คลังความรู้

The document describes a numerical problem in recovering probability densities with the COS method. The author compares truncation intervals built from cumulants through orders two, four, and six, and reports that the resulting densities shift substantially…

The note answers a request for data on structured products, including statistics by product type, issuance count, and location. It points readers to a regularly updated, freely available source focused on the United States. This makes the response useful as…

The note gives the Black–Scholes put-call parity relation for asset-or-nothing options. It expresses the asset-or-nothing put price as the prepaid underlying value less the corresponding call price, then substitutes the call pricing formula to obtain the put…

The document raises a conceptual question about combining seasonal ARIMA and GARCH models for time-series forecasting. It distinguishes the familiar SARIMA prediction of future series values from a GARCH forecast, which the author understands as producing…

The document presents ways to examine the financial-market stylized fact that upward moves can take longer than downward moves. One R example calculates, from each starting day, how long cumulative returns take to first cross positive and negative target…

The document derives the sensitivity of European option prices to the risk-free interest rate in the Black–Scholes model. Differentiating the call price and simplifying with the relationship between the normal density values at d1 and d2 produces call rho as…

The document explains how deflation affects the floating inflation leg of an inflation swap relative to its fixed leg. It compares the arrangement with an interest rate swap: if realized inflation is negative, the floating return can be negative, so the…

The document addresses a timing problem in backtests that use economic indicators. Monthly series may be labeled by reference month without recording the actual publication date, so using values as if they were available throughout that month can introduce…

The document gives a brief explanation of the role of structurers in financial markets and distinguishes their work from that of quants. It describes structurers as professionals who identify client needs, such as complex balance-sheet issues, risks that…

The document asks how a relationship for the screening of market-order flow is derived in a statistical model of a continuous double auction. In the quoted passage, a market order that survives to a price bin can be prevented from reaching the next bin when…

The document asks whether volatility measures calculated from intraday price data can help predict close-to-close squared returns. The intended use is estimating the profit and loss of a gamma scalping strategy that trades once daily, with trading assumed to…

The document asks whether a call spread’s value plotted against the underlying price must be symmetric before expiration. The response distinguishes the payoff at maturity from the option’s value earlier in its life. At maturity, the spread’s payoff may…

The document shows how to establish that two weighted combinations of log prices from correlated stochastic processes are uncorrelated. It starts with correlated geometric Brownian motions, takes logarithms, and forms a sum and difference using the assets’…

The document asks how to implement the adapted Roll measure attributed to Easley and coauthors using daily cryptocurrency OHLCV data. Its main questions concern the meaning of lagged price changes such as ΔP at t−w and t−w+1, whether the lookback window W is…

The document explains why sovereign credit default swap spreads in different currencies cannot be reliably harmonized using only interest rates. In an idealized setting with liquid, efficient markets, one could infer risk-neutral default probabilities using…

The document raises a conceptual question about what delta neutrality protects against. A position with zero delta at the current underlying price has no first-order price sensitivity at that point, but that condition alone does not describe how the payoff…

The document asks whether a standardized unexpected earnings score can be read as a z-score when earnings surprises are assumed to follow a normal distribution. Its answer highlights a distinction between standardizing an observation and knowing the…

The document explains how to describe a move in Treasury yields and what a yield to maturity represents. For a change from 1.00% to 1.10%, it favors stating the difference in percentage points, commonly expressed as 10 basis points, rather than a percentage…

The document clarifies a common confusion between a quantity being random over time and being known at a particular time. A call’s delta is the derivative of its price with respect to the underlying price; it is not calculated by dividing by a future, random…

The document considers whether a conventional t-test is suitable for testing the significance of trading returns when returns are modeled with a stable distribution. It points readers toward a paper on a z-test for the mean of a stable probability…

The document discusses implementing a finite difference pricing model for equity index options using local volatility derived from a fitted SVI volatility surface. The question is how to align the surface’s log-forward-moneyness coordinate with the pricing…

The document asks how to estimate the average influence of economic news on currency strength, using a history of calendar releases and currency indexes. It raises principal component analysis (PCA) as a possible approach but does not develop or apply a…

The discussion asks how small correlations might support reliable financial gains, while observing that strong correlations alone do not guarantee a dependable strategy. One answer links the idea to the Kelly criterion, which sizes bets according to expected…

The question asks whether a stochastic integral accumulated up to an earlier time is independent of the integral accumulated over the following interval. The answer rewrites the later increment as an Itō integral from the earlier time to the later time,…