নলেজ লাইব্রেরি

The document examines whether the reciprocal of an exchange rate following geometric Brownian motion is itself a Brownian motion. It applies Itô’s lemma to the function that takes a rate to its reciprocal, accounting for both the first derivative term and…

The document examines why an at-the-money European call and put on a non-dividend-paying stock can have equal value when interest rates are zero, despite their different-looking payoff diagrams. Its central explanation is that option prices reflect both…

The document proposes a repeatable way to identify liquid futures markets for research or systematic trend following. Rather than starting from a narrow published index or trying to query every contract through a terminal, it suggests parsing exchange…

The document explains how to read eigenvalues from a correlation matrix of stock returns. Each eigenvalue measures the variance associated with a corresponding mode of co-movement, while its eigenvector describes the combination of stocks that moves together…

The post asks how to transform one risk-neutral pricing expression for a derivative with funding and collateral rates into another expression using collateral-rate discounting and an adjustment based on the difference between funding and collateral rates.…

The post asks how to select conditional-mean terms when fitting GARCH-family models to South African, Australian, and US equity index returns. The author compares autocorrelation plots, information criteria, ARCH tests, and the significance of terms in…

The post investigates why a Sharpe ratio computed for SPY differs from figures reported by financial websites. The response explains that returns and the risk-free rate should be measured over the same interval, such as monthly or daily, and that the…

The document considers what is needed to simulate the year-end prices and portfolio variance of two stocks. It challenges the idea that historical means and standard deviations alone can be used to draw independent lognormal prices and average them. The…

The document outlines an empirical sequence for assessing whether two price series are cointegrated. First, test each series for a unit root. If both are stationary, model them in levels; if only one is nonstationary, difference that series. If both are…

The document addresses how to obtain intraday prices for an ETF when standard daily price retrieval is insufficient. It identifies Interactive Brokers as a possible data source through its API and says the API itself does not require payment, while noting…

The document explains how market-implied probabilities for Federal Reserve rate hikes can be estimated from fed funds futures. Under a simplified assumption that only two outcomes are plausible, the expected rate increase embedded in futures prices can be…

The document outlines how spline methods can fit functions defined over separate regions while enforcing continuity and differentiability at their boundaries. It first describes univariate splines, where each interval has a polynomial segment and neighboring…

The document explains how a long–short equity portfolio can target correlation with the market while keeping portfolio volatility fixed. It relates beta to market volatility, portfolio volatility, and their correlation, and notes that beta can alternatively…

The document discusses how to estimate a liquidation haircut for stocks with sparse or missing observations. It warns that carrying the last observed price forward can create flat returns followed by an artificial jump. One response suggests imputing missing…

The document derives a risk-neutral price for a contract that pays the average underlying price over an interval ending at maturity. It discounts the payoff at the final payment date and uses linearity to move the expectation inside the time integral. Under…

The document discusses models that may reproduce gain-loss asymmetry: the tendency for stock prices to rise gradually over longer periods and fall sharply over shorter periods. One response connects the phenomenon to the leverage effect and points to…

The document explains why jump intensity cannot be interpreted independently of the assumed jump-size distribution. To estimate a model’s jump frequency, it recommends fitting intensity and the other model parameters jointly, using maximum likelihood or…

To estimate the implied repo rate for a bond that has not yet been issued, the document recommends specifying its coupon and yield. Its issue date and maturity are treated as known; after the coupon and yield assumptions are set, the implied repo can be…

The document asks whether M&A research can support more quantitative methods than the small-sample OLS and fixed-effects studies the questioner has encountered. It points to two possible directions: forecasting M&A activity with a predictor model, and…

The document investigates how to reproduce CBOE’s discontinued single-name 30-day normalized skew field using historical options data. It describes the target as the 25-delta put implied volatility minus the 25-delta call implied volatility, divided by…

The document explains how bond weights shape a fitted government discount curve when the curve is calibrated by minimizing weighted price errors. Equal price weights give each bond the same influence. Weighting inversely by squared DV01 roughly shifts the…

The document discusses a volume feature used in a study of flocking behavior among US equities. The feature standardizes a stock’s trading volume for a particular minute of the trading day: compare that minute’s observed volume with its historical average…

The document asks whether indexes exist for hedge funds, private equity, and venture capital. The answer identifies HFR as a provider of hedge fund indexes, including an investable index, but says the respondent is not familiar with comparable private equity…

The document explains how an unpublished floating-rate fixing creates P&L exposure for an interest rate swap, measured as the difference between the published fixing and the market forecast. Once the fixing is known, the associated cash flow is fixed; the…