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 note clarifies which equity measures to use when applying the standard Merton model to a publicly traded company. It recommends market capitalization as the equity value and the stock’s implied volatility as its volatility input, with at-the-money…
The document asks how to set geometric Brownian motion inputs when simulating asset paths to price exotic options under a risk-neutral measure. It distinguishes pricing inputs from estimates drawn directly from historical price data. Its central guidance is…
The document explains why an option’s implied volatility can move even when that contract has no trading volume. Implied volatility is inferred from a quoted or traded option price, so market makers can revise an option’s bid and ask as their assumptions or…
The document asks how to derive the unconditional covariance matrix for a constant conditional correlation (CCC) GARCH model. It specifies a multivariate process with a fixed correlation matrix and time-varying component variances, whose dynamics depend on a…
The document asks how to interpret the rho parameter in the Surface SVI formula when the model is used to fit implied volatility. It notes two descriptions found in papers: rho is proportional to the implied-volatility smile's slope near at-the-money, and…
The answer derives the log-price identity for a diffusion with drift and volatility by applying Itô's lemma to the logarithm. The second derivative contributes a correction involving integrated squared volatility, yielding the relationship between the change…
The document asks how to estimate parameters of the Merton jump diffusion model from historical returns using the method of moments. It proposes expressions for return variance, skewness, and kurtosis in terms of diffusion volatility and jump intensity and…
The document discusses attempts to describe stock return distributions under the Heston stochastic volatility model, including a proposed unconditional density and later statistical comparisons with a lognormal distribution. It raises the concern that an…
The document asks what an expression involving the expected product of two stochastic differentials means, given that differentials of random processes are not ordinary standalone quantities. The answer explains a stochastic differential equation as…
The document asks how to interpret the time scale of a variance quantity computed from a local volatility formula, using the relationship between variance, volatility, and elapsed time. It wonders whether a value associated with a six-month horizon should be…
The discussion clarifies how to initialize Average True Range when using Wilder’s volatility formula. It answers that the initial simple moving average of true range should use the same period, N, as the subsequent Wilder smoothing. The source cited in the…
The discussion considers whether higher implied volatility for out-of-the-money calls and puts points to a particular options spread. It describes this pattern as a volatility smile and reasons within a Black–Scholes comparison: because option vega is…
The document describes common practical approaches to pricing European options. In liquid markets, practitioners often represent a vanilla option’s price through its forward price and Black-Scholes implied volatility for the relevant maturity and strike.…
The discussion considers how to account for convexity when bootstrapping a SOFR curve with futures and swaps. It distinguishes the task of calibrating to American options on SOFR futures from estimating futures convexity, and outlines approaches proposed by…
The document asks how volatility quants describe the shape of an equity options implied volatility skew using statistics beyond basic distribution summaries. It groups candidate features into level, represented by at-the-money implied volatility; skew,…
The document distinguishes risk, uncertainty in realized returns under a known distribution, from ambiguity, uncertainty about the return probabilities themselves. It reviews volatility of volatility and volatility of the mean as proposed proxies, then…
The document considers numerical valuation of American options when the underlying model has multiple sources of randomness, such as stochastic volatility. One response argues that lattice methods can remain preferable to least-squares Monte Carlo (LSMC)…
The document presents a question about applying a regression from Asensio (2013) to test forecast bias in the VIX term structure, motivated by the possibility that VIX futures are overpriced. It identifies the equation’s forecast errors and its horizon…
The document clarifies how sticky strike, sticky moneyness, and sticky delta describe implied volatility changes when the underlying spot moves. Sticky strike holds implied volatility fixed at an absolute strike. Sticky moneyness instead holds it fixed at a…
The document explains how forward premium enters currency option pricing and clarifies the role of overnight indexed swaps. In the Garman–Kohlhagen formulation, the domestic-minus-foreign interest rate differential determines the forward exchange rate…
The document asks how to characterize changes in an interest rate swaption surface beyond taking the average of cell-by-cell differences between two days. It gives an example of subtracting surface values across dates and averaging the resulting shifts,…
The document asks how a quoted volatility estimate is obtained for a fair coin-flip investment with two possible outcomes: a gain of 50% or a loss of about one-third. It also references the approximation that geometric average return is close to arithmetic…
The document introduces the frozen-drift approximation in the LIBOR Market Model (also called the LIBOR Forward Model). Freezing drift can make calculations more efficient and treats swap rates as approximately lognormal, but it may distort the terminal…
The document asks how to recover a Brownian increment over a time step when the starting and ending values of a Cox–Ingersoll–Ross variance process are known. The accepted answer applies a positivity-adjusted Euler–Maruyama approximation to the CIR equation…