নলেজ লাইব্রেরি

The discussion questions whether C is preferred over C++ for numerical optimization and offers several possible explanations. One answer argues that C is not generally favored for numerical optimization today, with continued use often reflecting legacy code…

The discussion addresses why discount factors inferred from put-call parity across strikes may appear nonconstant. The key missing input is dividends: the basic parity equation without dividend treatment does not describe the relationship correctly when the…

The discussion explains how to include cash dividends when calculating an asset’s year-to-date return for performance analysis or backtesting. If dividends are not reinvested, the suggested calculation adds dividends received during the period to the ending…

The discussion distinguishes standard conditional value at risk (CVaR), also called expected shortfall, from a separate copula-based measure called CCVaR. Standard CVaR is described as a coherent risk measure, whose properties include subadditivity: the risk…

The note shows how to establish that a call and put have the same vega when they share the same forward underlying, strike, maturity, and volatility inputs. It starts from put-call parity, which expresses the call-minus-put price difference as the forward…

The note examines a stock price modeled by geometric Brownian motion with zero drift and asks whether its expected one-period price ratio is one. It distinguishes the expected log return from the expected simple price ratio: the log return has a negative…

The note asks for the risk-neutral dynamics of a zero-coupon bond whose price is exponential-affine in a short rate following a linear diffusion. It gives the time equations for the affine coefficients and compares applying Itô’s lemma to the bond price with…

The note derives the familiar link between the smoothing factor of an exponential moving average (EMA) and the period of a simple moving average. It defines each observation’s age as the number of periods back from the current point. A simple moving average…

This thesis-related question asks how to choose bounds for the Heston model parameters kappa, theta, sigma, and rho when generating synthetic data to train a neural network for calibration. It compares one published set of ranges, described as excluding…

This discussion considers a European call with an early-exercise feature that lets the holder exercise a portion and receive that portion’s current Black–Scholes value. The proposed replication is to hold the call and sell the corresponding fraction whenever…

This short discussion addresses how to calculate the maturity amount for an overnight index swap over a short accrual period. It distinguishes a simple interest calculation over the full period from compounding a sequence of overnight rates. The answer says…

This discussion explains why a bond’s coupon is not a reliable stand-in for its credit spread when assessing a CDS–bond basis trade. A coupon includes compensation tied to the bond’s cash flows and market interest rates, while the z-spread measures the…

The document explains how to handle companies that fail during a historical stock study, such as an analysis comparing returns by corporate social responsibility ratings. Its answer recommends defining an investable universe using information available at…

The document poses a valuation question about floating-floating cross-currency basis swaps whose coupons reference overnight risk-free rates and whose discounting uses the same rate. It cites a par-value expression for a basis swap and notes that its…

The document describes a calibration problem for a Libor market model used to value a Bermudan swaption. The proposed volatility structure has a parametric time-to-maturity shape and period-specific scaling factors, while correlations follow an exponential…

The document explains how a 30/360 day-count convention affects discounting dated bond cash flows. Under this convention, elapsed time is computed by treating months as 30 days and years as 360 days, with details depending on the specific convention used.…

The document considers how to align closing-price histories for indices traded on exchanges with different holidays and weekly schedules. It outlines several treatments for missing observations and explains the trade-offs of each. Keeping only dates shared…

The document introduces a lookback option whose value depends on the underlying asset price and its running maximum. It defines the underlying as a diffusion process and presents the running maximum as the limit of an integral-based approximation using…

The document examines whether a futures contract’s price relative to its underlying asset predicts the underlying’s later direction. It proposes a historical check: compare the contract’s position above or below the underlying with the underlying’s eventual…

The document asks how proprietary trading firms account for large intraday exposures when assessing annual trader performance with a PnL-to-VaR ratio. It distinguishes end-of-day ex-ante VaR, based on a trader’s positions, from risk estimates based on…

The document explains how to calculate monthly price returns for many companies without allowing one company’s last price to affect the next company’s first return. Its main approach is to group observations by company name, then calculate each return from…

The document asks where to find historical S&P 500 book-value data to calculate a Graham-style earnings-to-book-value ratio over a long sample. The response points to the Ken French data library as a potential source of accounting and market data. It also…

The document considers how to estimate a portfolio’s quarter-end return when valuations for some illiquid private assets have not yet arrived. It frames the task as predicting missing asset values from the returns of assets already marked and the portfolio’s…

The document addresses why option pricing under the risk-neutral measure uses the risk-free rate rather than a stock’s real-world expected return. It begins with a discrete-time replication argument: a call payoff can be matched by a portfolio of stock and…