คลังความรู้

The document explains why a Treasury yield-to-maturity curve cannot be used directly as a spot-rate curve. A yield to maturity summarizes the discount rate for an instrument with multiple cash flows, whereas a spot rate discounts a payment at a particular…

The document clarifies how to interpret the intercepts of the Security Market Line and Capital Market Line when their vertical axis shows excess returns. The question notes that these plots use beta or standard deviation as the horizontal measure and appear…

The document asks how models can use the full open, high, low, and close record instead of relying only on closing prices. It explains that the high–low range contains information about variation within an interval and may help estimate volatility, including…

The document addresses why cross-hedging calculations often estimate a minimum-variance hedge ratio by regressing percentage changes in spot prices on percentage changes in futures prices, rather than regressing absolute price changes. The explanation is…

The document presents a savings drawdown problem: determine a level monthly withdrawal that exhausts an initial bank balance after a fixed number of months, with a stated monthly effective interest rate and no further deposits. The answer treats the…

The document asks how to price a European-style exotic payoff equal to the square root of the stock price at the end of a one-step binomial period. Its answer uses the risk-neutral probability implied by the current stock price and the two possible future…

The document explains why a calculation of a 3M SOFR futures final settlement can differ from values in a Bloomberg historical price table. It distinguishes the daily exchange settlement, which is quoted on a futures tick grid, from final settlement, which…

The document considers how to estimate a stock-return covariance matrix for portfolio value-at-risk when some holdings have only one or two years of data, while the desired estimation window is longer. It asks whether to fill unavailable observations with…

The document asks how the European equity factors in the Kenneth French data library are expressed in US dollars and whether the returns assume currency hedging. The response points to the research paper describing the international factor construction and…

The document diagnoses a mismatch between a European option’s net present value and the model value reported by a QuantLib Heston calibration helper. The example calibrates a Heston model to implied volatilities and then prices a put with what appear to be…

The document raises a core backtesting question: if a fitted price model represents the underlying process, why test a trading algorithm on historical prices rather than simulated paths? It suggests that simulation could expose a strategy to scenarios absent…

The document asks whether a proposed proof correctly shows that the process formed by integrating Brownian motion over time is not a martingale. The argument observes that the process has mean zero because Brownian motion has mean zero, then incorrectly…

The document explains an arbitrage argument linking Black–Scholes option values to total variance, expressed as volatility squared times time to expiration. For otherwise comparable options, the Black–Scholes price rises with this input. If total variance…

The document concerns estimating the Hurst exponent in a spreadsheet and a user’s difficulty when the calculated value sometimes exceeds one. The replies point to explanatory material on the exponent and to an Excel workbook intended to calculate it. The…

The document answers whether a trader can obtain a low-cost, raw NASDAQ TotalView-ITCH real-time feed. Its response says that a basic single-port feed without redistribution rights costs more than the stated budget, while historical data also carries a…

The document explains how dividends enter vanilla index-option valuation under the Black-Scholes framework. For options written on a spot index, one response describes using a continuous dividend yield inferred from put-call parity. Another notes that actual…

The document considers how to calibrate the Heston stochastic-volatility model and narrows its response to calibration from time series. Because volatility is latent, that task can be framed as nonlinear filtering. The answer points to research methods and…

The document asks how to price a contract that gives its buyer the right to select one cashflow from a finite set in a discrete-time, arbitrage-free, complete market. The proposed approach first prices each cashflow by summing the prices of its payments,…

The document presents a Monte Carlo setup for pricing a basket option on nine currency crosses. It updates each cross over multiple time steps using lognormal dynamics, with correlated normal draws supplied in a simulation array. At each simulation’s end, it…

The document explains two relationships in a Black Scholes derivation involving implied skew. First, it shows how a no arbitrage condition links the mean and variance of log returns to the difference between domestic and foreign rates, with higher cumulants…

The document considers how portfolio construction works in practice, contrasting mean variance optimization and related risk objectives with simpler diversification and factor based approaches. Its central caution is that optimized weights depend on…

The document explains how to convert a series of simple, or arithmetic, returns into continuously compounded log returns when the underlying price series is unavailable. The conversion uses each return itself, so past prices are not required. It also gives…

The document asks how to identify a useful subset of roughly one hundred market related variables for explaining or predicting global stock returns. It highlights two data settings: fewer observations than predictors and at least as many observations as…

The document examines whether a trader can earn positive expected value from a zero-drift random walk. It presents the martingale framework: when position sizes are chosen using only past information and remain bounded, the gains process has zero expected…