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20,364 dokumenter
A calendar spread between two bond futures can carry repo exposure even when both contracts have the same cheapest-to-deliver bond. The key mechanism is that contracts with different delivery dates respond differently to financing rates: the later contract…
A return regression can help estimate a strategy’s Sharpe ratio, but the regression alone does not determine it. The result depends on how the signal is converted into positions and, for portfolios, on the conditional covariance among assets. A tangency…
The document explains why Treasury yields shown by financial media may differ from yields published by the US Treasury. It identifies differences in observation timing and in the instruments or methodology used. The Treasury figure is described as using bid…
The document examines when optimizing expected utility leads to an investment fraction proportional to expected return divided by variance. It writes the first-order condition for an investor choosing a fraction of wealth in a risky asset, then identifies…
The document explains why gamma exposure is expressed using the square of a change in the underlying price. It uses dimensional analysis: option-price changes are measured in dollars, while gamma measures the second derivative of option value with respect to…
The document discusses sources for a fitted one-year real yield series for Treasury Inflation-Protected Securities (TIPS), sampled monthly, and notes that similar data may be available through bank research portals. Its main focus is a caveat: quoted real…
The document considers how to choose a parameter that divides observations into two groups, with the aim of making their empirical distribution functions as different as possible. It compares maximizing the largest pointwise absolute gap between the two…
Dispersion has a broad statistical meaning: the spread of a distribution around its central tendency. Variance is a common measure of that spread, and standard deviation is its square root. In finance, volatility usually refers to standard deviation as a…
The Hansen–Jagannathan bound links the volatility of a stochastic discount factor (SDF) to the Sharpe ratio of excess returns it prices. The pricing condition is that the expected product of the SDF and an excess return equals zero. This implies that the…
The note asks why a textbook calculation integrates a differential involving a stochastic process using what looks like an ordinary Riemann integral. The answer distinguishes integrals with a variable integrand from the integral of a differential alone. For…
The note asks why American option valuation is expressed as the best conditional expected discounted payoff over stopping times rather than over fixed exercise dates. A fixed date is a stopping time, so optimizing over all stopping times cannot produce a…
This note describes a reported mismatch between a covariance matrix that appears positive definite under Cholesky decomposition and negative eigenvalues returned by a symmetric eigensolver. The matrix is built from historical forward-rate data imported…
The document describes a workflow for forecasting financial time series with technical indicators and machine learning: calculate indicators, remove highly correlated features, lag inputs, train with a rolling or expanding window, and evaluate on held-out…
The document asks why the variance accumulated by a geometric Brownian motion over a time horizon is represented by the integral of instantaneous variance, and how time averaging enters the stated realized-variance expression. The answer builds the result…
The document addresses how traders can identify economic announcements that move different markets, with a particular question about agricultural commodities. It cites a study examining the immediate responses of commodity prices and short-term Treasury bill…
The document asks how to convert quarterly observations into monthly data and how to format dates in Excel so that Stata recognizes them. The suggested interpolation method is cubic splines, which construct a smooth curve through the quarterly values and use…
The document asks how to price American options when the underlying follows risk-neutral dynamics with volatility that varies with spot. The response identifies this as a special case of a local volatility model, where volatility may depend on time and spot,…
The document addresses whether a futures position used to reduce a bond portfolio’s duration should be included when estimating portfolio yield to maturity. The response says to include it by using the future’s implied yield to maturity and assigning that…
The document asks whether an equity’s implied volatility skew can reveal the probability of an equity move conditional on a change in implied volatility. It defines skew as the difference between implied volatilities at two option deltas and explains why…
The document compares two ways to summarize an asset’s historical return and volatility. One method averages daily log returns and scales the mean and standard deviation to an annual horizon; the other calculates each calendar year’s simple return and then…
The discussion addresses why a Carr–Madan fast Fourier transform calculation can return complex-valued quantities when pricing caplets. The accepted answer says the complex form is expected in the method and that the option price is obtained from the real…
The response points to an intuitive route to understanding Gyöngy’s theorem through European call prices and generalized derivatives. It starts from an asset whose drift follows a risk-neutral specification and whose volatility may depend on the adapted…
The discussion compares QuantLib pricing approaches for geometric and arithmetic Asian options. It reports that the finite-difference Black–Scholes Asian engine supports discrete arithmetic averaging, not continuous geometric averaging. A discrete geometric…
The discussion explains a first-order way to think about a bond’s return over a holding period: combine its yield with the price effect of changes in yield, scaled by the bond’s DV01. Roll-down return is a special case of that price effect, calculated under…