คลังความรู้

The discussion considers how to convert assets denominated in different currencies into an account currency during portfolio backtests. The central tradeoff is computational cost versus fidelity: applying an FX rate to every market tick may be expensive,…

The document asks how to normalize eigenportfolio weights when some components are negative, in a setting based on statistical arbitrage in U.S. equities. It contrasts dividing each weight by the signed sum with dividing by the sum of absolute weights. The…

The document asks why historical volatility is commonly measured as the standard deviation of log returns. The author points out that a sequence of identical daily percentage changes would have constant log returns and thus zero standard deviation, even…

The document questions an apparent U-shaped implied-volatility pattern in SPX options, especially at far out-of-the-money strikes. A response compares the displayed pattern with a snapshot of implied volatilities for weekly options, reporting generally…

The document examines how to estimate expiration probabilities and expected value for a two-leg put credit spread. It divides outcomes into three price regions: above the short strike, between the strikes, and below the long strike. The author asks whether…

The document asks whether the Calmar ratio, defined as expected return divided by maximum drawdown, satisfies monotonicity as a performance measure. It contrasts Calmar with the gain-loss ratio, which the author describes as monotone, and the Sharpe ratio,…

The document poses a portfolio risk question about estimating value at risk when the portfolio value is a nonlinear cubic function of one normally distributed risk factor. At the stated current factor level, both the first and second derivatives are zero, so…

The document explores how to derive a variational or weak formulation for the Black–Scholes partial differential equation. Its central issue is integration by parts in the diffusion term, where the coefficient depends on the underlying price variable.…

The document asks which scheduled economic releases can cause substantial price moves in tradable assets and points readers toward an economic calendar as a source of release dates. It relays a historical ranking from a 2007 bank analysis of German Bund…

The document clarifies a basis swap pricing question about why a six-month forward rate can differ from the rate implied by two consecutive three-month periods. The key distinction is between the underlying reference index and the loan exposure: a…

The document addresses how to construct an implied volatility smile from US equity options when no traded option has a strike exactly equal to the underlying price. It asks how to estimate at-the-money volatility and connect out-of-the-money put and call…

The document outlines a basic Monte Carlo procedure for estimating single-asset Value at Risk: choose a return distribution, estimate its parameters, simulate returns, revalue the position under each scenario, and read the loss quantile for the chosen…

The document considers how to turn over-the-counter FX option quotes, reported at different strikes and maturities, into a usable volatility surface. One proposed workflow starts from standard delta quotes, converts each maturity’s deltas to strikes using…

The document derives an index’s single-period total return from security weights, price changes, and income. It rewrites each holding’s contribution as the sum of its price return and income return, then takes the weighted sum across holdings. This makes the…

The document investigates a negative value appearing in a plotted down-and-out call price when the underlying starts below the barrier. It presents a Black–Scholes barrier pricing expression, defines its parameters, and compares that expression with an…

The document presents a two-day example of a pairs trade that goes long one stock and short another, using roughly equal dollar amounts in each leg. It calculates the opening and closing cash flows from the share quantities and prices, then adds them to…

The question examines why a sinking fund example might assume that the fund earns a higher rate than the interest charged on a loan. The proposed setup keeps making interest payments to the lender while accumulating money separately to repay principal, which…

The document explains duration times spread (DTS) as a way to express a bond’s sensitivity to relative spread changes. It decomposes each bond’s relative spread movement into a shared sector or market component and an idiosyncratic component. Multiplying…

The document examines how credit risk and contract terms affect the Black-76 valuation of options on corporate bonds. It highlights that the forward bond price must reflect the bond’s risky market value and financing or discounting assumptions; treating a…

The document connects volatility drag to the compounding effect of a gain followed by a loss of equal magnitude. If daily returns alternate between positive and negative moves of size equal to daily volatility, their two-day compounded return is negative,…

The document explains that integrating Brownian motion over time is an ordinary pathwise Riemann integral, since Brownian paths are continuous. The resulting process is also an Itô process: applying Itô’s product rule to the product of time and Brownian…

The question seeks a way to estimate the risk-neutral variance of an underlying stock’s gross return and considers option-implied distributions alongside estimates made from data under the physical measure. One reply assumes geometric Brownian motion under…

The document asks how to distinguish interest and principal payments in cash-flow schedules generated for amortizing floating-rate bonds with QuantLib’s Python interface. The example shows multiple payments on shared dates across a series of dates, and notes…

The document describes a Texas Instruments BA II Plus calculation of an effective annual rate from a nominal rate compounded daily. The user rounds the intermediate value shown on the calculator to five decimal places, then raises that displayed value to the…