คลังความรู้

The document describes an LSTM trading model using RSI, MACD, a ratio of two exponential moving averages, and recent returns as inputs over a short history. It assigns separate long and short outputs based on whether a hypothetical trade reaches a…

The document defines Day One Profit or Loss as the difference between a financial instrument’s transaction price and its estimated fair value when a deal begins. It says fair value is typically estimated from market data and valuation models. The concept can…

The document explains how closing a futures or perpetual futures position changes a trader’s net exposure. A trader closes a long by selling the contract, which opens or increases a long position for whoever buys it. The original short position remains open;…

The document describes a practical signal-processing problem in a trading system that receives live bid and ask data. The author reports that offline backtests can use non-causal smoothing methods with access to future observations, but those methods lag…

The document describes using a normal, or Gaussian, model to price caplets and floorlets when rates can be negative. Under the stated setup, the forward rate evolves as a Gaussian martingale with constant absolute volatility, so its value at expiry has a…

The document explains why options on the same underlying can imply different volatilities across strikes even though the Black-Scholes model assumes constant volatility. It presents several interpretations: the smile can reflect model misspecification,…

The discussion considers whether high-dimensional Sobol sequences are practical for large market simulations and Monte Carlo pricing, where the required dimension may exceed the limits of common implementations. One answer points to established Sobol…

The question attempts to find the distribution of the stochastic term in a Heston-style asset process by substituting an integral expression for the variance process, taking a square root, and applying Brownian differential identities. The response…

The document explains why foreign exchange option data may arrive as volatility quotes and delta-based smile points rather than as a ready-made table of implied volatilities by strike and maturity. In much of the over-the-counter market, options are quoted…

The discussion examines why observed broker spreads across currency pairs may look counterintuitive and whether spreads are useful as a rough measure of trading cost. One explanation is a quotation-unit effect: comparing the dollar cost of one unit of each…

The document derives a static option replication for a payoff equal to the square of a non-dividend-paying stock’s terminal price. It rewrites the square as twice the integral, over strikes from zero to infinity, of the call payoff at each strike. This…

The document considers statistical tools for testing whether historical changes in a market variable appear random, with the aim of identifying unusual patterns and consistency over time. It points to the NIST test suite, a collection originally used to…

The document addresses how a T-forward measure can be used when a directly observed zero-coupon bond for the required maturity is unavailable. It explains that market curves are built from instruments spanning different horizons: spot borrowing rates anchor…

The document explains why standard CDS settlement after a credit event does not generally depend on the trade’s original coupon or upfront payment. Those amounts reflect the trade’s earlier mark-to-market and are treated as historical once the event occurs.…

The document presents ways to explain bond P&L in a format resembling swap curve attribution. One method maps each bond’s risk to maturity buckets, such as splitting a bond between adjacent swap tenors, then estimates bucket moves by minimizing the…

The document asks whether a double-barrier knock-out call can be assembled from an up-and-out option and a down-and-out option. The accepted response says this decomposition does not work: satisfying one barrier condition does not by itself enforce both…

The document derives the finite-horizon change in log price when log price, after subtracting a linear time trend, follows an Ornstein–Uhlenbeck process. The drift pulls the detrended log price toward zero at a rate set by the mean-reversion parameter, while…

The document considers how to hedge a 30-year bond when the most liquid bonds extend only to 10 years. As the bond ages, its maturity eventually enters the liquid part of the curve, where a 10-year bond may provide a closer hedge. The difficult period is the…

The document explains why a minimum-risk portfolio optimization with fully equal active weights can return the benchmark itself. It defines each active weight as the difference between a portfolio weight and its benchmark weight. If both the portfolio and…

The document discusses the arbitrage-free valuation of a claim paying a power of the terminal stock price in the standard Black–Scholes model. The questioner applies Itô’s lemma first to the power process and then to its logarithm, but obtains an exponent…

The document examines whether the conditional covariance of two assets at a later date can be decomposed by conditioning on their forward values at an intermediate expiration. It starts from the usual expression for covariance as the conditional expectation…

The document outlines a way to reconcile instrument identifiers when OTC derivative trades arrive from systems using Bloomberg and Refinitiv symbols. Its proposed first check is to compare ISINs when both are supplied, then consult an internal lookup table…

The document presents an apparent contradiction from three two-sided t-tests: one fails to reject a zero mean for a company’s monthly stock returns, another rejects a zero mean for the market index, and a third fails to reject equal means for the stock and…

The document explains why the term duration can refer to different bond measures and how compounding conventions affect their relationship. Macaulay duration is described as a time-weighted measure of fixed cash flows, while modified duration measures the…