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20,364 dokumenter
The document reviews a commonly cited set of empirical regularities in asset returns, including heavy tails, volatility clustering, slow decay in the autocorrelation of absolute returns, leverage effects, and relationships between volume and volatility. It…
The document examines a proof claiming that a positive martingale can be expressed as an exponential driven by a Brownian stochastic integral. The proof applies the martingale representation theorem to write the martingale differential in terms of Brownian…
The document describes a problem generating Monte Carlo paths from a QuantLib Black variance surface. The surface is interpolated and extrapolated from market data, with checks for decreasing total variance across maturities and butterfly irregularities, yet…
The document explains why simple returns and log returns aggregate differently when a portfolio contains multiple trades and is measured across multiple days. With fixed weights for a given day, simple returns combine linearly across trades. Across time,…
The document explains that an issuer-level credit rating does not necessarily determine the rating of every individual bond. Even bonds from the same obligor that share a seniority category can receive different issue ratings, because features in each bond’s…
The document raises two practical problems in estimating correlation from market time series: missing observations within a trading day and trades that arrive at different times for each security. It points readers toward methods designed for irregularly…
The discussion considers estimating implied volatility at each intraday option tick when end-of-day implied volatility and Greeks are available alongside tick-level option and underlying prices. One shortcut estimates volatility changes from option price…
The discussion concerns software choices for building fixed-income portfolio risk analytics when QuantLib and its Java interface are unavailable. The questioner reports problems with JQuantLib, including a bond-yield calculation error, and asks for pure Java…
The note asks how the Black–Scholes framework extends to a stock paying a continuous dividend yield. It outlines a proposed construction that converts the dividend-paying stock into an auxiliary process by reinvesting the yield, then applies a change of…
The note addresses a pairs trading setup that selects pairs using the sum of squared distances between normalized prices, then monitors the resulting spread. It raises concerns about unequal dollar values in the long and short positions and whether the…
The note explains how to interpret a question from Grinold and Kahn’s portfolio theory exercises about the characteristic associated with the Major Markets Index portfolio. The proposed interpretation is to identify the attribute for which the MMI portfolio…
The question asks how to derive the covariance between values of a mean reverting Vasicek process at two times. The answer first expresses the process as the solution to its stochastic differential equation: its initial level and long run mean terms are…
The response discusses ways to protect portfolio value and manage open positions. It describes portfolio insurance as hedging share exposure with put options, with puts placed below the acquisition price so they can gain value during a sharp decline. It…
Treasury credit risk is the assessment of the creditworthiness of banks and other counterparties that a bank engages through its treasury function. The treasury office oversees liquidity and capital, and may lend surplus funds to other banks or raise funding…
The document raises questions about why daily and monthly portfolio return plots derived from a data provider’s return index might differ. It describes calculating daily returns as consecutive index changes and monthly returns from month-end index values. It…
The document asks whether the standard covariance-matrix formula for portfolio variance remains valid when some portfolio weights are negative, as they are for short positions. It presents a futures portfolio with both positive and negative contract…
The document distinguishes a delta-neutral hedge from a self-financing trading strategy in the Black–Scholes setting. A portfolio holding an option and a changing number of shares may cancel local price risk, but changes in the share position create…
The document explains how to calculate an asset’s return across multiple periods when it pays dividends. A single-period gross return includes both the ending share price and the dividend, divided by the starting price. To find the gross return over several…
The document outlines a filtered historical simulation approach to market risk for vanilla swap portfolios. Historical observations should be represented as changes in selected curve risk factors, such as discounting and forwarding zero rates at chosen…
The document explains how to calculate the time-zero delivery price of a bond forward in a discrete-time, risk-neutral fixed-income model. Its pricing relation takes the expected discounted value of the underlying bond at the forward date and divides it by…
Historical default rates are probabilities under the real-world measure, but they cannot be converted directly into risk-neutral probabilities using Girsanov’s theorem alone. A model for the underlying process and its dynamics under the real-world measure…
The exchange considers how to estimate a CDS spread between quoted maturities, such as a spread for an intermediate tenor between shorter and longer quotes. It asks whether hazard rates calibrated to quoted CDS contracts can support a direct spread…
The post asks how to convert a US Treasury bond yield into a price by discounting the remaining coupon and principal cash flows. The author reports a calculated value that differs from a quoted market price and tests alternative day-count and compounding…
The document raises a modeling question about computing option theta from the Black-Scholes partial differential equation when market implied volatility varies across strikes. It compares three approaches: standard Black-Scholes Greeks with implied…