নলেজ লাইব্রেরি

The document considers a sequential decision game: three coins have known head probabilities, but their assignments are hidden. The player can pay for either a single identified flip or a paired flip whose outcome reports only the total number of heads, then…

The document explains how a swap’s discounting can change when the collateral poster may choose between eligible currencies. This choice resembles a cheapest-to-deliver option: the poster prefers the collateral class with the most favorable return, and the…

The document asks for intuition behind a forward variance stochastic differential equation used in rough volatility research. The displayed dynamics depend on the forward variance level, a volatility parameter, the Hurst parameter, the time to the forward…

The document describes a portfolio risk simulation that combines GARCH-filtered standardized residuals, semiparametric marginal distributions with Gaussian-kernel interiors and generalized Pareto tails, and a time-varying Gaussian copula. The author…

The document investigates why a SABR calibration using Bloomberg cap volatility figures produces a poor match across strikes. The question provides an example with caplet-related strikes and volatilities, estimates a forward from interest-rate curve inputs,…

The document describes a proposed volatility forecasting exercise using ARCH, GARCH, and EGARCH models on daily returns for two stocks. The author divides the observations into a training portion and a later testing portion, estimates model parameters on the…

The document clarifies the distinction between a bond’s clean price and dirty price when the bond changes hands between coupon dates. A quoted market price is generally the clean price, which excludes accrued interest. At settlement, the buyer pays the clean…

The document discusses what a payer of fixed interest on a swap can do when market rates move, distinguishing the original purpose of a fixed-for-floating swap from a wish to exit or offset it. One answer frames the floating leg as a hedge for floating-rate…

The document explains how the Markowitz mean-variance framework treats portfolio returns over a chosen investment period. Its example combines stocks and bonds with equal weights and shows that the portfolio’s expected return is the weighted average of the…

This question asks how to estimate the chance that at least one borrower in a portfolio defaults when companies have different default probabilities. Under independence, the probability of no defaults is the product of the individual survival probabilities;…

This answer distinguishes designing execution methods from monitoring individual trades. It argues that quants can analyze strategies, test them, and work with programmers to implement execution algorithms, while traders or managers typically oversee live…

This exchange explains how a portfolio with positive alpha in a single-index model can be paired with market exposure to isolate its modeled excess return. For each unit invested in the portfolio, the construction shorts 1.4 units of the market portfolio and…

This note explains why Black–Scholes vega can look large when volatility is entered as a decimal. Vega measures the option price’s sensitivity to a one-unit change in volatility, equivalent to a 100 percentage point move. The quoted S&P 500 example has vega…

The document challenges a proposed expression that would price a down-and-out call as a scaled European call with the same initial asset price, strike, volatility, rate, and expiry. The response explains that a barrier option cannot generally be represented…

The discussion explains how traders can ask for options on an unlisted stock, additional strike prices, or longer expirations. It says an exchange may accept suggestions, but a request alone does not guarantee a listing. Stocks must satisfy exchange…

The document presents a numerical attempt to apply Jamshidian’s trick to a European put on a coupon bond. It compares the bond option’s Black-76 value with the sum of Black-76 values for options on the bond’s individual cash flows. In the example, intrinsic…

The document investigates why a QuantLib overnight index swap does not reproduce the quoted rate used to build a curve through DatedOISRateHelper. Its example compares a swap starting on the evaluation date and ending on a date that falls after a weekend…

The document asks for examples of spectral clustering in finance and why it might be selected over other clustering methods. One response describes a time-series decomposition approach: apply singular value decomposition to a univariate series, cluster the…

The document introduces tick imbalance bars, which group market ticks until the cumulative signed tick count crosses a threshold based on its expected magnitude. Tick direction is assigned by the tick rule: price upticks are buys, downticks are sells, and…

The document asks how modified duration relates to observed bond price and yield changes when time passes and a bond’s remaining maturity shrinks. It defines modified duration as the negative proportional sensitivity of price to yield, using a derivative…

The document discusses time variables used in Haug’s presentation of the Turnbull-Wakeman approximation for arithmetic-average rate options. It identifies the option’s remaining time to maturity, the original averaging-period length, the time elapsed since…

The discussion describes how to calculate periodic returns for a long-short portfolio formed from high- and low-ranked asset groups. With equal allocations to the long and short sides, combine the two leg returns using their portfolio weights, reversing the…

The answer explains how the skewness and kurtosis of cumulative returns change with the number of periods when returns are independent and identically distributed. For a sum of such returns, variance grows in proportion to the number of observations, while…

The discussion recommends introductory references for learning probability, random variables, Brownian motion, Itô integration, jump processes, and stochastic calculus. Suggested books range from finance-focused texts by Steven Shreve to compact or more…