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The document explains why faster mortgage prepayments tend to raise yield to maturity for a bond bought below face value, but lower yield for one bought above face value. It uses fixed coupon bond examples with different repayment dates to show how the gain…
The document discusses using proxy time series when a risk factor lacks enough historical observations for market risk measurement. It contrasts older Basel II guidance with the newer Fundamental Review of the Trading Book (FRTB), where insufficient real…
The document considers how to scale minute-by-minute trading volumes into a bounded range when an unusually large observation distorts ordinary normalization. It proposes a dynamic cap based on twice the sample median, then clips values above that limit…
The document addresses whether a joint probability density can be used only for rectangular events, such as separate constraints on each random variable. It explains that a density definition may be stated first for product sets without restricting…
The document explains why legal entity identifiers, Bloomberg tickers, and security identifiers do not generally map one to one. An LEI identifies an entity, while instruments such as bonds issued by that entity have their own identifiers. A single entity…
The document clarifies why option volatility models may express moneyness using the underlying’s forward price or spot price. It distinguishes this choice from forward volatility, which means volatility over a future time interval. Forward based moneyness…
The document asks what a Bloomberg spreadsheet expression calculates while attempting to reproduce it with another data source. The expression retrieves a security’s last price with a historical data request and divides it by a technical-analysis request for…
The document clarifies two return calculations used when measuring event-study abnormal returns. A stock’s size-adjusted return for a day is its own return minus the equal-weighted return of stocks in the same size decile. The described reference group uses…
The document describes a two-period portfolio comparison using historical returns. It estimates an in-sample efficient frontier from the first period’s empirical covariance matrix, generating portfolios across target returns. It then keeps those portfolio…
The document asks how to state the Black–Scholes free-boundary problem for an American put. It contrasts two proposed condition sets involving the exercise region, continuation region, terminal payoff, behavior at large stock prices, and value and delta…
The document explains the intuition behind a claim that a par bond has zero key rate duration at curve points other than its maturity-matched rate. The key assumption is that a shocked par yield curve remains a par curve. Under that convention, a shift at a…
The document examines a claim that at-the-money-forward implied volatility in the Heston model is below the square root of expected variance. The response connects variance swap volatility to an expectation over squared values of a transformed, or modified,…
The document explains why the Fama-French three factors can be correlated without invalidating the model. In a classical factor model, researchers specify factor return series and estimate each asset’s factor loadings with time-series regressions. Those…
The document compares guidance on how banks should represent non-performing exposures (NPEs) in interest rate risk in the banking book. EBA guidance says to treat exposures net of provisions as interest-sensitive instruments, using expected cash flows and…
The document addresses finite difference pricing when an exotic option has a discontinuous payoff, such as a binary or barrier, and nearby vanilla strikes are used for hedging. A coarse asset-price grid may fail to represent the payoff boundary accurately…
The document explains why squared returns divided by estimated conditional variance can be used to check a GARCH model. Under the model, returns are written as conditional volatility times an independent, zero-mean, unit-variance innovation. A GARCH(1,1)…
The document explains why historical OHLCV records for the same listed share can disagree across Google Finance and Yahoo Finance. Possible causes include distinct vendors and trading platforms, different aggregation rules, post-trade corrections,…
The document surveys modeling concerns when interest rates can fall below zero, focusing on products whose pricing frameworks assume lognormal rates. Black-style option formulas and some volatility conventions become unsuitable when rates may be negative.…
The document explains the beta adjustment behind the betting-against-beta factor. It treats a risky asset's return above the risk-free rate as a zero-cost excess return, then scales that return by the inverse of its market beta. This changes the portfolio's…
The document resolves a terminology question about Japan’s overnight reference rate. The question contrasts the Bank of Japan’s use of TONA with the TONAR name found in another reference source, and asks whether they identify distinct rates. The accepted…
The document weighs whether investors should include commodities in diversified portfolios. It presents arguments on both sides, noting that asset-allocation products and some institutional portfolios use commodity exposure, while the cited research is not…
The document examines how to derive the variance of the short rate in the Cox–Ingersoll–Ross model, whose diffusion volatility depends on the square root of the rate. One proposed derivation transforms the rate, applies Itô’s lemma to its square, and then…
The document describes a two-step Fama–MacBeth procedure for estimating risk premia. First, each stock’s return is regressed on a market index to estimate its market beta. The second step is a cross-sectional regression for each date, using the stock betas…
The document explains how to find the fixed coupon rate that makes a coupon bond's value at its starting date equal its face value. Under evenly spaced payment dates, each coupon is the rate multiplied by the accrual interval and face value. The bond price…