คลังความรู้

The document asks how the equivalent martingale measure changes when an asset follows an arithmetic Brownian motion with an additive drift, rather than a geometric Brownian motion whose drift multiplies the price. It frames the issue using a bank-account…

The document examines an apparent conflict between two presentations of European put-call parity. One writes the call-minus-put value as the discounted difference between forward price and strike; another presents it as the undiscounted difference. The…

The document describes a forecasting problem: applying compound annual growth rates separately to business lines does not necessarily produce the same next-period total as applying a CAGR to their combined value. The reason is that aggregate growth depends…

The document discusses how to design trading systems that use both historical market data and live feeds. One approach is to expose a common interface so strategies can reuse the same logic in both settings, reducing implementation differences. The accepted…

The document explores why an inversion between three-month and ten-year U.S. Treasury yields has preceded recessions. It offers several proposed mechanisms: risk aversion can shift demand toward government bonds and lower longer-term yields; investors may…

The document asks whether each eigenvector from a principal component analysis of an asset covariance matrix can be interpreted as an eigenportfolio. With no components discarded, it proposes that a portfolio of n assets yields n such portfolios, ordered by…

The document asks how to automate margin calculations for a portfolio of Eurex-listed products, noting that the available calculation tool is a Windows application with a graphical interface. The accepted response describes a simpler approach for estimating…

The author describes an hourly forex classification pipeline using fractional differentiation, CUSUM event sampling, technical features, and XGBoost. Reported test accuracy rises substantially in some configurations, especially when labels are based on…

The document introduces statistical methods for investigating whether one time series tends to lead another. Lagged correlation, also called cross-correlation in this context, measures association after shifting one series relative to the other. Examining…

A beginner with programming and mathematics experience asks how to build a basic system for viewing market data and placing trades, with both simulated and live modes. The responses discuss broker access, demo and paper accounts, data costs, APIs, and…

The document asks how to estimate implied volatility for an American option on a deferred commodity futures contract when the option expires on the date associated with a nearer futures contract. It distinguishes volatility by both option expiration and…

The document poses an interview question about calculating a bond position’s market value from available holdings and market data. It clarifies that the task is to value an existing position, rather than calculate a bond’s present value by discounting future…

The document considers how to reconstruct historical forward rate agreement (FRA) levels after a Mexican market moved from a 28-day fixing to an overnight index. With the new OIS index published only from September 2024, a direct history for the new-index…

The document explains how yield moves can change which bond is cheapest to deliver (CTD) into a bond futures contract. It defines net basis as a bond’s forward price at delivery minus its futures invoice price, calculated using the futures price and the…

The document discusses representing a fixed-rate, amortizing loan in QuantLib when a built-in loan or mortgage class is not apparent. The response constructs a fixed-rate bond for coupon payments, adds an initial amortizing payment for the loan principal,…

The document introduces the idea that a futures hedge may require a ratio other than one contract for each unit of spot exposure, even when the hedge and underlying have matching maturity and asset. It asks how the tailing factor affects the hedge when…

The document asks whether a US investor who trades a euro-denominated commodity future, such as a carbon contract, takes on ongoing EURUSD exposure. It compares the question with foreign equity index futures and explains that a futures position is…

The document explains why the usual present-value sum of known cash flows and discount factors cannot be applied directly when the cash flows depend on future interest rates. In that case, the cash flows are random variables, so their discounted sum is…

The document discusses how to represent long and short futures positions when estimating portfolio Value at Risk. One answer recommends converting contracts to notional exposure using the contract count, point value, and underlying futures level; it also…

The document interprets the stock return term in the Black–Scholes setting as a proportional, rather than dollar, rate of price change. Dividing the instantaneous price change by the current price expresses movement as a percentage change. The discrete-time…

The document explains why the risk-neutral long-run mean of the state variables in an arbitrage-free Nelson–Siegel term-structure model may be fixed at zero. The answer frames this as an identification restriction: latent factors can be rotated without…

The document explains that implied volatility is inferred by applying an option-pricing model in reverse to quoted option prices. In the Black–Scholes framework, a higher quoted option price corresponds to a higher implied volatility, so the displayed…

The document explains how to calculate a six-month change from a monthly TED spread series. For each month, subtract the value from six months earlier from the current value. This gives the absolute change in the spread over the six-month interval. The…

The document asks whether historical implied volatility can be downloaded from Interactive Brokers. The responses indicate that a dedicated utility may not be available and describe a possible workaround: retrieve historical option prices through the API,…