คลังความรู้

The document explains the intuition behind representing a variance swap hedge as a weighted portfolio of vanilla options across strikes. The integral represents a continuous strip: at each strike, the portfolio holds an amount determined by a weighting…

The document discusses how to calculate a stressed performance scenario under the PRIIPs framework when the product has a recommended holding period (RHP). The response distinguishes the historical data used to estimate stressed volatility from the future…

The document asks how to estimate combined demand when two firms charge fixed prices. It starts from a linear demand expression for the overall market and allocates that demand between firms using a price-sensitive logit share. The central modeling issue is…

The document examines how to define a return for a futures spread when entering the position does not require paying its notional value. Initial and maintenance margin do not, by themselves, provide a stable measure of the capital committed or at risk. The…

The document addresses calibrating the SABR parameters rho and nu when beta and alpha are fixed. The target is to minimize the sum of squared differences between observed market volatilities and model-implied volatilities. The questioner’s R call supplies…

The document considers which discount curve to use for an uncollateralized cross-currency swap when valuation is expressed across two currencies. It weighs choosing a reporting currency and building a second curve with foreign-exchange forward or…

The document discusses how to include cash currencies in the market-capitalization benchmark used to initialize a Black–Litterman portfolio. One response says weights depend on the investor’s risk-free reference currency: domestic cash may serve as…

The document compares approaches for calculating American-option implied volatility repeatedly in a production setting. It discusses closed-form approximations, including Barone-Adesi–Whaley, Roll-Geske-Whaley, Ju–Zhong, and Bjerksund–Stensland, while…

The document explains why banks can trade at very different price-to-book ratios and why the ratio is an imperfect valuation measure. Book value may need adjustment, and small changes to asset or liability valuations can have large effects because banks…

The document asks how to apply a three-day overlapping log-return correction when estimating stock betas, following the approach described in the Betting Against Beta paper. The key practical point is that the same overlapping-return construction should be…

The document asks how today’s implied volatility for a forward-start call relates to the implied volatility observed when the option begins. The call’s strike is set as a multiple of the stock price at a future start date, and its payoff depends on the stock…

The document considers the no-arbitrage relationship between prices of call options on the same stock with the same expiry but different strikes. A lower-strike call should be worth at least as much as a higher-strike call, since its payoff is never smaller.…

The document explains how to limit the number of assets selected by a linear portfolio optimizer. The motivating case has a large monthly universe, limited trading capacity, and an objective that maximizes the sum of each asset’s score multiplied by its…

The document raises whether power derivatives should be discounted and, if so, which curve should be used. It contrasts the usual use of overnight indexed swap rates, grounded in an assumed risk-free hedge, with commodity pricing that adjusts for dividends…

The document explains why an autocall with a linear payoff can still have volatility exposure. The payment date is determined by whether a second index crosses a barrier: with low volatility it may never cross, while higher volatility increases the chance of…

The document raises a pricing question about crypto options: whether a reported discount rate around 10% is unusually high, and whether observed option quotes imply a rate near 12% when checked against put-call parity. It presents bid and ask snapshots for…

The document explains why a contract for difference (CFD) tends to track its underlying asset. A CFD is a contract with a provider, so its value depends on the terms and creditworthiness of that provider; the holder does not own the underlying asset and may…

The document explains why a portfolio’s computed Sharpe ratio can rise when daily returns are multiplied by a leverage factor, even though the arithmetic daily Sharpe remains unchanged. Under the standard formulation, portfolio excess arithmetic mean and…

The document investigates why a QuantLib fair rate for a Mexican TIIE swap differs from the market quote used as a curve node. The response identifies two setup issues: the example’s swap start date does not match the stated one-day settlement convention,…

The document explains how to obtain a partial differential equation for a discount factor used to express a futures price. It starts with a pricing PDE for a claim depending on the spot price and interest rate, then substitutes the similarity form in which…

The document asks whether two bond valuation approaches treat default risk inconsistently. One approach defines expected yield to maturity for a zero-coupon corporate bond by discounting its probability-weighted expected payoff. The other values expected…

The document explains how dollar bars can be used in a machine-learning workflow despite their irregular time spacing. A bar retains the familiar structure of a time bar, such as open, high, low, and close, so these values can be supplied as model features.…

The document discusses ways to investigate whether returns lead volatility or volatility leads returns. One suggested exploratory approach is to compare correlations between time-shifted returns and volatility with correlations between time-shifted…

The document clarifies that the E-mini S&P 500 futures session open for a given trading day is tied to the evening session start on the prior calendar day. The contract begins its next trading day at 6 p.m. New York time, so the listed open can differ from…