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20,364 dokumenter
The document asks whether portfolio variance computed from a fixed vector of weights equals the quadratic form using the return covariance matrix, and whether the same identity holds with sample estimates. The answer applies linearity of expectation: for…
The document corrects a digital-call valuation under the stated risk-neutral dynamics, where the price has drift proportional to its current level and constant diffusion. The original calculation omitted the conditional mean of the terminal price, leading to…
The document addresses how a sequential financial series becomes usable in a supervised machine-learning model. The key idea is to form examples by pairing information available at a decision time with the later outcome being predicted. Each such…
The document distinguishes zero rates, used to derive discount factors for valuing cash flows today, from forward rates, which are implied by zero rates and no-arbitrage relationships to describe rates over future periods. It frames curve selection as…
The document considers estimating the dependence between two random variables when observations of one variable are available only below a cutoff. The target is a joint probability involving an event for each variable, expressed through their marginal…
The document asks how matrix notation expresses the ordinary least squares objective and how differentiation produces the estimator. It starts from the linear model, writes residuals as the observed response minus fitted values, and expands the residual sum…
The document asks what information a binomial tree must retain when valuing an up-and-in barrier option. The response assumes a European-style contract and proposes using knock-in/knock-out parity: the value of the corresponding vanilla European option…
The document presents a question about implementing Tilley’s algorithm for pricing American options through simulated asset paths. The shown R approach generates risk-neutral paths, works backward through exercise dates, sorts paths by asset value, estimates…
The document asks how to estimate a portfolio volatility measure at a fixed time in Berlin when the portfolio spans US, European, and Japanese equity indices trading in different time zones. It considers using observations aligned to that local time and asks…
The document explores whether implied volatility in a diffusion model must be bounded by the model’s instantaneous volatility. It assumes the asset follows a stochastic-volatility diffusion under the pricing measure and considers a setting where…
The document compares two regressions for testing whether average returns differ by weekday. One includes an intercept and four weekday indicators, leaving one day as the reference category. The other includes an indicator for each weekday and omits the…
The document considers whether a proposed Kelly fraction is appropriate for a trading record described by a win rate and average win and loss sizes. One response gives the standard expression for the special case where every win has the same size and every…
The document asks how to attribute performance for an individual portfolio with a small number of stocks across several sectors. It compares the portfolio’s sector weights with sector weights in the S&P 500 and considers normalizing the benchmark sector…
The discussion explains how negative risk free rates affect equity and index option valuation. It says the Black Scholes framework can accommodate negative rates, and an answer suggests setting very small negative CHF rates to zero as a practical…
The document asks whether a Heston stochastic volatility model and a local volatility model derived from it produce identical option prices. It points to a comparison in Gatheral’s book and asks whether the equivalence depends on spot and variance having…
The document addresses how to extend EURUSD history to dates before the euro existed, for quantitative analysis. One suggested proxy is the European Currency Unit (ECU), a pre-euro basket currency. Its constituent weights can be used to construct a…
For puts with the same underlying and expiry, the displayed bid and ask quotes generally increase as strike prices rise. The question arose because some last-traded prices appeared to violate that pattern, leading the answers to distinguish current quotes…
In investment banking, a curve is a set of values indexed by date, such as discount factors across maturities. A practical curve stores values at selected dates and uses interpolation to estimate values between them, since a value for every possible date is…
The document compares principal component analysis applied to yield curve levels with PCA applied to daily rate changes. The researcher reports that both input choices produce component shapes resembling a parallel level shift, a slope change, and a…
The document explains how a trading system can update position quantity, cost basis, average price, and realized and unrealized profit and loss incrementally as fills arrive. Under average-cost accounting, the update uses the prior position and cost, plus…
The document asks how to interpret the ratio of a standard normal upper-tail probability to its density when evaluated at Black–Scholes d₁ for a put option. It identifies this as the Mills ratio and relates its reciprocal to the normal hazard rate, a concept…
The document distinguishes three option price references. The last-traded price records the most recent execution and can remain unchanged when no further trades occur, even as current quotes move. A closing price may reflect the market around the exchange’s…
The document discusses the practical standing of the Linear Gauss–Markov model for interest rates and its relationship to other short-rate frameworks. It reports that one reference treats LGM under the name “Hagan and Woodward Parameterization,” and that two…
The document considers whether market makers can find opportunities in two share classes with equal cash flow rights but different voting rights and liquidity. Its answer suggests that the classes’ market values may move together over time, while liquidity…