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The document asks how to calculate a ten-day, 99% Value at Risk for a portfolio that combines shares with short European calls on the same company. It gives the share value, annual volatility, and option delta, but the response cautions that delta alone does…
The document considers whether a return variance-covariance matrix should be identical under the physical probability measure and the risk-neutral measure. Its answer emphasizes that equality is not generally supported by empirical evidence. In particular,…
The document addresses how to obtain historical shares outstanding and market capitalization for companies currently in the S&P 500. The questioner wants monthly market-cap figures extending back to 2013, ideally for use in Python, and notes that Yahoo…
The document asks how to validate a performing-loan Loss Given Default model by comparing its estimates with realized workout LGD. It distinguishes a model developed using a through-the-cycle sample of defaulted loans from estimates produced for a…
The document considers a lookback call in a two-period Cox–Ross–Rubinstein binomial model. Its payoff is the terminal asset price minus the lowest price reached across the life of the option, so the payoff depends on the path as well as the terminal price.…
The document asks how to transform short-rate dynamics in a one-factor Linear Gaussian Markov model from its associated numeraire measure to the risk-neutral measure, in order to identify the Hull–White form. The questioner derives the diffusion of the…
The document discusses how to choose the number of hidden states in a hidden Markov model, using financial return data as an example. It compares selecting states by out-of-sample log likelihood with choosing the best in-sample fit using an information…
The document addresses backtesting crypto strategies that calculate indicators on daily candles while processing finer-grained data for entries, exits, and risk controls. Its accepted answer recommends using Backtrader’s data replay feature with minute data…
The document explains how to choose observations for an exponential moving average (EMA) on bars longer than one day. It reports that closing prices are a common input: the final trading-day close for a weekly bar and the final trading-day close for a…
The document asks how Lie groups might be applied in finance and offers a tentative analogy with their use in physics. The response suggests using a transformation group to impose invariance on a model, which can introduce additional terms into its…
The note answers a narrow options question: what happens to the Black–Scholes delta of an out-of-the-money call as implied volatility tends to infinity. It presents the call delta formula and observes that, for a remaining time to expiry, the formula’s…
The document asks for an intuitive explanation of the drift that appears when a forward rate in the LIBOR market model is expressed under a different forward measure. It presents the adjacent-rate drift adjustment, which depends on the correlation between…
The document compares constructing a pairs trading spread from a price difference with using a price ratio. Its practical answer is to calculate the spread for the position the strategy will actually trade, since alternative leg weightings produce different…
The document examines how the index factor should enter the exercise price of an option on a credit default swap index. It contrasts the factor included in the live portfolio swap value at option expiry with the factor that might belong in the exercise…
The document examines how the risk-free rate affects risky debt yields and credit spreads in the Merton structural credit model. It presents the model’s zero-coupon debt yield formula and differentiates the spread with respect to the risk-free rate,…
The document derives the covariance between two Ornstein–Uhlenbeck processes whose Brownian drivers have instantaneous correlation. Starting from each process’s centered stochastic-integral solution, it takes the expectation of their product and uses the…
The document asks how to turn forecasts from an ARIMA model of daily power futures returns into prediction intervals for prices. It describes a simple approach: reverse the data transformations, compound the forecasted returns from the latest observed price,…
The note asks whether an underlying’s risk-neutral implied distribution can be recovered from forward prices, as it can from a cross-section of option prices using the Breeden–Litzenberger relationship. The answer explains that a forward price alone does not…
The discussion examines whether Brinson performance attribution can be adapted from sectors to style factors such as size, momentum, and volatility. It contrasts returns-based regression, where factor coefficients describe portfolio exposure, with a…
The document explains how to find the weights of a three-asset portfolio that minimize variance while requiring the weights to sum to one. It expresses portfolio variance using each asset’s variance and the pairwise covariances, then presents two solution…
The note classifies operating income divided by total assets as a profitability measure, commonly used in banking. It distinguishes profitability from leverage, asset composition, and liquidity by considering what the ratio’s inputs capture. Because the…
The document formulates a maximum expected return portfolio as minimizing negative expected return, subject to fully invested weights and nonnegative positions. It asks how to construct the Lagrangian and derive a closed-form solution for the portfolio…
The document asks whether correlations should be calculated from simple returns, log returns, or log prices, and whether the choice is merely conventional. The response ties the answer to the intended use: when correlations will drive a simulation, estimate…
The document questions whether a prominent spike in the autocorrelation of squared intraday price changes supports the usual account of volatility clustering. It compares a figure in a highly cited article with a later figure in a book by the same authors,…