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.
12,303 documents
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 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 clarifies how to classify a LIBOR market model extended with stochastic volatility. Adding a stochastic variance or volatility process to the dynamics of forward rates makes the resulting model a stochastic volatility model. The framework is…
The document explains why a square-root diffusion, also known as the Cox–Ingersoll–Ross process, has a transition distribution related to the noncentral chi-squared law. It gives a geometric argument: represent the process through the squared radius of…
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…
The document asks whether daily return skewness and kurtosis can be forecast in a manner similar to variance models such as GARCH, using only daily S&P return data. It raises the presence of fat tails and negative skewness as motivations for studying higher…
The question asks whether an instrument’s historical variance can help predict its future variance and whether variance is stable over time. The response recommends a basic GARCH(1,1) model as a starting point: it uses past information about volatility to…
The document examines an open foreign-exchange forward that lets its holder choose when to draw down or settle within a defined period, while requiring the full amount by maturity. The accepted response treats this flexibility as an option-like feature: at…
The document explains how the return forecasting model relates to a GARCH volatility model. It distinguishes the conditional mean of returns from the residual process: returns equal their model-implied conditional mean plus an error, and the error is…
The document explains the interpretation of two volatility measures: the SPX convexity spread, defined as variance swap volatility minus at-the-money implied volatility, and the convexity ratio, defined as variance swap volatility divided by at-the-money…
The document presents a Python attempt to reproduce results from Duan’s 1995 GARCH option pricing paper. It specifies GARCH parameters and a risk-neutral adjustment, simulates daily variance and innovations, evolves a stock price, and estimates a call price…
The discussion addresses how to turn a series of monthly returns into annualized return and volatility estimates. An answer proposes multiplying the mean monthly return by twelve for an arithmetic annual return estimate, and multiplying the monthly return…
The document examines why a put option’s premium may rise by much less than its new intrinsic value plus its earlier out-of-the-money premium after the underlying falls through the strike. The explanation is that option Greeks describe changes in the total…
The document explains why the familiar square-root-of-time scaling for volatility applies directly to aggregated log returns under zero autocorrelation, but not generally to discrete returns. It first expresses the variance of an aggregate log return in…
The document examines whether a fund’s reported NAV may be smoothed by comparing annualized volatility estimates from daily, weekly, and monthly returns. It explains that smoothing can make daily volatility look too low, while positive autocorrelation in…
The document examines the relation between an option’s volatility, the underlying stock’s volatility, and the option’s elasticity. It asks whether this relation depends on the Black–Scholes model, referencing a textbook proof but supplying no derivation of…
The document discusses what an intraday volatility estimate means in a market impact model and how to construct one when a trade begins shortly after the market opens. The response interprets the paper’s reference to every transaction during a day as an…
The document asks how to compare bond return volatility before and after a scheduled shock, and whether separate GARCH fits across event windows provide a sound test. It explains that returns can be dependent while remaining uncorrelated, so a conventional…
The document derives a log-linear approximation for the risk-neutral expectation of next-period return variance in a stochastic-volatility model with recursive preferences. It starts from the stochastic discount factor and rewrites the approximation using…
The document derives an approximate mark-to-market value for a variance swap partway through its life. It splits total realized variance into the portion already observed and the expected variance over the remaining period, then weights each by its number of…
The document frames a model selection question for calculating option Greeks from a fitted volatility surface. It compares a local volatility model that matches the observed vanilla surface closely with a stochastic volatility model that may better represent…
The document explains why Vibrato Monte Carlo can estimate sensitivities when a derivative has a discontinuous payoff and full valuation under the model is difficult. It contrasts pathwise sensitivities, which require differentiating the payoff, with the…
The document compares analytic approximations for American option exercise boundaries, including Kim’s integral equation and the Whaley approximation, with numerical PDE methods. It argues that PDE solvers can be preferable when pricing requires reliable…
The document derives a European call price when the forward price follows a lognormal process with volatility that changes deterministically over time. The option expires at an earlier date than the forward's delivery date. Integrating the instantaneous…