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 wavelet analysis can smooth noisy prices in illiquid instruments and whether higher time frame data could add context to lower time frame estimates. It explains that wavelets decompose a time series into components at different…
The document challenges a proposed rule linking an option’s time value to its delta. The claim is that when time value makes up at least a specified fraction of an option’s price, delta must be below a corresponding threshold. A Black–Scholes call example…
The document describes a calculation of the probability that a price following geometric Brownian motion exceeds a threshold. The questioner reports a probability of one where the supplied solution gives a lower value, then identifies the source of the…
The document asks how to estimate Student-t distribution parameters for Value-at-Risk analysis of assets whose returns are not normally distributed. One answer connects the Student-t degrees of freedom to the tail shape exponent and suggests estimating that…
The document asks how to plot a one-month implied volatility smile when call and put implied volatilities and option deltas are available, but spot and strike prices are missing. It notes that volatility smiles are often displayed against delta, so the…
The document describes an attempt to assess a GARCH model fitted to S&P 500 returns. It shows a rolling backtest setup and reports difficulty using mean absolute percentage error (MAPE) to compare predicted and realized values. The reply explains that MAPE…
The document corrects an attempt to infer the mean and variance of an Ito process by multiplying its instantaneous drift and variance rates by elapsed time. An Ito differential is shorthand for an integral over the path: the state at time t equals its…
The document asks whether large options positions can make the underlying’s price respond to derivatives activity, especially when dealers must hedge positions with high gamma. It describes the proposed feedback: negative gamma hedgers may buy into sharp…
The note clarifies that buying volatility is not always identical to buying an option, although vanilla options generally rise in value when implied volatility rises, all else equal. For a long option delta-hedged under a Black–Scholes model, it gives a…
The document considers pricing a call-like payoff on the difference between the product of two correlated geometric Brownian motions and a scaled version of one process. It explains how to express the product process as a single geometric Brownian motion,…
The document presents implied volatility as a way to express option prices in familiar Black–Scholes terms. Because the model maps a vanilla option price to a volatility input, implied volatility helps compare options across strikes and maturities, track…
The document explains why adding jumps to an option pricing model represents a different risk from simply increasing diffusion volatility. In a diffusion model, variability grows with the square root of time, while a Poisson jump component contributes…
The document clarifies how conditional variance depends on the variable being modeled, in response to a question about comparing implied volatility with GARCH forecasts. Under information available at the prior time, a price and its simple change have the…
The document asks how to calculate volatility from three closing prices: 101, 100, and 102. The response treats the changes between consecutive closes as returns and says their standard deviation can serve as a proxy for historical volatility. With three…
The document asks how to choose volatility and interest-rate inputs when pricing American puts with a binomial model and comparing estimates with market prices. The author proposes using the standard deviation of recent log returns for volatility and…
The document summarizes a distinction between local volatility and stochastic volatility models when representing equity option markets. It reports that local volatility can fit observed vanilla option prices but may produce unrealistic forward volatility…
The document examines whether an option’s extrinsic value, also called time value, follows a normal or lognormal shape as the underlying price changes. It describes an interpretation of the Black–Scholes call formula using a lognormal distribution of future…
The document asks whether Black–Scholes call and put prices are convex as functions of implied volatility. The answers explain that convexity can vary with moneyness rather than holding uniformly. Vega, the derivative of option value with respect to…
The document explains why a callable bond generally has a higher yield to maturity than a comparable noncallable bond. Its price can be viewed as the value of the noncallable bond minus the value of the issuer’s embedded call option. Since that option has…
The document describes pricing a plain vanilla interest rate swap from a discount curve in QuantLib and simulating short-rate paths with the one-factor Hull–White model. It includes a detailed setup for fixed and floating legs, historical index fixings, a…
The document presents the risk-neutral Variance Gamma stock model, including its drift adjustment and the time-changed Brownian representation of the log return. It describes sigma as controlling volatility, while nu and theta jointly determine asymmetry and…
The document explains why the VIX should not be expected to equal a quoted at-the-money implied volatility for SPX or SPY options. The key distinction is that VIX represents a variance-swap-style measure derived from a broad range of SPX option strikes,…
The document outlines ways to investigate persistent losses at a trading desk that sells structured bonds with embedded options and hedges them in the market. It first asks whether the products and hedges were intended to earn zero net P&L. If the desk…
The discussion explains robust standard errors in GARCH estimation as a quasi-maximum-likelihood approach associated with White’s covariance estimator. The central point is robustness to a misspecified conditional distribution: for example, estimation can…