คลังความรู้

The document raises a practical question about a statement in a diversification paper: principal component eigenvalues correspond to the variances of uncorrelated portfolios. The author compares eigenvalues from the covariance matrix of asset returns with…

The document clarifies how to calculate the endpoint probability for a simple symmetric random walk, in the context of applying the reflection principle. The number of paths ending at a given location is determined by the required counts of up and down…

The document explains a way for a domestic investor to hold a foreign currency security without taking direct foreign exchange exposure. It compares three economically equivalent approaches: combine spot and forward FX transactions around the security…

The document sketches why a constant-maturity swap (CMS) payment differs from a swap rate’s value under the swaption annuity measure. A swaption payoff is naturally valued under that measure, while a CMS coupon paid at a later date is expressed under the…

The document examines why maximum-likelihood estimates for an exponential Hawkes process can drive the decay rate and excitation parameter toward very large values when tick records share millisecond timestamps. In the stated likelihood recursion, zero…

The document presents a SABR calibration problem in which an optimizer minimizes the difference between model and market volatilities across many strikes. The data are converted before fitting, and a differential evolution routine searches within parameter…

The document asks whether diffusion or heat-equation methods can price a derivative whose payoff has a nonzero lower bound. The answer rewrites the proposed payoff as a standard call payoff plus a constant, then values the pieces separately under the…

The document clarifies that increasing option maturity means moving toward longer time to expiry. It explains how a volatility surface table can show a flatter implied-volatility smile at longer maturities: the relevant comparison is the wings' implied…

The document raises an accounting and position-treatment question about a short position during a reverse split. It sets out a long-share example in which the fractional share created by a two-for-three split is converted into cash, then asks how the…

The document discusses model features that can better represent equity-market behavior than a basic constant-volatility diffusion. It proposes a flexible stochastic-volatility framework in which log prices follow Brownian motion, volatility varies over time…

The document explains how to construct a secured barrier call from an up-and-out European call and a cash-or-nothing digital call. The target pays the ordinary call payoff if the underlying remains below the barrier through expiry, pays the barrier level if…

The document discusses how to choose time and underlying-price boundaries for a finite-difference grid used to approximate an option pricing function. It recommends covering the option’s life from the valuation time through maturity. For the upper price…

The document explains how to calculate sample variance from consecutive close-to-close log returns while accounting for their estimated drift. The question begins with a sum of squared log returns and asks how the drift adjustment appears in an alternative…

The document frames a cash-and-carry trade in a contango market: buy the underlying asset and sell a futures contract. It compares a nearer contract with a higher annualized yield against a later contract that may offer a larger absolute basis. The trader…

The document explains how to classify a stock as overvalued or undervalued by comparing its forecast return with its CAPM required return. The example adjusts a historical beta using a forecast formula, then applies the market risk premium and risk-free rate…

The document presents a dual digital option whose payoff depends on two foreign exchange rates crossing specified thresholds at maturity. Because the payoff requires both conditions to hold, its value is sensitive to the correlation between the rates. The…

The document questions the practice of using sovereign credit risk as an input to a country's equity risk premium. It notes that estimates may draw on ratings, bond default spreads, or credit default swap spreads, with an adjustment factor applied to…

The document frames return replication as a least-squares portfolio problem: choose weights on a set of assets so their daily returns track a target asset. It introduces the unconstrained regression solution, then explains that requiring weights to be…

The document describes a researcher calculating monthly Sharpe ratios for a large set of mutual funds over a ten-year sample and finding that every result is positive. The stated calculation takes each fund’s average monthly excess return and divides it by…

The document investigates conflicting reported lows for Paladin Energy on a specific trading day. Its accepted answer distinguishes raw traded prices from adjusted historical prices: the raw low was confirmed by an exchange course-of-sales feed, while a…

The document examines a linear factor model in which an observed vector is represented by an intercept, factor exposures, and residual terms. It asks how to interpret the condition that factors are uncorrelated with residuals, and whether mutually…

The document describes calibrating a geometric Brownian motion model from daily prices. It gives formulas for estimating diffusion from the variance of daily returns and drift from their mean, adjusted by half the estimated variance. The questioner then asks…

The document asks whether multiple risk estimators can be considered together, including whether their divergence might be summarized with a ratio or whether their correlation makes this redundant. The response suggests using GARCH and Value-at-Risk (VaR) in…

The document compares Yahoo Finance’s ^GSPC and ^SPX symbols, which both refer to the S&P 500 index. One answer reports that historical daily, monthly, and weekly data retrieved under ^GSPC appeared identical to historical SPX data. Another suggests ^GSPC…