คลังความรู้

The document examines whether a standard LIBOR floating-rate leg remains worth par when its cash flows are discounted using the OIS curve. It introduces the single-curve bond and forward-rate identity that would imply par value, then asks whether that…

The document explores how carry and delivery optionality can affect the basis between a Treasury futures contract and its cheapest-to-deliver bond near contract expiry. It considers a long basis position under both upward-sloping and downward-sloping yield…

The discussion surveys resources and cautions for applying statistical tests to trading ideas. It recommends evidence-based technical analysis as an introduction to objective indicator testing, including statistical inference, Monte Carlo permutation…

The document asks how to value a European payoff when a stock follows risk-neutral geometric Brownian motion whose volatility depends on its history. It contrasts this setting with the standard Markovian case, where volatility depends only on the current…

The document examines a long call hedged by shorting stock in an amount equal to the option’s initial delta. It considers a sudden underlying-price decline alongside an increase in implied volatility, and asks whether the hedge must make money. A Taylor…

The document asks for a stock market anomaly that is straightforward to reproduce in an event study. The motivating constraint is that some candidate anomalies, such as post-earnings-announcement drift, are harder to demonstrate because company events occur…

The document raises a question about a constrained expected-utility problem: maximize expected utility of terminal wealth while requiring discounted wealth to have a specified risk-neutral expectation. It focuses on a textbook exercise involving the function…

For a European option on the December Brent futures contract that expires earlier, the relevant volatility describes the distribution of that same December contract at the option’s expiry. Under the Black model for futures options, the payoff is determined…

The document explains why buying volatility exposure after a quiet period is not a cost-free way to profit from a future volatility spike. VIX is a spot index rather than a security that investors can hold directly, so traded exposure is typically obtained…

The discussion asks how closely Monte Carlo (MC) and finite-difference methods (FDM) should match exact option prices and Greeks under specified path and grid counts. It describes a delta obtained by bumping an FDM price that differs modestly from the exact…

The document explains how the variance of a trader’s wealth can be calculated from the risks and co-movements of the assets held. If wealth is a fixed dollar-weighted sum of asset prices, its variance is the sum of each holding’s price variance scaled by…

The document clarifies a market interpretation of declining open interest in long Bitcoin futures positions. The question asks how closing futures longs could limit further declines in Bitcoin, given that futures are often viewed as bets on the underlying…

The document explains why an unconstrained full Kelly portfolio can have the same relative asset weights as a mean-variance tangency portfolio. Its central claim is that maximizing long-run growth leads to maximizing the portfolio’s Sharpe ratio, so the…

The discussion explains why a USD three-month LIBOR coupon in a cross-currency swap can accrue over 90 days even when its payment arrives 92 days after the deal date. The trade starts at settlement, two days after the valuation or deal date, and the LIBOR…

The document asks how to simulate a multifactor Ornstein–Uhlenbeck process with matrix-valued mean reversion and diffusion. It contrasts the scalar exact time-step formula with the multivariate solution, whose random increment has correlated components.…

The answer considers a price following geometric Brownian motion under a probability measure where its drift is nonzero. It explains that the drift can be absorbed into a shifted Brownian motion: under a new measure, the original Brownian motion plus the…

The document raises a practical portfolio-construction question: whether a long-short equity portfolio can reduce risk by balancing its exposures to factors such as value, momentum, size, and volatility. The motivation is that a covariance-matrix optimizer…

The document explains why conditional heteroskedasticity does not conflict with a constant unconditional variance. A stationary return series may have finite, constant overall variance while its variance given past information changes over time. This…

The document distinguishes estimating mean reversion from historical rate observations from calibrating a pricing model to market instruments. Under the historical measure, it describes representing rates with a discrete autoregression: regress the next rate…

The document asks how to calculate beta-weighted delta and gamma for a portfolio of options on different stocks. Its answer gives a relationship for an individual option’s beta: multiply the underlying price by the option’s delta and the underlying asset’s…

The document collects approaches to generating synthetic price series that remain within a chosen range while exhibiting a specified, but imperfect, relationship to historical prices. One answer proposes modeling returns with an Ornstein–Uhlenbeck process…

The document describes a calibration problem in the Guéant–Lehalle–Fernandez-Tapia market-making model. The author estimates bid- and ask-side order-arrival intensities using the last traded price as a reference, updating it at short intervals, and separates…

The document asks how options volume, dollar volume, and open interest across strikes and expirations might inform implied sentiment, volatility surfaces, option premiums, or Greeks. It contrasts modeling each contract on its own with measuring activity…

The document investigates whether discount factors calculated from a Nelson–Siegel–Svensson yield curve are implausibly small. It applies the model to maturities from six to thirty months, converts the fitted zero-coupon rates into discount factors, and uses…