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20,364 dokumentů
The document explains how to remove the random component from a portfolio made of an option and its underlying stock. Applying Itô’s lemma to the option value shows that the portfolio’s Brownian-motion exposure is proportional to the option’s delta and the…
The document addresses a common confusion in stochastic calculus: an Itô process can have zero quadratic variation while still having nonzero variance at a fixed time. In the example, integrating Brownian motion with respect to time yields a process whose…
The document explains convertible bond arbitrage as buying a convertible bond while shorting the issuer’s stock to create a delta-hedged, long-volatility position. The strategy seeks to benefit when realized volatility exceeds the bond’s implied volatility,…
The document asks whether reliable foreign-exchange prices are available during the weekend, when conventional spot markets are largely closed. The response cautions that quotes visible during quiet hours can be stale, making them poor evidence of current…
The document asks how to derive risk-neutral dynamics for a dividend-paying asset when the bank account is the numeraire. It outlines the martingale condition for the discounted asset plus accumulated discounted dividends, then applies Itô’s formula and…
The document explains why futures positions commonly end without physical delivery. It describes offsetting as closing a position by taking the opposite side in the same number of standardized contracts before expiration. The responses distinguish exposure…
The document asks whether credit markets have a volatility index comparable to familiar measures for equities and interest rates. Its answer points to four daily implied-volatility measures covering North American investment-grade and high-yield CDX indices,…
This document identifies financial laws and regulatory frameworks that may affect investment advisers, European financial firms, commodity markets, anti-money-laundering work, taxation, broker-dealers, and securities exchanges. Its examples include US…
The document shows why subtracting calendar dates does not reliably locate observations in daily financial data. Weekends and market holidays create gaps, so the number of elapsed days can differ from the number of rows between two trading dates. The example…
The document explains XIRR as the annualized rate that equates a dated series of irregular cash flows with an equivalent constant-rate investment. Its examples contrast a simple loan with interest paid at different dates and a short holding-period trade,…
The document compares QuantLib Greeks for a stylized foreign exchange option with Bloomberg values, focusing on a mismatch in theta. It explains that QuantLib's analytic Garman-Kohlhagen engine reports model theta: the derivative of option value with respect…
The document explains why the calendar spread between nearby German government bond futures can differ from zero and why rolling a position has a cost. Ignoring delivery options and margining, a bond future can be approximated as a forward whose fair value…
The document discusses reports of inconsistent Yahoo Finance downloads after changes to its data access method. The answer describes a retrieval process that relied on extracting a token from a webpage, along with reported irregularities in adjusted-close…
The document describes a credit-risk data preparation workflow for estimating probability of default. The example defines a default event from arrears, term-expiry, or bankruptcy indicators, recodes the outcome for modeling convenience, and uses stratified…
The document derives a rough out-of-sample observation length for testing whether a strategy’s mean return exceeds zero. Assuming independent, identically distributed returns, it models the sample mean’s uncertainty as the return standard deviation divided…
The document considers how to value a fixed-for-floating swap whose floating leg references a rate other than LIBOR, with a CNY example. It explains that the appropriate discount curve depends on the transaction’s collateral terms: for fully collateralized…
The document asks whether solutions to a linear stochastic differential equation become differentiable when Brownian noise is filtered through the system’s dynamics. The question contrasts Brownian motion’s irregular paths with the intuition that a colored…
The document asks why volatility models used to estimate Value at Risk may pass a backtest at a 5% confidence tail while failing at a 1% tail. The response says this pattern is common: as the tail becomes more extreme, the assumed return distribution matters…
The document presents an implementation question about fitting a Heston–Nandi GARCH model by maximum likelihood. The author scales log returns, recursively computes conditional variance and standardized residuals, and uses differential evolution to search…
The document asks how Markit defines spot dates for several currencies and how intermediate discount factors enter swap-curve bootstrapping. Its central example is a two-year EUR swap: the coupon schedule needs an 18-month discount factor, while quoted LIBOR…
The document examines how to reproduce the stress performance scenario in a PRIIPs key information document example for a category 2 product. The questioner reports being able to match the other scenarios from the stated return dataset but finding…
The document discusses how to estimate continuous-time credit rating migration dynamics from observed rating histories. It contrasts discrete-time cohort transition matrices, formed from beginning-to-end rating changes over a period, with a continuous-time…
The document considers Monte Carlo pricing of barrier options under a Dupire local-volatility model. The questioner has calibrated smooth implied-volatility surfaces and calculates local volatility at simulation dates, but finds daily stepping slow for long…
The document asks how to price two claims under Black–Scholes: one paying the time integral of the asset price and another paying the squared log of its terminal price. For the integral claim, the answers use discounted risk-neutral expectation and…