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 asks whether credit markets have a volatility index comparable to familiar measures for equities and interest rates. Its answer points to four daily implied-volatility measures covering North American investment-grade and high-yield CDX indices,…
The document asks whether solutions to a linear stochastic differential equation become differentiable when Brownian noise is filtered through the system’s dynamics. The question contrasts Brownian motion’s irregular paths with the intuition that a colored…
The document asks why volatility models used to estimate Value at Risk may pass a backtest at a 5% confidence tail while failing at a 1% tail. The response says this pattern is common: as the tail becomes more extreme, the assumed return distribution matters…
The document presents an implementation question about fitting a Heston–Nandi GARCH model by maximum likelihood. The author scales log returns, recursively computes conditional variance and standardized residuals, and uses differential evolution to search…
The document considers Monte Carlo pricing of barrier options under a Dupire local-volatility model. The questioner has calibrated smooth implied-volatility surfaces and calculates local volatility at simulation dates, but finds daily stepping slow for long…
The document asks how to obtain an FX option’s volatility from a surface quoted by delta and tenor. The proposed workflow first reads the at-the-money volatility, determines the option’s corresponding delta, then interpolates the volatility surface at that…
The document shows how to express a structured note’s terminal payoff as a combination of the underlying index and call options. In the example, the payoff follows the index below the principal level, stays flat over an intermediate range, and gains…
This note describes a numerical approach to pricing European and American options under Kou’s double-exponential jump-diffusion model. The implementation uses a Crank-Nicolson time scheme for the partial integro-differential equation, a nonuniform spatial…
The discussion considers what risk information can be inferred from a portfolio snapshot containing prices, position values, share counts, and stock betas, but no time series. One response suggests using beta to approximate a stock’s volatility if market…
The document identifies a stochastic volatility specification in which the asset follows geometric Brownian motion while volatility is the exponential of an Ornstein–Uhlenbeck process. The log volatility mean-reverts, and its driving Brownian motion may be…
The document explains why annualized volatility is commonly calculated by multiplying monthly return volatility by the square root of twelve. Under independent, identically distributed monthly log returns with finite variance, annual log return is the sum of…
The document explains why changing interest-rate or dividend-yield inputs can make an option implied-volatility smile appear unusual, especially for in-the-money options. Under Black–Scholes intuition, a higher interest rate raises a call’s modeled value; if…
The question asks whether Black–Scholes can use an expiration measured in hours after converting that duration to years, and why an option calculator returns a different value when the input changes from a day to an hour. The answer interprets the change as…
The discussion outlines ways to study high-frequency quotes and trades when observations arrive at uneven intervals. It recommends first defining the target, such as volatility or correlation, and accounting for how measurement intervals affect the…
The document explains how derivative volatility relates to the volatility of its underlying asset through elasticity, also called leverage or lambda. Elasticity measures the derivative’s percentage price response to a one-percent change in the underlying,…
This document asks how to translate an earnings event volatility estimate into an implied one-day expected return using a formula from a volatility trading text. The formula combines the exponential of half the event variance with the normal cumulative…
The document considers how to estimate volatility when a return series contains complete monthly observations plus a final observation covering only part of a month. It proposes a weighted variance calculation: first scale the partial-period return to an…
The document discusses numerical instability when optimizing a custom GARCH quasi-maximum-likelihood objective in R. Its proposed safeguard is to clamp each filtered conditional variance to a chosen lower and upper limit, preventing extreme parameter values…
The document addresses whether an exchange rate and its reciprocal, such as a currency pair and the inverted pair, should have the same at-the-money implied volatility. It models one exchange rate as a diffusion with proportional volatility and applies Itô's…
The document asks whether every twice-differentiable call-price surface across maturities and strikes can be generated by a local volatility function of time and the underlying asset price. It points to the assumption used in Dupire’s approach and seeks a…
The document explains dual delta as the sensitivity of an option’s value to its strike, distinguishing it from ordinary delta, which measures sensitivity to the underlying price. In the Black–Scholes–Merton framework, call dual delta is negative and relates…
This document describes an R function for simulating multivariate constant conditional correlation GARCH processes. It distinguishes the original CCC model, where ARCH and GARCH parameter matrices are diagonal, from an extended version that permits full…
The document presents a Python workflow for fitting a SABR volatility smile with QuantLib. The example supplies option strikes and implied volatilities, constructs a NoArbSabrInterpolatedSmileSection, sets initial values for alpha, beta, nu, and rho, and…
The document describes a local volatility pricing implementation that derives volatility from an SSVI implied volatility surface using Dupire's formula and finite differences. The author checks the implementation by repricing the vanilla options used to…