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 answer proposes using the shape and fit of an implied-volatility smile to flag bad option data. It fits near-the-money observations to estimate an at-the-money volatility, then models the left and right sides separately with quadratic functions of…
The document compares error assumptions in simple ARIMA models with those used in ARIMA-GARCH estimation. It explains that some ARIMA or ARMA models can be fitted with ordinary or iterative least squares, while maximum likelihood estimation is often used…
The document asks how to price equity quanto options with a local-stochastic volatility model, building on a proposed Heston approach that adjusts equity and variance dynamics for quanto effects. The supplied answer recommends modeling both the equity and…
The document considers how to size three long and short currency positions to target a specified annual portfolio volatility while allocating risk equally. The proposed procedure first scales each currency position separately so that each standalone position…
The document describes a learner's attempt to estimate a GARCH(1,1) volatility model by hand after fitting an AR(1) model to a return or time series. The AR(1) residuals supply the lagged squared innovations used in the conditional variance equation, while…
The document explains why an asset forward price has the same percentage volatility as its spot price when the interest rate is constant and the cost of carry equals that rate. In this setting, the forward price is the spot price multiplied by a…
The document outlines a model for pricing a call on realized volatility by treating realized volatility as the maturity value of a volatility swap. It assumes the swap price follows a lognormal process driven by the same Brownian motion as the underlying…
The document examines why a set of out-of-the-money FXI puts appears to become much more expensive with added time to expiration than a simple square-root-of-time rule would predict. The quoted example lists ask prices and implied volatilities across several…
The document discusses the common binomial-tree choice of an up factor based on volatility and the square root of the time step, with the down factor set as its reciprocal. This reciprocal relationship makes the recombining tree compact: after each step,…
The document asks how to choose the decay half-life when estimating an x-day value at risk (VaR) from an exponentially weighted moving average of return vectors. It gives the relationship between the half-life and the EWMA decay factor, then asks whether the…
The document explains why implied volatility calculated from in-the-money (ITM) and out-of-the-money (OTM) equity calls may appear higher for ITM strikes. For calls, ITM contracts have strikes below spot, while OTM contracts have strikes above spot; the…
The document examines whether the sum of squared log returns is an unbiased estimate of variance under geometric Brownian motion. At finite sampling intervals, the estimate can reflect drift as well as volatility. The response explains why this convention…
This discussion considers whether commercial derivatives-pricing software will reduce the need for pricing quants. The responses describe a changing role: less development of entirely new pricing formulas in some settings, and more adaptation of existing…
This explanation examines the shift parameter in a lognormal model for forward interest rates. It writes a caplet payoff in terms of the shifted rate and strike, assumes the shifted forward follows a lognormal process under the appropriate forward measure,…
This document investigates inconsistent results when fitting a lognormal SABR volatility smile with pySABR. In the failing example, the fitted parameters produce volatility estimates that diverge sharply from the observed quotes when reused in another…
The note describes two ways to estimate implied volatility skew. One approach prices calls and puts across strikes, converts their prices to Black–Scholes implied volatilities, and estimates the smile’s slope. Another uses a call and a digital call at a…
The document gives brief definitions of two terms encountered in derivatives pricing and volatility smile fitting. “Pillars” generally refers to maturities or expiry dates used as reference points, a usage associated with fixed income. A pricing or…
The document examines why vega may give a misleading picture of volatility risk for options whose gamma changes sign, using a binary option as its example. Under Black–Scholes, it differentiates the discounted probability-based binary price with respect to…
The document examines a one-factor Hull–White short-rate simulation and explains why a one-year time step can produce poor paths. Euler–Maruyama approximates the drift over a step of length h and scales the random shock by the square root of h; the presented…
The document presents an eGARCH(1,1) fit to weekly Bitcoin log returns over a multi-year sample, using a generalized error distribution and a date-related dummy variable. The broader research aim is to compare volatility dynamics across Bitcoin, Ethereum,…
The document describes a proposed EUR/USD forecasting workflow: take end-of-day closes, log-difference them to seek stationarity, fit an ARMA model using Box–Jenkins methods, inspect residuals, and use their assumed normal distribution to form cumulative…
The discussion points readers seeking variance and volatility swap strategies toward sell-side research and foundational papers. It frames relative-value trading as comparing implied variance across markets using historical relationships: buy the market that…
The document asks how to rank assets by variation in their daily trading ranges without relying on their average range. It proposes quadratic variation: take successive observations in the range series, calculate each change, square the changes, and sum…
The document compares the Yang–Zhang volatility estimator as presented in Euan Sinclair’s book with the implementation in the TTR package. It focuses on the open and close variance terms: the book’s displayed formulas use open-to-open and close-to-close…