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Dokumentumok száma: 20,364
The document gives an intuitive account of the Martingale Representation Theorem in a Brownian-motion setting. It describes martingales as stochastic integrals of Brownian increments, with an adapted process controlling the size of each increment. The…
The note clarifies the distinction between unit gamma and dollar gamma for a variance swap. Unit gamma is expressed with an inverse-square dependence on the underlying price, while dollar gamma multiplies gamma by the square of the underlying price. This…
The document describes where C++ is used in high-frequency trading and why firms rely on it. The main use is the latency-sensitive path that receives market data, updates forecasts or risk information, makes a trading decision, and sends, changes, or cancels…
The document clarifies that the VIX is not a measure of protective-option trading volume. It is an options-based estimate of the market-implied variance over a forward horizon, expressed as volatility, and is related to the fair strike of a variance swap.…
The document explains how to estimate total and idiosyncratic volatility for an individual stock over a fiscal year. Total volatility is the sample standard deviation of daily returns, annualized by multiplying by the square root of the number of trading…
The document examines why interpolating five FX volatility quotes by delta and then plotting the same quotes against their transformed strikes can produce a different-looking smile. The accepted response attributes the change to interpolation sensitivity:…
The document asks whether an equivalent martingale measure guarantees a replicating portfolio for every derivative, then distinguishes that question from the case of a complete market with a unique equivalent martingale measure. It notes that a trinomial…
The document asks whether sample variance and standard deviation should use Bessel’s correction when fitting the drift and volatility of a geometric Brownian motion to historical security returns. It frames the issue as a distinction between treating…
The document models a file transfer in which each round’s success probability depends on a two-state Markov channel. Given the channel states, the total blocks received by round l has a binomial distribution with success probability determined by the product…
The question asks whether “vol” in an equity, credit, and volatility liquidity-risk label means trading volume or volatility. The clues are database query and table names, along with columns including Vega, maturity, ticker, liquidity type, and PctVol. The…
The document examines how deterministic interest rates and dividend yields affect the asymptotic behavior of implied-volatility skew as option maturity grows. It starts from the forward price of a dividend-paying asset and notes that the Black–Scholes…
The document considers how to express floating-rate bond sensitivities, including BR01, when discounting and coupon curves are built from different instruments. It proposes representing the input sensitivities as a vector and mapping them into a chosen risk…
The discussion separates how traders use options from how options are priced. Options can provide leverage, insurance, or hedging, but those uses do not by themselves alter an option’s fair value under a risk-neutral pricing framework. The framework is a…
The document explains portfolio terminology through examples involving dividend reinvestment, depositing cash, and selling one asset to buy another. It presents a portfolio as a collection of asset positions whose composition can change over time. In…
The document asks how to compare volatility forecasts from ARMA(1,1)-GARCH(1,1) models fitted to S&P 500 returns under normal, Student-t, and GED innovations. The author describes generating rolling forecasts with an out-of-sample period and asks whether…
The document considers how to represent a reported correlation between interest rates and S&P returns. It notes that geometric Brownian motion is often used for equities, while interest rate models commonly need to keep rates positive and capture mean…
The document distinguishes exchange liquidity provision and retail broker execution from agency trading performed for a named client. It explains that identifiers in options FIX messages, including fields such as ClientID and CustomGroupID, support tracking…
This discussion compares ways to summarize the price-to-earnings ratios of stocks in an index. For a free-float market-capitalization-weighted index used to represent an index fund or a portfolio holding stocks at index weights, it recommends the weighted…
This discussion distinguishes mean-variance efficiency from preferences over skewness and kurtosis. Mean-variance analysis focuses on expected return and variance, so it does not directly describe whether returns are positively or negatively skewed or how…
The document explores a technical analysis workflow for finding significant swing highs and lows, then plotting trendlines through those points. The example code identifies local extrema by comparing each bar with its immediate neighbors. It filters those…
This discussion explains how to calculate a portfolio’s expected return and volatility, then outlines how to find the global minimum variance allocation between two stocks. Expected portfolio return is the weighted sum of constituent expected returns.…
The document explains cheapest collateral in a collateral optimization setting where a party can choose which asset to post. For securities, one view is that the economically cheapest asset is the one with the highest repo funding rate: delivering it avoids…
The document considers a mean-variance portfolio optimization with short positions allowed, linear equality constraints, and a bound on the absolute size of each position. It asks whether an auxiliary variable and a large penalty are needed to express the…
The document outlines a simulation-based approach to counterparty and own-credit valuation adjustments for an inflation-linked swap. It proposes dividing the valuation horizon into intervals, generating future CPI paths calibrated to a forecast and…