নলেজ লাইব্রেরি

The document explains why converting an FX option delta into a strike requires the market’s quoting conventions and the correct definition of at-the-money. In the example, the pair uses unadjusted deltas, and the at-the-money strike is delta-neutral: the…

The document addresses the expected value of an asset's time average when the price follows geometric Brownian motion, in the context of arithmetic Asian option pricing. The response derives the risk-neutral expected asset price at each future time as its…

The document clarifies how group constraints differ from general linear inequality constraints in portfolio optimization. Both can express limits on a weighted sum of asset positions. A group constraint is a specialized case in which every included asset has…

The document explains how to obtain one-step-ahead conditional mean and volatility forecasts across a time series after fitting an sGARCH model with rugarch. A standard call to the forecast function returns a forecast at the end of the fitted sample, which…

The document compares answers about downloading Bloomberg data through Excel and APIs, focusing on how request limits may apply and what can happen when they are reached. One explanation says limits count requests by ticker rather than by the number of…

The document describes a continuous futures series built by adding a cumulative roll adjustment to settlement prices and applying the contract multiplier. With this additive adjustment, the resulting notional can become negative even when the underlying…

The document poses a portfolio-weighting problem: combine the returns of several models so that the resulting portfolio has as many positive periods as possible. Its objective is the fraction of periods in which the weighted sum of model returns exceeds…

The document considers an asset-backed security with a long legal maturity and an earlier anticipated repayment date. Missing that date triggers a higher interest rate and a full cash sweep. It asks how to interpret those terms when valuing the debt,…

The document describes estimating a risk-neutral density as a weighted mixture of normal kernels centered on a strike grid. The weights are constrained to be nonnegative and sum to one, and are fitted to observed put prices by minimizing pricing errors. It…

The document sketches how to construct spot discount factors from short-term deposit rates and a one-year swap rate. For deposits, it uses simple interest with the stated day-count fractions to convert each quoted rate into a discount factor. It then takes…

The document offers career-development advice to a mathematics PhD with derivatives valuation experience who wants demonstrable C++ work implementing financial models. The answer suggests exploring public repositories focused on topics such as option pricing…

The document addresses how to turn daily closing prices for several stocks into quarterly returns in R. The proposed approach is to store the price series together, then apply the quarterly-return function to each series through a list operation. The…

The note asks how power-law distributed pauses would change the first-passage-time density of Brownian motion with drift. It frames the process as motion that advances according to a drifted Brownian model but intermittently waits, and proposes convolving…

The note proposes a market-mechanics hypothesis about how options open interest could relate to underlying price moves. It suggests that large put positions might behave like support and large call positions like resistance, and that some short option…

The note explains why quoted bid-ask spreads matter for investor transaction costs and why they do not capture every trade price. Trades can occur inside the displayed spread when another venue posts different prices, or when orders meet between the bid and…

This note motivates bivariate time-series models for quarterly stock returns and dividends. It highlights features a model may need to capture: managers have discretion over payouts, dividends tend to remain stable or rise modestly, and cuts are often…

The document asks how to interpret the Kraken XBT-USD order book when estimating how many price levels are needed to trade a specified amount. It distinguishes asks from bids, asks which currency the displayed volume uses, and raises the problem of trading…

The document considers an exchange-traded product combining a butterfly payoff with a double no-touch condition: the payoff follows a butterfly profile if the underlying stays between two barriers until maturity, and becomes zero if either barrier is…

The document asks why a fixed coupon bond appears to trade near its face value as maturity approaches, even though discounting its final principal and coupon at the stated coupon rate seems to imply a price above par. It sets out a three-year par bond…

The document explains a leveraged ETF structure using an unleveraged basket plus a total return swap (TRS). The fund holds index exposure directly and receives additional index returns through the swap, while paying the dealer a financing rate such as LIBOR…

The document asks for an authoritative citation for the definition of return on investment when writing a paper. The response does not state a formula or compare competing definitions; it points instead to corporate finance and investment textbooks as…

The document addresses poor Monte Carlo pricing accuracy for deep out-of-the-money options under a stochastic volatility model. The question focuses on Euler simulation of the Heston process and asks whether importance sampling can reduce variance and speed…

The discussion examines option price changes near expiration that appear larger than delta and theta alone would suggest. It explains that gamma exposure is most pronounced near at-the-money strikes and presents gamma scalping as a way to manage a long gamma…

The document describes how to turn a piecewise linear profit-and-loss graph at expiration into a portfolio of calls, puts, and possibly cash or the underlying. It proposes placing option strikes at the graph’s breakpoints, then solving a linear system whose…