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20,364 dokumenter
The document asks how to create synthetic one-minute bars from daily open, high, low, and close values for testing an algorithm’s speed and memory use. The synthetic path need not resemble actual market behavior, but its minute bars should preserve each…
The document examines whether a portfolio that is neutral to vega is also neutral to gamma and theta. One response gives a specific result for portfolios of calls and puts sharing the same maturity: under the Black–Scholes framework, gamma neutrality and…
The document considers whether the leading principal component of historical interest-rate changes can serve as the volatility curve for calibrating a Hull–White or Black–Derman–Toy tree. It contrasts estimating a separate standard deviation at each tenor…
The document asks where forward prices can enter a Monte Carlo derivatives-pricing workflow. It describes a system that accepts calibration instruments, a model choice, initial underlying levels, a yield curve, and a forward curve. The follow-up clarifies…
The document introduces an ATM implied-volatility correction in a free-boundary extension of SABR, motivated by pricing under negative rates. It describes a small-time heat-kernel approximation and gives a first-order correction for the at-the-money case…
The document asks how to find the risk-neutral conditional expectation of a process built from geometric Brownian motion and an accumulated constant term. The process is expressed as a GBM multiplied by an integral involving its reciprocal, and it also…
The discussion considers whether historical asset prices should be adjusted for inflation and which inflation series to use. It identifies the U.S. Consumer Price Index for All Urban Consumers as the commonly cited headline measure, distinguishing it from…
The discussion explores estimating one-day downside risk for a portfolio that combines linear assets with short option exposure. It contrasts fitting a generalized Pareto distribution to the tail of repriced historical portfolio returns with simulating…
The discussion asks how to infer a stochastic process from a long observed series and questions whether a histogram can identify its dynamics. The response recommends beginning with discrete-time time-series analysis rather than trying to recover an…
The discussion addresses how to obtain historical Eurozone fixed-income index data for a multi-factor study of European bond funds when Bloomberg is unavailable and replacement ETFs lack sufficiently long histories. The response names Yieldbook index…
The discussion considers how to price same-day-expiry options on futures across equity indexes, energy commodities, and Treasury markets. The response says many futures options are European and can be priced with Black–Scholes, while some contracts are…
The document considers how high-frequency market making works when short selling is restricted. It explains two ways a participant may still provide ask-side quotes: an official market maker may receive a short-selling waiver, or another participant may…
The document asks why long-horizon realized excess returns on agency mortgage-backed securities may fall below their average option-adjusted spread over duration-adjusted Treasuries. The response attributes the gap to borrower prepayment behavior changing…
The document raises a mathematical question about deriving an asymptotic option-price expression used in the Hagan SABR implied volatility formula. It focuses on a partial differential equation for option value, with terms involving the forward price,…
The document discusses choosing a real-world stochastic model for property price index risk in Monte Carlo analysis. It recommends considering a factor model that links local and national property indexes with economic predictors such as GDP, while noting…
The document asks how to estimate the dollar impact of a change in cross-currency basis for a portfolio of swaps hedging loans or bonds. The answer offers a rough approximation: use the book’s weighted average tenor, with each trade weighted by the notional…
The document explains the sharp decline in high-yield corporate bond ETFs during the Great Recession despite falling interest rates. The key distinction is between Treasury yields and the yields investors demand on risky corporate debt. A high-yield bond’s…
The document compares two ways to extract risk-neutral information from option prices. Breeden-Litzenberger (BL) uses the curvature of call prices across strikes to estimate an entire risk-neutral density. Bakshi-Kapadia-Madan (BKM) methods estimate…
The document discusses how to simulate trade prices that behave like a random walk. One answer recommends modeling the bid-ask spread and using Poisson or Hawkes point processes for order arrivals and cancellations. A price move can occur when the queue at…
The document addresses whether factor betas that are imprecisely estimated in time-series regressions can still produce a statistically precise risk premium in a cross-sectional regression. The answer is yes in principle, but beta measurement error works…
The document raises questions about Merton’s derivation of the security market line from the tangency portfolio. Its focus is the covariance between an individual asset and the market portfolio: the reader asks why that covariance can be written as a…
The document explains how to interpret a credit default swap (CDS) spread when the contract pays a standardized coupon. The quoted par spread represents the annual premium that would make a new contract’s value zero; it is not itself the upfront price. The…
The document describes a global equity portfolio hedged with short benchmark futures using beta estimated from a trailing year of volatility data. The investor observes that beta rose during a market crash, leaving the hedge short of the portfolio's losses,…
The document sketches a multifactor geometric Brownian motion framework for pricing options whose payoffs depend on multiple assets. Each asset has its own volatility, while shared Brownian factors create dependence; factor loadings determine the modeled…