คลังความรู้

The document explains how to calculate covariance between two portfolios from their asset weights and a covariance matrix. The key is the order and orientation of the vectors: use the first portfolio's weights as a row vector, multiply by the asset…

The document considers a discrete random walk with independent, identically distributed increments that have positive mean under the original probability measure. It explains that a candidate measure can make the process a martingale by giving each next…

The document outlines how to approximate critical values for an augmented Dickey–Fuller test by simulating the test statistic under its null hypothesis. The test is based on a regression for the change in a series that includes its level, an intercept and…

The document describes why financial institutions clean vendor and market data before using it in quantitative models. It distinguishes high frequency trade and quote records from reference data such as dividends, maturities, coupons, and amortization…

The document raises questions about interpreting an optimal stopping value function, the conditioning notation, and why a strategy that waits one time step is valued by an expectation over future states. It also asks whether the inequality between the…

The document asks whether negative state prices, which may appear when extracting risk-neutral distributions from option prices, can have an economic interpretation. It describes a state price as the current value of a claim paying one unit in a particular…

The document considers whether countries or exchanges have banned algorithmic trading and whether such cases could support a comparison of markets. The responses report no known current exchange that operates only through traditional pit trading, making a…

The document explains a proposed link between Federal Reserve bond purchases and lower borrowing rates. QE adds reserves to the financial system and can increase liquidity; at the same time, purchases can raise bond prices and reduce their yields. The answer…

The document describes a QuantLib issue encountered while bootstrapping a futures-based yield curve. A FuturesRateHelper constructed with explicit start and end dates, an ASX futures type, and numeric price and convexity inputs returns a null maturity date;…

The document frames look-ahead leakage checks as mutation testing. At a historical cutoff, a valid mutation preserves information available at that time while changing only future data; if the historical artifact changes, this suggests the pipeline used…

The document asks whether portfolios built from simple rules should be called efficient. In Markowitz portfolio theory, efficiency has a specific meaning: for a given expected return, a portfolio has the lowest possible risk, placing it on the efficient…

The document distinguishes the market exposure of an equity CFD from the additional risks created by the contract structure. It argues that, for the same underlying equity, market risk should be similar, while leveraged CFD trading adds liquidation risk and…

The document asks why the stated theta of an Apple put appears large when compared with its midpoint and the time remaining before expiration. The question treats the option’s value divided by theta as if it directly represented the number of days until the…

The document addresses how to measure more than the largest drawdown: it seeks the count, average depth, and average length of drawdown episodes that exceed a chosen duration threshold. It presents two approaches using price data in Pandas. One calculates…

The document asks how to create a QuantLib business calendar from a supplied list of holidays and weekends when standard country or currency calendars do not match the relevant market schedule. The answer shows the basic approach: start with a weekends-only…

The document examines a beginner’s attempt to use a fast Fourier transform (FFT) on Apple’s adjusted closing prices, including plots reconstructed with only a few frequency components. The resulting curves fall sharply near the end of the sample, prompting a…

The document compares discounted cash flow intuition for stocks and bonds with derivative pricing. For an option, the future payoff is uncertain and depends on an underlying asset, so a discounted-cash-flow approach would first require a probability…

The document raises a statistical inference problem for a time series of variance risk premia derived from options and realized variance, following Carr and Wu. The author wants to assess whether the series has a statistically significant mean and considers…

The document explains how to construct curves for valuing cross-currency swaps in a multicurve framework. It starts with overnight-indexed swap discount curves and single-currency forward curves, then uses cross-currency swap quotes, spot FX, and the…

The document surveys ways to measure stock-market liquidity beyond the Amihud measure and bid-ask spreads. It groups candidate measures into spread proxies and price-impact proxies, naming Effective Tick, Holden, LOT variants, Roll, Gibbs, zero-return…

The document describes a replication attempt involving empirical equity premium prediction. It calculates a dividend-inclusive return from consecutive index prices, adds dividends to the ending index value, converts the resulting return to logarithms, and…

The document explains the usual debit and credit rules through two perspectives: historical left and right entries in T accounts, and the accounting equation. Assets increase with debits because they sit on the equation’s left side, while liabilities and…

The document outlines how to price American options when the underlying pays discrete dividends. Because exercise may be optimal before expiration, the problem is treated as an optimal-stopping problem. A numerical grid method, such as a recombining tree or…

The discussion corrects a misunderstanding about the Heath–Jarrow–Morton framework. The familiar expression that determines the forward-rate drift from its volatility applies under the risk-neutral measure, where it is part of the no-arbitrage restriction.…