คลังความรู้

The document raises a question about how a market-cap-weighted index should behave when one constituent rises in price and another is unchanged. It contrasts changing portfolio weights with the index level, and asks whether major equity indices recalculate…

The document examines why Monte Carlo estimates of a European call option vary when the random-number seed changes. A seed determines a reproducible pseudorandom sequence, so changing it changes the simulated terminal prices and the resulting sample-average…

For a quarterly price return, the document recommends comparing the index closing price at quarter end with the prior quarter-end close, rather than averaging daily prices. For the example of a first-quarter return, this means using the March close relative…

The document discusses approaches to modeling concentration risk in credit portfolios within the Basel IRB context. One approach starts from the Asymptotic Single Risk Factor model and modifies it to align with Basel II, then compares sector concentration…

The document explores an analogy between the short side of a zero-investment momentum portfolio and selling a call on the broad equity market. It references research describing how momentum can suffer sharp losses when markets rebound rapidly after declines:…

The document describes problems backing out implied volatility from 30-minute options bars, especially for in-the-money contracts near expiration. The question uses a numerical root-finding approach with a short-term Treasury yield as the risk-free rate…

The document asks how to compare credit risk for the same business partners across two periods. The described data include customer identifiers, ratings, rating-based default probabilities, loss given default, exposures, exposure at default, risk-weighted…

The document asks how to derive a 99% expected shortfall for a long position using a two-day forecast from an ARMA(1,1)-GARCH(1,1) return model. It outlines the model’s conditional mean and volatility equations, assumes independent standard normal…

The discussion explains how a copula separates the marginal distributions of variables from their dependence structure. For continuous variables, applying each variable’s cumulative distribution function maps its values to uniform variables. A copula…

The answer describes a model-based way to relate default probabilities to credit spreads. It distinguishes physical default probabilities, estimated from real-world outcomes, from risk-neutral probabilities used in pricing. Within a Merton-style framework,…

The discussion surveys ways to build or choose software for testing trading strategies. It contrasts vectorized or iterative backtests, which process data in a loop, with event-driven systems that respond to incoming data. The answer suggests that simpler…

The document explains why a currency call option payoff can be calculated by subtracting a strike exchange rate from the market exchange rate. In the example, both values are quoted in euros per dollar, so their difference is also an exchange-rate amount,…

The document recommends Python tools for work commonly taught through time series software. It presents pandas as the core library for representing and managing dated observations, with Series and DataFrame structures. The capabilities highlighted include…

The document considers whether a portfolio optimizer can impose a minimum active share relative to a benchmark. Active share is expressed as half the sum of absolute weight differences, or equivalently as one minus the sum of the smaller portfolio and…

The document explains a bootstrap comparison designed to test whether pairs trading returns reflect pair-specific reversion or simply the tendency of recent losers to rebound and recent winners to fall. On each historical date when a selected pair opens, the…

The question concerns pricing an American put when the underlying follows a square-root diffusion, and asks whether QuantLib-Python can use its SquareRootProcess class. The author proposes parameter values for mapping the stated process to that class, but…

The discussion asks how to assess the effect of rising LIBOR on companies with foreign currency debt when available balance-sheet data does not identify the debt’s currency or whether its rate is fixed or floating. The answer explains that those details…

The document clarifies what a forex position represents after a series of buys and sells. For a currency pair, the running signed trade amounts alone can describe net exposure, but the worked answer tracks the balances of both currencies created by each…

The document explains the sign of convexity for payer and receiver swaptions by starting with the underlying interest rate swap. A payer swap pays fixed and receives floating, so it benefits when rates rise. However, the gains from higher rates are…

The document raises foundational questions about how yield relates to duration and discounting. It distinguishes Macaulay duration, the present-value-weighted average timing of a bond’s cash flows, from the bond’s final maturity. A bond with duration shorter…

The document explains how traders summarize the shape of an implied volatility smile or skew. It defines the risk reversal as the difference between 25 delta call and put volatilities, and the butterfly as their average relative to at-the-money volatility.…

The document considers whether a currency’s returns can be regressed on an average return across currencies to estimate beta, and whether that beta has a CAPM interpretation. One reply argues that this benchmark may be unsuitable because exchange-rate…

The document asks how to include yesterday’s forecast error in a regression intended to predict future equity returns. Its replies connect lagged residuals to moving-average terms: an MA model uses past errors, while combining lagged observations and lagged…

The document compares ways to estimate value at risk for a call option. If historical prices for the option are available, an analyst can calculate returns over the chosen horizon and estimate VaR from a tail percentile. For a current option without a usable…