คลังความรู้

The document explains why shares can retain value even when a company pays no dividends. A share represents partial ownership of the company’s net assets, while retained profits can expand those assets by funding growth, buying property, or reducing debt. As…

The document asks how to show that a portfolio’s percentage contribution to loss equals its percentage contribution to risk, in the setting of a quantitative equity portfolio management exercise. It defines percentage contribution to risk for asset i as that…

The document presents Gyöngy’s theorem as a way to construct a local volatility process whose one-time probability distributions match those of a given stochastic process. In the stated result, the local drift and variance are conditional expectations of the…

A moving average period counts observations in the data series being used. For a five-period EMA calculated from 15-minute candles, the period refers to five candles, not five calendar days. The candle interval therefore determines the time span represented…

The document addresses how to infer forward rate or caplet volatilities from cap prices or quoted cap volatilities. Its central method is volatility stripping: order caps by maturity, take price differences between consecutive maturities, associate each…

The document examines claims that artificial neural networks outperform Black–Scholes in option pricing. The cited study generates Black–Scholes estimates using simplified inputs, including a closing spot price, fixed volatility and interest rate, no…

The document explains why a backtest based only on the best bid and best ask can overstate achievable execution quality. Those quotes represent the most favorable available prices for limited quantities; larger orders may consume that liquidity and fill at…

The document asks whether the process driven by an imaginary multiple of real Brownian motion has negative variance. The answer distinguishes the process’s imaginary-valued increments from its variance: at time t, the process is an imaginary multiple of…

The document explains how to represent a Wiener process on a uniform time grid for simulation. Divide the interval into equal steps, then construct each sampled value by adding the next increment to the previous value, starting from zero. The increment over…

The document asks how the return of a function of an asset changes when the underlying asset’s drift rises by a constant, assuming the asset follows geometric Brownian motion. It applies Itô’s lemma to the function, separating the stochastic term from the…

The document examines whether negative forward variance inferred from at-the-money-forward implied volatility across two maturities signals an arbitrage. It defines forward variance from the difference in total implied variance over the two time intervals.…

The document explains that 3-month Euribor is generally quoted as an annualized rate for clarity and comparison with other interest rates. ACT/360 specifies the day-count convention used to calculate interest: the actual number of days in the accrual period…

The document compares shorting borrowed shares with constructing a synthetic short using a long put and short call at the same strike and expiry. Its example uses a hard-to-borrow stock and reports that the option combination produces a credit and an…

The document outlines a scenario-based approach to assessing the richness or cheapness of a government bond futures basis and asks how to value the end-of-month switch option. The described steps estimate historical betas for yield changes, apply directional…

The answer distinguishes preferences for return skewness according to an investor’s objective. It says that maximizing expected log wealth can favor higher odd moments, such as mean return and skewness, while favoring lower even moments, such as volatility…

The discussion considers how to allocate capital to an automated crypto strategy whose backtest suggests substantial drawdowns, and when to scale its exposure or stop trading as its edge may fade. The response emphasizes that changing position size is a…

The document asks which machine learning and statistical methods candidates should prepare for quantitative researcher and developer interviews at hedge funds and proprietary trading firms. It situates the question alongside probability puzzles and coding…

The document asks which partial differential equation is satisfied by an expectation of a function evaluated at a Wiener-driven, exponentially transformed variable. The proposed derivation differentiates the expectation and applies Itô’s rule to the…

The document compares two ways to measure a relationship between two stocks for pairs trading. A price ratio represents a dollar-neutral position: the trader invests equal dollar amounts in each asset. A regression-based spread instead uses a hedge ratio,…

The document asks whether a time-series model that chooses a fully invested long or short position could be trained by maximizing simulated terminal portfolio value instead of minimizing squared prediction error. It proposes simulating daily positions from…

The document gives an intuitive argument for uniqueness of the risk-neutral probability measure in the Black–Scholes setting. It invokes Arrow–Debreu claims, each paying one unit in a particular state. If the same claim must have the same arbitrage-free…

The document explains why a bond forward’s impliedYield method does not directly return the yield of a forward-starting bond. In the example, applying it to the spot bond price and clean forward price produces a curve zero rate, because the forward price…

The document considers how to select a floating-rate fixing for a short initial accrual period in a USD interest rate swap. The accrual dates run from the end of April to the end of July, while the three-month LIBOR fixing convention gives a value period…

The document examines a one-period market with three assets and states, asking whether a European call can be priced by replicating its payoff when the market admits arbitrage. The stated replication produces a cost of 0.5, but solving for state prices…