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20,364 dokumenti
The document describes a general way to value a call option when the underlying’s terminal price distribution is known. The option value is the discounted expected payoff under a risk-neutral probability distribution: integrate the payoff above the strike…
The document explains how to calculate each asset’s contribution to a portfolio’s volatility from the covariance matrix and portfolio weights. For covariance matrix Σ and weight vector w, portfolio variance is wᵀΣw. The covariance between asset i and the…
The document asks how to interpret the Phillips–Ouliaris test in R’s urca package and whether its output contains an estimated cointegrating vector. It constructs a bivariate example with a known relation, runs the test, and reports a statistic above the…
The document explains how to convert a correlation matrix and a set of standard deviations into a covariance matrix. For each pair of variables, multiply their correlation by both standard deviations. On the diagonal, each variable’s covariance with itself…
The document discusses a machine-learning return forecast evaluated with walk-forward validation while varying training-window length, prediction horizon, step size, and embargo. The reported out-of-sample results deteriorate as the step or embargo…
The document presents a Python function intended to calculate Donchian channel bounds from high and low price arrays over a rolling window. It identifies a specific bug in the lower-bound loop: the function appends the entire low-price input array to the…
The note raises two implementation questions about the time-series momentum method described by Moskowitz, Ooi, and Pedersen. First, it asks how to interpret the paper’s ex-ante volatility estimate when the strategy uses a twelve-month return signal: whether…
The note poses a continuous-time question about a dividend-paying stock whose price follows a diffusion with drift reduced by a continuous dividend yield. It asks how the value process changes when dividends are continuously reinvested into the same stock,…
The note asks how to measure the relationship between a portfolio of assets and an external series, such as housing prices. Averaging each asset’s correlation with the external metric, weighted by portfolio holdings, may seem appropriate, but the response…
The note distinguishes two short-dated foreign-exchange swap tenors used to move settlement forward. Under the usual T+2 spot convention, a tomorrow/next swap exchanges currencies on the next business day and reverses that exchange on the following business…
The document poses a quantitative finance problem: how portfolio values evolve when the underlying investment follows geometric Brownian motion and a fixed dollar amount is withdrawn at the beginning of each year. It asks whether an approximate analytical…
The document discusses ways to assess whether a strategy’s live profits reflect a repeatable signal or chance, especially when market volatility is large relative to the observed gains. One proposed test, attributed to Alfred Cowles, preserves the trader’s…
The document examines daily returns for a portfolio holding one stock long and another short, with cash proceeds from the short sale included in net asset value. It shows that the portfolio return for a later day should be calculated from the change in total…
The document addresses an attempt to derive stochastic differentials for integrals involving Brownian motion by treating the integral itself as a function of time and the current Brownian value. The response clarifies that the differential notation for a…
The discussion considers whether an economics researcher who prices options and calibrates models should learn C++ to speed computationally intensive work, and how to connect it with higher-level languages. One respondent recommends a derivatives-pricing…
The document works through the valuation of a forward rate agreement (FRA) that pays fixed and receives floating. It calculates the accrual fraction for the contract period, estimates a missing tenor’s Libor fixing by linear interpolation between available…
The document explains how an index future or the underlying spot index can serve as the market return proxy when estimating stock betas. Spot returns are straightforward to calculate, and closing index values are described as reliable; opening and intraday…
The discussion clarifies that risk neutrality is about how an interest-rate model is calibrated, rather than an inherent property of the Vasicek process. Calibrating parameters to traded instrument prices under pricing and hedging assumptions gives a…
The discussion considers an empirical method for estimating a credit portfolio loss distribution from monthly account snapshots. The proposed procedure groups loans by origination vintage, measures defaults over a fixed horizon, applies a common recovery…
The discussion explains how to calculate a corporate bond’s Z-spread when its yield to maturity and annual coupon schedule are known. The conventional approach is to solve numerically for the parallel shift to a reference swap curve that makes the present…
The discussion examines why the mean estimated market-model beta for Australian All Ordinaries constituents can be below one. The researcher estimates separate betas for 300 firms over a one-year window and asks whether the index’s market-cap weighting…
The document asks whether Black–Scholes call valuation should use a point estimate of variance from historical returns or average option values across the sampling distribution of that estimate. It describes treating the sample variance as uncertain, mapping…
The document examines whether investors who remain in a bond fund can lose value because other shareholders redeem during a market decline. A stylized example tracks a fund through a bond price shock, redemptions by half its holders, and a subsequent…
The document asks how to combine conditional default probabilities for different institutions into a single measure of systemic impact. The response proposes comparing each institution’s default probability conditional on another bank’s default with its…