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The document introduces replication of common option strategies, including vertical spreads, butterflies, straddles, and strangles. Its central idea is to build a target payoff by combining simpler instruments, particularly zero-coupon bonds and European…
The discussion explains that counting Brownian drivers and risky assets alone does not establish market incompleteness. In the example, the two assets depend on three named Brownian motions, but their exposures can be rewritten using only two independent…
The document asks whether TA-Lib can speed up calculation of an exponentially weighted moving standard deviation. It distinguishes TA-Lib’s rolling standard deviation from the exponentially weighted statistic provided by pandas. The proposed custom Numba…
The document compares financial mathematics with risk theory and risk management, noting that their methods can overlap while their scope and probability conventions differ. Financial mathematics is presented as quantitatively focused, with applications such…
The document explains that “not rated” does not have one universal industry meaning. Its interpretation depends on the credit-rating agency or agencies included in the analysis. In common usage, an issuer may be described as not rated when none of the major…
The document asks how to estimate annual mean returns and a four-asset covariance matrix from quarterly observations. It states the correct compounding relationship: an annual return is the product of the four quarterly gross returns minus one. The proposed…
The document derives a strong solution for a stochastic differential equation whose drift is inversely proportional to the state and whose diffusion is proportional to the state. One approach applies Itô’s formula to the squared process, turning it into a…
The document discusses the exposure profile of a buyer of credit protection in a single-name credit default swap. It explains the contract’s value as the protection leg minus the premium leg: as time passes, fewer premium payments remain, while the…
The document asks how a positively skewed stock-price distribution affects Black–Scholes–Merton option valuations across strikes. It includes two brief responses: one links right-skewed outcomes to greater probability of high terminal prices and a higher…
The document asks whether investors can build a diversified portfolio with higher expected returns by combining risky investments whose returns are uncorrelated. It frames the question with an asset-pricing relation in which price depends on expected future…
The document presents a simple moving-average backtester for shares, with signals based on a fast and slow average, position sizing, cash accounting, and portfolio equity. The reported output contains missing values, and the answer points to a likely cause…
The document clarifies several measures of interest-rate sensitivity whose names are used inconsistently. Bond DV01 is described as the price change for a one basis point move in the bond’s own yield, commonly its yield to maturity. This differs from…
The document evaluates whether the Stratonovich integral of Brownian motion with respect to itself is a martingale. It derives the integral from symmetric partition sums: each term becomes a difference of squared Brownian values, and the sum telescopes.…
The document considers how to calculate option deltas across strikes when implied volatility varies with strike. It frames the key issue as selecting the implied volatility input to Black–Scholes when the volatility surface is skewed, especially for hedging…
The document addresses the intuition behind the Black-Scholes call price as volatility grows without bound. An accepted explanation states that the call approaches the discounted value of the underlying forward, which is the spot price when dividends and…
The document surveys lower-cost sources for historical financial statements, aimed at students or researchers who need panel data on US companies. The requested fields include balance-sheet, income-statement, and cash-flow items, along with ticker, period…
The document asks how to adjust statistical significance when a trading rule is selected by optimizing continuous parameters, using moving-average lengths as an example. It contrasts this with calendar-effect research, where a finite set of candidate rules…
The document compares using one size-adjusted micro-price to guide both sides of a market-making quote with maintaining separate bid and offer fair values. Its examples use futures order-book prices and displayed sizes: the micro-price shifts toward the side…
The document explores how to interpret an integral whose integrand is the terminal Brownian value, which depends on future information and therefore is not admissible in the ordinary Itô integral. It contrasts the stated identity for this anticipating…
The document distinguishes two definitions of tracking error and explains how each relates to a portfolio’s beta against its benchmark. When tracking error is the volatility of active returns—the portfolio return minus the benchmark return—a beta of one is…
The document explains why the estimated constant in a GARCH return model may differ from the ordinary sample mean. The sample mean gives every observation equal weight. Under a GARCH model, observations have different conditional volatility, so…
The document corrects a claim about the delta of a down-and-out call as the underlying approaches its lower barrier. It explains that delta generally falls toward zero near the barrier, since reaching the barrier knocks out the option. For options close to…
The document outlines a practical workflow for stock factor investing: define an investible universe, collect and process factor data, then rank or score securities. It describes several ways to turn scores into holdings, including selecting a subset and…
The document presents a dividend-entitlement question involving an investor who holds shares before an ex-dividend date, buys additional shares during that date, and sells the entire position later the same day. It asks whether the eventual cash dividend is…