คลังความรู้

The VIX calculation uses out-of-the-money SPX options with nonzero bids, so its option count changes as volatility and the available strike range change. The document asks how many options might be needed to replicate the index, but provides no practical…

A par yield curve shows the coupon rate at which a bond would trade at par across maturities. The document explains why practitioners use this representation instead of plotting yields of existing coupon bonds: coupon differences and bond-specific pricing…

The document clarifies notation for the Fama-French three-factor model and explains why subscripts and the intercept matter. A conventional time-series regression expresses an asset or portfolio’s excess return as an intercept plus its loadings on the market…

The document presents the credit triangle as a quick way to infer an annualized default probability from a loan’s credit spread and expected recovery rate. It defines the spread as the loan rate minus a comparable default-free rate, with known administration…

The document explains a cross-sectional regression used to study whether stock returns in one half-hour interval respond to returns from earlier intervals. For each lag and time interval, the researchers regress the cross-section of current stock returns on…

The document examines a linear weighted moving average in which more recent closing prices receive larger weights. The original function computes each window with a loop and divides the weighted sum by the sum of the weights. The answer confirms that this…

The document discusses ways to backtest a daily signal that indicates buying, selling, or holding an equity position. It names R packages for strategy testing and portfolio analysis, while noting that a simple strategy can also be modeled with return and…

The document asks how foreign exchange brokers decide whether to hedge a customer’s trades externally or keep the exposure in-house. It describes a proposed distinction: brokers may internalize trades from customers they expect to lose and hedge trades from…

The document explains why the product of a pricing density and a self-financing portfolio value is a martingale in the Black–Scholes setting. Its central point is that martingales are defined relative to a probability measure. Under the physical measure, the…

The document explains the approximate conversion between volatility swap notional and variance swap notional. A volatility swap payoff changes with volatility, while a variance swap payoff changes with squared volatility. Applying a local linear…

The document outlines end-of-day statistics that can be computed for each ticker after a market closes. These include price and size summaries for bids and asks, spreads, executed volume, volume share, VWAP, execution counts, and intervals between trades. It…

The document explains why cross-currency basis swaps exchanging overnight risk-free rates may trade away from zero, despite a theoretical flat-pricing argument based on covered interest parity. It describes a proposed arbitrage: borrow in one currency at its…

The document examines how to construct option positions when an investor knows bounds on one or more future absolute stock price changes. It discusses using the first observed move to update the remaining bound for the next interval, then divides possible…

The document describes how an insurer can model claim arrivals with a Poisson process and total claim costs with a compound Poisson process. In its auto liability example, a large, geographically dispersed group of similar policyholders generates claims that…

The document derives a change-of-numeraire Radon–Nikodym derivative for two positive assets. It assumes the ratio of their prices is a martingale under the original measure, uses that ratio to define a density process with expectation one, and constructs the…

The discussion explores whether equal risk contribution portfolios can be built using tail measures such as value at risk or expected shortfall, and what conditions support the approach. It highlights positive homogeneity: for a differentiable risk measure…

The discussion checks a far-field boundary condition for a continuously averaged Asian call under the risk-neutral Black–Scholes process. When the current asset price is very large, the option is expected to finish in the money, so its value can be…

The discussion considers a trading research process that clusters historical intraday observations, such as daily vectors of hourly exchange rates, and then measures the next day's average return for each cluster. A researcher might use the return associated…

The discussion explains how the sign of a cointegration coefficient affects the positions implied by a spread. With the stated spread defined as Stock A minus beta times Stock B, a negative beta makes the second term positive, so a long spread corresponds to…

The document discusses timestamp reliability in free historical data from Gain Capital, especially for combining non-FX instruments or multiple feeds in a backtest. One respondent reports that observations were correctly ordered within individual CSV files…

The document offers guidance for choosing a short applied mathematics project involving financial data and time-series analysis. It recommends aligning the topic with the supervisor’s research interests and adapting an existing empirical paper into a smaller…

The document asks how to interpret and scale parameters estimated for a Bates stochastic volatility model from daily log returns, using the mean reversion parameter κ as an example. It distinguishes estimates under the real-world probability measure from…

The document asks whether positive gamma is generally costly, negative gamma earns premium, and theta tends to have the opposite sign from gamma. It frames theta as the carrying cost of holding long gamma and asks whether these observations can be proved…

The discussion examines whether principal component analysis of yield curves has practical value beyond describing movements as level, slope, and curvature. One answer argues that PCA may help create a denoised correlation matrix, but questions using…