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20,364 dokumenter
The document corrects an attempt to infer the mean and variance of an Ito process by multiplying its instantaneous drift and variance rates by elapsed time. An Ito differential is shorthand for an integral over the path: the state at time t equals its…
The document explains why a slightly in-the-money American option does not generally have a delta of one. Delta reflects how the option’s total value, including remaining time value, changes with the underlying price; it is not determined solely by the slope…
The document asks whether large options positions can make the underlying’s price respond to derivatives activity, especially when dealers must hedge positions with high gamma. It describes the proposed feedback: negative gamma hedgers may buy into sharp…
The document asks how to model convexity adjustments for a payoff on the spread between two constant maturity swap rates when the rates are dependent. It notes that some approaches model each rate through an annuity mapping function and then use a copula to…
The document outlines a proposed event study of scheduled FOMC announcements and the Dow Jones Industrial Average across two periods, using daily open and close data. The researcher wants to examine price behavior in the days before announcements for…
The document derives an approximate link between the compound annual growth rate and the arithmetic mean of a finite sequence of returns. Starting from the product of gross returns, it takes logarithms and expands each log return around the log of the…
The note explains why fractional shares offered by brokers do not fully replace stock splits as a way to adjust a share’s trading price. On exchanges, orders generally trade in whole shares, while brokers can aggregate customers’ fractional orders to execute…
The note clarifies that buying volatility is not always identical to buying an option, although vanilla options generally rise in value when implied volatility rises, all else equal. For a long option delta-hedged under a Black–Scholes model, it gives a…
The note explains that an asset pricing factor does not have to be an excess return or even a traded portfolio. In a one-factor model where the factor is itself an excess return, its risk price can be read directly from its average value: the factor has a…
The document examines why the Fama–French model regresses stock returns on market, size, and value factor portfolio returns instead of directly using firm size and book-to-market ratios. One answer argues that factor returns keep regressors in return units,…
The document asks whether open-source software can support commodity pricing and risk management, noting that commodity contracts may involve a wide range of specialized payoffs. The answer says the author is not aware of a dedicated open-source library for…
The document considers how to balance uncertain expected-return forecasts against covariance risk and trading costs in a constrained portfolio optimization problem. Its proposed method is to multiply the return signal by a shrinkage coefficient between zero…
The document considers pricing a call-like payoff on the difference between the product of two correlated geometric Brownian motions and a scaled version of one process. It explains how to express the product process as a single geometric Brownian motion,…
The document poses a fixed-income question: how to lock in a one-year rate that begins three years from now using zero-coupon bonds with maturities from one to four years. It supplies annually compounded spot rates for each maturity and asks which bonds to…
The document shows how to calculate a final balance when each day has a different rate and interest compounds discretely. Starting from an initial principal, multiply the balance successively by one plus each day’s rate. The same calculation can be expressed…
The document presents implied volatility as a way to express option prices in familiar Black–Scholes terms. Because the model maps a vanilla option price to a volatility input, implied volatility helps compare options across strikes and maturities, track…
The document explains why adding jumps to an option pricing model represents a different risk from simply increasing diffusion volatility. In a diffusion model, variability grows with the square root of time, while a Poisson jump component contributes…
The document explains why near-zero short-term rates are usually a reason to begin quantitative easing, rather than a reason QE stops working. In the account presented, rate cuts first make cash funding cheaper and holding cash less attractive. Once short…
The document discusses why money market funds may place cash in the Federal Reserve’s overnight reverse repo facility even when its rate is near zero. One explanation is a shortage of Treasury bills: reduced bill issuance alongside demand for liquid…
The document clarifies how conditional variance depends on the variable being modeled, in response to a question about comparing implied volatility with GARCH forecasts. Under information available at the prior time, a price and its simple change have the…
The document surveys commercial suites that combine market data, backtesting, event processing, and automated trading. It asks about leading vendors, practical tradeoffs, integration costs, customization, and typical users, but provides only a partial…
The document asks how a 99.9% confidence level used in a Basel context corresponds to an event described as occurring once in a thousand years, and how to express a rarer event such as one in ten thousand years. It raises the distinction between a…
The document asks whether equity factor models can tell a portfolio manager how to position a portfolio to earn alpha, beyond identifying its factor exposures. The response gives a limited conceptual distinction: in the stated arbitrage pricing theory…
The question asks why changing the correlation between two equity assets appears not to change the revalued value or risk of a portfolio containing a call on one asset and a digital put on the other. The proposed workflow simulates asset prices to an…