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 discussion considers statistical and numerical software for options statistical arbitrage, with needs including regression and optimization and priorities such as speed, usability, and compatibility with C# and C++. One answer lists managed .NET and C++…
The discussion distinguishes the mathematical use of Feynman–Kac from financial pricing under a chosen numeraire. When a probability measure changes, the same process may acquire a different drift when written using the Brownian motion under the new measure.…
The document raises a model implementation question about inferring a firm’s leverage from equity option prices. It describes using put implied volatilities within a structural credit risk framework, citing the Hull, Nelken, and White approach and a related…
This note outlines the Gamma-Vanna-Volga approach for constructing an implied volatility curve from three traded vanilla options. Starting from a local stochastic volatility setting, it relates an option’s price changes to delta, gamma, vega, volga and vanna…
The document explains why finite-difference estimates of option Greeks may disagree with analytical Black–Scholes–Merton values in QuantLib. Numerical estimates depend on the size of the perturbation: reducing the volatility increment improves the vega…
The document explains how to value a log contract paying minus twice the logarithm of the asset price at maturity under the Black–Scholes model. It starts with the risk-neutral price dynamics, then applies Itô’s lemma to derive the drift and volatility of…
The document addresses risk management for an over-the-counter vanilla FX option book as Morocco transitions toward a floating exchange rate. It identifies two exposures to consider: a period of elevated currency volatility and a large one-time repricing of…
The document describes a practical copula-based approach for pricing constant-maturity-swap spread options. The inputs are the basis-point volatilities of the two rates and a correlation estimate. In the described workflow, these inputs are used to fit the…
The document derives bounds for a call price at a lower strike when prices at two higher strikes are known. Its example gives call values at strikes 100 and 90, then asks what can be inferred at strike 80. Convexity supplies a lower bound, while a payoff…
The document explains how to value a European option with payoff max(S1 − K·S2, 0) when both assets follow geometric Brownian motion under Black–Scholes assumptions. It presents two equivalent viewpoints: treat the payoff as a rainbow option on S1 and K·S2,…
The note explains why a traded stock can be treated as a special case of a derivative in a pricing equation. It distinguishes the deterministic pricing function v(t,S), whose inputs are time and the underlying price, from the stochastic price process V_t…
The document addresses how implied volatilities from puts and calls are represented in a volatility smile by strike. Under put–call parity, a put and call with the same strike and expiry imply the same volatility in theory, after accounting for intrinsic…
The document asks whether forecasts of realized volatility over a short interval can improve delta hedging or gamma scalping for an option with a longer remaining life. It starts from the familiar intuition that hedged option profit and loss is related to…
The document asks how to generate a Brownian bridge between two different simulated price points in a geometric Brownian motion path. The setting is an arithmetic Asian option whose averaging window begins before expiration, leaving a short interval between…
The document explains how a synthetic put can be approximated through delta-based adjustments to a stock portfolio. A put’s delta measures how its value changes for a small change in the underlying stock price; because put delta is nonpositive, the hedge…
The document addresses why a MATLAB numerical integral for an expected call payoff can disagree with an analytic calculation under geometric Brownian motion. It derives the terminal stock price distribution: the logarithm of the terminal price is normally…
The document asks how to estimate the realized volatility of an asset over a trading day from intraday tick data, in the context of estimating the profit and loss of a delta-hedged option. It starts from the approximation that gamma-related gains or losses…
The document surveys categories of systems used by hedge funds for automated trading and explains why platform choice depends on the instrument and workflow. It names examples spanning Bloomberg order and execution tools, futures-focused systems,…
The discussion examines whether buying a European call and shorting a chosen number of shares can guarantee a profit at expiry. It sets up a portfolio containing the call, short stock, and a bond. The initial portfolio value is constrained to zero, then the…
The document describes a proposed comparison of calibration methods for Merton’s jump-diffusion model using S&P 500 option quotes. Its baseline method minimizes root mean squared error between market prices and prices computed with the Carr–Madan formula,…
The question asks whether Black–Scholes provides an analytic value for a payoff that activates when the underlying first reaches an upper barrier and then depends on the terminal asset price. The answer observes that the barrier event is equivalent to the…
The document considers how to extend an arbitrage-free interpolated equity option price curve beyond the last observed point. The questioner reports that a cited smile extrapolation technique produced prices that could admit arbitrage, and expresses doubt…
The document asks about a boundary condition in a textbook treatment of perpetual American options. The setup includes a one-shot derivative that pays a fixed amount when the stock first reaches a specified level. The questioner accepts that its value equals…
This note considers an option on an electricity and gas spread that can be exercised hourly, even though liquid gas prices are observed only daily. The question proposes modeling seasonality-adjusted log prices as correlated mean-reverting Ornstein–Uhlenbeck…