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 clarifies the distinction among a Libor fixing date, the start of the accrual period, and its end. In many markets, the rate is fixed shortly before the accrual period begins; it is a forward rate for the period from start to end. This means the…
The document surveys approaches to forecasting asset returns, including time-series, cross-sectional, and panel models. Time-series examples include autoregressive models, moving averages, and ARIMA; the discussion says lag choice should be guided by…
The document asks why historical volatility estimates can differ when calculated from closing prices, high-low ranges, open-high-low-close data, or returns. Its central guidance is that the measure should match the quantity modeled: use price volatility when…
The discussion asks how volatility that changes over time affects option prices and implied volatility, and how those effects vary with maturity. One response reasons that greater uncertainty in the underlying’s path can raise an option’s value, while…
The document reports a stated convention for calculating a three-month realized beta between VIX and the S&P 500. It describes blending first-, second-, and third-month VIX futures to form a three-month volatility measure, using changes in futures levels for…
The question concerns calibrating a swaption model when Bloomberg provides normal volatilities at several strikes around the at-the-money forward swap rate. A least-squares calibration requires market prices as targets, but the author does not know which…
The document examines why a variance swap’s market price may differ from a theoretical price based on replicating the payoff with a strip of European options. The standard replication formula relies on a continuous, jump-free price process. A contract’s…
The document presents possible master’s thesis directions in option pricing, aimed at a beginner seeking a manageable empirical or model-comparison project. One suggestion is to fit a GARCH volatility model to market data, use it in Monte Carlo option…
The discussion considers whether the standard SABR implied volatility approximation can be calibrated to quotes with negative strikes. The accepted answer explains that the cited Hagan formula relies on a log-moneyness expression and does not apply when…
The document explains why pricing a multi-index structured option requires more than estimating historical average returns and covariance, then simulating under a multivariate normal distribution. It identifies risk-neutral pricing as the framework: discount…
The document outlines a simulation procedure for a multivariate DCC-GARCH(1,1) model. First, simulate each series’ univariate GARCH volatility and returns, then standardize returns to obtain residuals. Use those residuals to update the DCC latent covariance…
The document explains how to estimate expected shortfall (ES), also called conditional value at risk, with a GARCH volatility model. It separates returns into a conditional mean, conditional volatility, and standardized residuals. ES for the standardized…
This question asks how the general Hagan SABR implied-volatility expression simplifies at the at-the-money point. It focuses on understanding why the ratio involving the transformed variable and its auxiliary function takes its limiting value, allowing the…
The document discusses why the standard Black formula cannot be applied directly to a zero-strike interest-rate floor: its log-forward-to-strike term is undefined when the strike is zero. The answers explain that model suitability depends on the forward…
The document explains why the differential of the fourth power of standard Brownian motion includes a time term as well as a stochastic term. It applies Itô’s lemma to a general Itô process, then specializes to standard Wiener motion, whose drift is zero and…
The document discusses replicating a variance swap with a strip of delta-hedged out-of-the-money calls and puts when the available single-stock options are American. It asks whether those contracts can be handled like European options if the replication…
The answer explains how to continue a fitted GARCH(1,1) volatility series when historical data is unavailable. Keep the previously estimated parameters fixed, then initialize the recursion with the most recent residual and conditional volatility estimate.…
The document addresses how to compare implied and realized volatility for swaptions when rates approach or fall below zero. The questioner uses broker-quoted normal at-the-money volatility, expressed in basis points, and finds that converting percentage…
A power reverse dual-currency note can be viewed as a leveraged bet on the exchange rate relative to its forward curve. In a simplified USD/JPY example, each coupon is a positive-part payoff that becomes a call option on USD/JPY, with the strike determined…
The document examines a VIX change hedged against S&P 500 returns using a zero-intercept linear regression. The resulting residual has very low correlation with the equity return series, yet shows apparent drift and a chart resembling the index. The author…
The document describes how to choose the forward input when extracting implied volatility from European SPX options. It treats the forward as the primary quantity for a given maturity, with the yield rate derived from the forward and spot index level.…
The document explores how an issuer might set the coupon on a barrier reverse convertible (BRC), a structured product with a comparatively high stated payment. It proposes that the coupon may be linked to the value of the embedded down-and-in put on the…
The note explains how to read volatility shocks in the CCAR 2018 severely adverse scenario. It clarifies that the listed shock sizes are additive percentage-point changes to implied volatility, rather than relative percentages or basis-point changes. For…
The document asks how to derive an approximation for the volatility of the profit and loss on a hedged short at-the-money option. It describes a simulation setup in which an underlying follows geometric Brownian motion, the option is priced using the process…