely identify an option strike. Delta is calculated from an option pricing model and depends on inputs such as spot, maturity, rates, option type, and volatility. To invert a reported delta for strike, the…
This discussion diagnoses a mismatch between a foreign exchange vanilla option price calculated with a Black–Scholes framework and a Bloomberg quote. The replies focus on conventions that can materially change the result: whether the exchange rate is quoted…
The answer introduces several Fourier approaches to option pricing and explains what mathematical background helps make them understandable. Carr–Madan transforms a damped option-price function across log strikes; other methods transform the risk-neutral…