নলেজ লাইব্রেরি

The document distinguishes GARCH forecasts from realized volatility (RV) measures. GARCH models use discrete observations, commonly squared returns, to estimate conditional variance and forecast volatility. RV instead aggregates high-frequency observations…

The document compares exercising a call with selling it before expiration. In its example, a call bought for $1 has a market value of $2.10 when the stock reaches $12, above the $10 strike. Exercising and immediately selling the shares produces a $1 gain per…

The document asks how to construct historical break-even inflation curves in Brazil, where two inflation-linked government bond series reference different price indices: NTN-C is tied to IGP-M and NTN-B to IPCA. The response recalls that Deutsche Bank used…

The document addresses exporting daily closing prices for many Russell 2000 constituents from Bloomberg into Excel. A historical data query returns dates alongside prices, which can interfere with copying formulas across adjacent columns. One response…

The question considers a discrete price process with normally distributed independent shocks and asks whether the affine closure property of normal random variables can replace the Central Limit Theorem in deriving a continuous-time limit. It specifies an…

The document discusses using ARCH or GARCH models to describe time-varying volatility in a financial series, prompted by a researcher studying copper prices. These models relate current conditional variance to past observations or shocks. The proposed…

The document asks how Yahoo Finance produces a stock’s annualized growth estimate for the coming five years. The answer says the figure comes from Refinitiv’s Institutional Brokers’ Estimate System, a database of analyst forecasts. It describes the displayed…

The discussion considers how to examine whether emerging markets change in volatility and in correlation with developed-market indices. Rather than prescribing a split into halves or thirds, one answer recommends plotting rolling estimates to locate periods…

Mean-variance optimization can produce unstable allocations when expected returns and covariance inputs are estimated with error. The discussion surveys practical ways to reduce that sensitivity: shrink historical estimates toward common targets, use robust…

The document works through the reciprocal of a stochastic process that follows geometric Brownian motion, as a step toward finding the process for a ratio of two correlated processes. It identifies a likely notation error in the stated reciprocal formula:…

The document explains how to fit a Svensson yield curve using prices or quoted yields for coupon-paying bonds, even though the model directly describes zero-coupon rates. The fitted zero rates imply discount factors at each cash-flow date. Applying those…

The document presents a question about translating a multi-period asset allocation problem into a dynamic programming formulation. Wealth evolves through investment returns applied to current wealth plus income, while the investor chooses portfolio fractions…

The document examines Hull’s two formulations for choosing a minimum-variance futures hedge. One uses the correlation and standard deviations of absolute spot and futures price changes, then scales the hedge ratio by the quantities of the asset and futures…

The document explains why buying a bond and shorting a futures contract can be viewed as a synthetic reverse repo. In a reverse repo, an asset is sold with an agreement to repurchase it later; the price difference represents financing interest, while the…

The document compares a covered call with a cash-secured put on the same underlying, strike, and expiration. Their similar payoff profiles can still show different displayed maximum gains when the call and put have different prices or implied volatilities.…

The document presents an attempt to calibrate the raw SVI parameterization to market implied volatilities. The code converts quoted volatilities to total implied variance, computes model variance at log-moneyness values, and minimizes the root sum of squared…

The document distinguishes the probability that a stock reaches a specified multiple of its initial price at a fixed horizon from the probability that it reaches that level at any time before the horizon. Under geometric Brownian motion, it rewrites the…

The document asks how to evaluate the integral in the semi-closed Heston formula for call options. Its answer says Monte Carlo simulation can approximate the integrals, while Newton-Cotes formulas and Gaussian quadrature are also possible numerical methods.…

The document examines whether average return per period can distinguish between investments that reach zero over different lengths of time. It defines gross return as the ratio of ending price to starting price and explains that multiplying single period…

The document compares R with commercial tools such as Matlab and Mathematica for quantitative research. It notes that R has packages for statistical analysis, simulation, optimization, and numerical integration, then gathers user reports about areas where…

The document examines why sponsors may not issue an exchange-traded note alongside an inverse version. It explains that daily leveraged and inverse notes are path-dependent: their exposure resets as their values change, so the pair’s gains and losses do not…

The document poses a calibration question for a stock modeled as a monthly random walk with independent, identically distributed changes. Each monthly change is assumed to equal either a positive or negative fixed amount with equal probability, giving the…

The document explains why at-the-money implied volatility can rise or fall across option maturities. It challenges the assumption that the term structure should be monotonic and identifies several possible drivers, including return autocorrelation,…

The document derives the density ratio between two forward measures by applying the change-of-numéraire principle. A numéraire is a strictly positive price process used as the unit for valuing other assets; changing the numéraire changes the associated…