คลังความรู้

The discussion distinguishes listed options from over-the-counter foreign exchange options. Conventional option chains are associated with listed contracts. Interbank FX options are predominantly over the counter and are usually quoted in implied volatility,…

The question concerns whether a short-horizon foreign exchange forecasting model should use bid prices, ask prices, or a blended series, and how to evaluate trades in a backtest. The response distinguishes measuring market movement from simulating executable…

The document discusses how to design a cross-asset pricing library that supports multiple models and numerical methods while keeping products and payoffs immutable for serialization. Its central design principle is to keep a payoff focused on contract terms…

The discussion asks whether variance is a convex risk measure and tests the question by expanding the variance of a weighted combination of two random variables. The key method is to bound covariance by its maximum possible value, attained when the variables…

The document shows how to derive a par coupon from a zero-rate curve. First convert each continuously compounded zero rate into a discount factor using its maturity. Then price a hypothetical coupon bond by discounting each coupon and principal payment.…

The document considers bull and bear equity performance bonds that pay periodic coupons linked to stock returns, subject to a minimum coupon. It raises a modeling ambiguity: the coupon might be a minimum plus a positive performance component, or the maximum…

The document explains how a Gaussian short-rate model with a multivariate Ornstein–Uhlenbeck state process produces a yield curve. Its derivation includes a maturity-dependent covariance adjustment; omitting that term gives the familiar Nelson–Siegel curve…

The discussion addresses frequent Value at Risk exceedances in backtests of portfolios whose VaR was estimated with historical simulation using rolling samples of 250 or 500 daily returns. It frames the issue as potential underestimation of risk and mentions…

A default-free yield curve reflects more than current short-term yields. Its shape combines expectations for future short rates, the bond risk premium, and the value investors place on convexity. A curve can slope downward when markets expect rates to…

Volatility forecast evaluation depends on what quantity is forecast and what observation serves as the benchmark. Possible targets include volatility, variance, or log volatility; because true volatility is latent, evaluation may use implied volatility or a…

The document raises practical questions about using XGBoost to predict whether the next candle’s closing price will move above or below a chosen threshold from the current open. The proposed feature set combines market sentiment, macroeconomic variables,…

The document asks how to approximate a portfolio’s loss distribution with a single-factor Vasicek model when individual loans have different default probabilities and correlations to the risk factor. The stated goal is to match the aggregate expected loss…

The document describes a numerical failure when calculating implied volatility for American options with RQuantLib: the solver reports that it cannot bracket a root, even though the user obtains values by entering observations manually. The suggested…

The document connects portfolio theory, CAPM, factor models, and the Sharpe ratio to the problem of analyzing short-term loan repayment data. It explains that loan portfolios are often assessed through loss distributions, since losses are a central driver of…

The document derives a linear state-space representation for estimating parameters in a futures price model with two latent factors. The state variables follow continuous-time stochastic processes: one mean-reverts, while the other accumulates shocks.…

The document examines whether a covered call can earn a relatively reliable profit by waiting for time decay. Its example sells calls against a large stock holding, but the response points out that the stock’s price movement dominates the small option…

The document asks whether potential pairs can be screened faster than testing every stock pair across every tick. It describes a theoretical approach based on fast matrix multiplication, which can reduce the asymptotic cost of computing a correlation matrix.…

The document addresses how to prove subadditivity for an entropic risk measure, after monotonicity, positive homogeneity, and translation invariance have been established. The response introduces an auxiliary function of a random variable and a positive…

The document asks how to choose a function when applying Itô’s lemma to solve a stochastic differential equation, using the logarithm of a geometric Brownian motion process as an example. It seeks a systematic way to identify a useful transformation rather…

The document raises a modeling question about whether the short rate is Markov in the Heath–Jarrow–Morton framework. It presents an expression for the instantaneous forward rate and a derived spot-rate dynamics expression that includes a stochastic integral…

The document contrasts two approaches to generating alpha: forecasting future prices or returns, and estimating an asset’s intrinsic value. Valuation methods such as discounted cash flow and peer comparisons can identify a gap between estimated value and…

The document addresses a question about why portfolio weights from a mean variance optimization may not sum to one when short selling is allowed. It presents the Lagrange multiplier setup for minimizing portfolio variance subject to a budget constraint and a…

The document explains the popularity of GARCH(1,1) as a volatility model. Its simple structure, connection to established time series methods, and ability to represent volatility clustering and heavy tailed returns help explain its use. The discussion cites…

The document considers whether technical patterns may lose predictive value as central banks, passive investors, and algorithmic trading change market structure. Its answer separates patterns that work because traders believe in and act on them from patterns…