নলেজ লাইব্রেরি

The note explains why a discount rate in discounted cash flow analysis can be viewed as a minimum acceptable return. It frames the rate as a risk-free benchmark: an investor can generally earn that return without taking risk, so a cash flow discounted at a…

The document addresses apparent half-tick price changes in Micro E-mini futures despite the stated minimum tick size. Its accepted answer suggests first checking whether the data show executed trades or midquotes. When the bid–ask spread widens from one tick…

The document explains that implied volatility is the Black–Scholes volatility that matches an observed option price; it is a way to express market prices through that model, not proof of a uniquely correct price. It also cautions that the strike pattern…

The document presents a regression question about two predictors whose individual coefficient tests produce relatively large p-values, while a joint test of both coefficients being zero produces a smaller p-value. It asks why this can happen and seeks…

The document asks how to find past expiration dates for futures, especially stock index contracts, and contrasts calculating dates with retrieving recorded contract data. One answer describes querying historical instrument definitions from a market data…

The document examines whether a lower estimated expected shortfall implies lower sample standard deviation. Under a normal distribution, it describes a relationship in which scaling volatility changes expected shortfall in the same direction, while the sign…

The document asks how to deploy a fixed cash allocation into an asset class while seeking a favorable average purchase price. Its example splits an allocation into several buys at progressively lower index levels, then contrasts that idealized path with…

The discussion distinguishes the effect of firm-specific events on a stock’s value from their effect on expected returns. An adverse event such as an oil spill can lower expected future cash flows through potential fines and other costs, reducing the present…

The document compares pricing an at-the-money European call on a two-stock basket with a multivariate local volatility model using constant correlation and a Gaussian copula using the same correlation. It reports a result for models calibrated to each…

The document concerns a numerical issue in the Longstaff–Schwartz least-squares Monte Carlo method for valuing early-exercise options. At each exercise date, the continuation value is estimated by regressing future cash flows on basis functions using only…

The document compares two ways to value a fixed-for-fixed FX swap under multiple curves. One approach discounts the foreign-currency leg using a curve adjusted for cross-currency basis, then converts its present value at spot. The other converts each foreign…

The document presents a Bernoulli differential equation with a quadratic term in the unknown function and asks how to solve it. It describes a substitution that takes the reciprocal of the function, differentiates that reciprocal, and converts the original…

The document asks how to size overweights and underweights in a ten-asset portfolio relative to benchmark weights. The investor has views on four assets and wants to scale active positions so their risk contributions are balanced, while keeping the remaining…

The document addresses how to construct a hedge across two-, five-, and ten-year Treasury futures that is neutral to parallel shifts and changes in yield-curve slope. It describes running principal component analysis on a returns matrix and interpreting the…

The document poses a relative valuation problem: comparing callable bonds from the same issuer when their call schedules differ. It asks whether option-adjusted spread can be compared directly across those bonds, given that OAS accounts for embedded option…

The document explains why least squares and maximum likelihood can produce the same parameter estimates in a linear regression with normally distributed errors. Writing the conditional likelihood for each observation and taking its logarithm gives a constant…

The document describes an observed inverse relationship between strike and Black–Scholes implied volatility for Ibex 35 options. The author says the option prices and strikes came from daily exchange data, plots spot alongside the volatility curve, and…

The document explains how to create an implied-volatility curve from option prices generated by a Heston model. For each strike, first evaluate the Heston call price using the chosen model parameters and maturity. Then find the Black-Scholes implied…

The document distinguishes mean-variance optimization from maximizing the Sharpe ratio. Mean-variance analysis can mean constructing the frontier of portfolios that minimize variance for a target expected return, or choosing a portfolio based on an…

The document asks how a continuous-time price and variance process relates to a discrete-time stochastic volatility model. Applying Itô’s lemma to log price and log variance gives a mean-reverting log-variance process and a log-return process whose…

The document compares SOFR curve construction and cash-flow projection with legacy IBOR approaches. One answer says curve building still depends on the available liquid market inputs and chosen interpolation, while projecting cash flows follows the rate’s…

The document derives the value and duration of a semiannual floating-rate note with coupons reset to the prevailing six-month rate. Working backward from maturity, the answer shows that each reset-date value equals par: the principal and next coupon…

The document asks where historical or current intraday prices for government bonds can be obtained. The response identifies Interactive Brokers as a source of historical intraday bond data and gives a T-bill as an example of a security checked. It also…

The document explains why an RQuantLib valuation of an American option can return a price while showing missing values for delta, gamma, vega, theta, rho, and dividend rho. The accepted answer attributes this to the selected pricing engine: the simplified…