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 sets up a Heston stochastic volatility model for log price and variance, then states an exponential-affine conditional moment-generating function in the terminal log price and variance. It also presents a known expression for an unconditional…
The document asks whether the CBOE SKEW index can serve as the shape parameter of a skew-normal distribution alongside VIX. It explains the index conversion to a skewness measure and notes that the shown skew-normal parameter is constrained to a bounded…
The document discusses pricing and risk analysis for derivatives on dividends paid by constituents of equity indices, with particular interest in dividend futures. One response distinguishes futures from options: dividend futures are linked directly to…
The document asks how to represent a portfolio’s vega when its original volatility surface has many strike pillars but the target surface retains only three. Vega is described as distributed across the original grid of maturities and strikes, leaving the…
The document considers the square of a geometric Brownian motion and asks how to derive its stochastic differential and quadratic variation. Applying Itô’s lemma to the function that squares the price adds a drift adjustment from the second derivative, while…
The document explains how to specify a three-branch asset-price tree when a single-period move can be up, middle, or down. The three branch probabilities and three move sizes initially leave six parameters. Probability normalization and matching the expected…
The document asks which parametric forms are commonly used to fit implied volatility smiles in VIX markets. It situates the question against SPX options, where the author says stochastic volatility-inspired and surface stochastic volatility-inspired forms…
The document discusses whether GARCH variance estimates remain useful when returns have heavy tails. It relays the concern that if a return distribution has a tail exponent near three, its fourth moment may be infinite, making the variance of squared…
The document discusses using proxy time series when a risk factor lacks enough historical observations for market risk measurement. It contrasts older Basel II guidance with the newer Fundamental Review of the Trading Book (FRTB), where insufficient real…
The document clarifies why option volatility models may express moneyness using the underlying’s forward price or spot price. It distinguishes this choice from forward volatility, which means volatility over a future time interval. Forward based moneyness…
The document examines a claim that at-the-money-forward implied volatility in the Heston model is below the square root of expected variance. The response connects variance swap volatility to an expectation over squared values of a transformed, or modified,…
The document addresses finite difference pricing when an exotic option has a discontinuous payoff, such as a binary or barrier, and nearby vanilla strikes are used for hedging. A coarse asset-price grid may fail to represent the payoff boundary accurately…
The document explains why squared returns divided by estimated conditional variance can be used to check a GARCH model. Under the model, returns are written as conditional volatility times an independent, zero-mean, unit-variance innovation. A GARCH(1,1)…
The document surveys modeling concerns when interest rates can fall below zero, focusing on products whose pricing frameworks assume lognormal rates. Black-style option formulas and some volatility conventions become unsuitable when rates may be negative.…
The document examines how to derive the variance of the short rate in the Cox–Ingersoll–Ross model, whose diffusion volatility depends on the square root of the rate. One proposed derivation transforms the rate, applies Itô’s lemma to its square, and then…
The document asks whether stock price paths can be simulated with different models while holding the initial price and historical mean and standard deviation fixed. It names geometric Brownian motion (GBM), Merton jump diffusion, and Heston stochastic…
The discussion estimates the one-day profit and loss of a short call when the underlying moves sharply. The answer first assumes the position is delta hedged, so the starting portfolio has no first-order exposure to the spot move. It then treats the stated…
The discussion asks how to describe the sampling distributions of estimated autoregressive and moving-average coefficients in an ARMA-GARCH model. The answer gives the standard asymptotic result: under suitable assumptions, parameter estimates are consistent…
The document explores delta and vega hedging, exotic-product risk, and pricing when a derivative references an investment fund. The question highlights practical constraints: fund shares may be difficult or impossible to short, listed options may be…
The document asks how to identify, from a stock universe, the three names likely to produce the highest premium for a worst-of put. Its payoff depends on the weakest normalized asset outcome at maturity, so the question concerns both individual price…
The document describes a one-expiry SPX implied-volatility calibration using the SSVI parameterization. The initial implementation produced implausible estimates when fitting market option prices, and the author also found that the fitting objective had…
The document corrects a proposed method for estimating a lower-tail portfolio return threshold using a Student-t distribution. It explains that the standard deviation of observed returns should not be divided by the square root of the sample size when…
The document asks why a single-look CMS cap and a CMS floor with the same expiry and at-the-money strike can show different vega exposures. The observation comes from pricing a ten-year-expiry CMS30 cap and comparing it with the corresponding floor. The…
The document raises a risk-management problem for a vanilla option that terminates if realized volatility over the option’s life exceeds a preset barrier. Such a condition could reduce the option’s price, but it also makes the payoff depend on the path of…