คลังความรู้

The document considers whether counterparty risk invalidates the Black–Scholes hedging argument. It distinguishes listed options, where central clearing and collateral arrangements are intended to mutualize or mitigate default exposure, from over-the-counter…

The document explains why forward prices can matter to option valuation even when a Black–Scholes formulation is written using spot and an interest rate. For equities, no-arbitrage cash-and-carry reasoning connects spot, funding, dividends, and the forward…

When calibrating an option pricing model across several maturities, the risk-free input should come from securities whose prices primarily reflect interest rates, rather than being chosen to fit the options themselves. The answer recommends building a…

The discussion checks whether a forecasting routine uses the correct observation for a one-step-ahead AR(1) conditional mean forecast. Its answer clarifies the time indexing: when the latest observed sample is at time t−1 and the forecast target is time t,…

The document considers how to quantify liquidity in listed equity, index, and ETF options for scanning or analysis. It recommends looking beyond contract volume to bid–offer spreads, option notional traded, changes in quotes relative to movements in the…

Finite difference methods are not limited to parabolic partial differential equations such as the heat equation. The answer explains that they are also routinely used for hyperbolic equations, including first- and second-order wave equations, and for…

The document describes a thesis analysis using randomly selected stocks grouped into portfolios and asks why estimated Fama–French three-factor betas, especially SMB and HML, have p-values above 0.05. The proposed workflow constructs SMB and HML portfolios…

The document asks why a multi-curve framework remains necessary after the transition from LIBOR to overnight risk-free rates. It outlines a common intuition: an OIS curve built from SOFR swaps can serve as the discount curve, and the quoted swap rates might…

The document defines IMM dates as the third Wednesday of March, June, September, and December, then gives an Excel date formula for generating the next quarterly date from a starting date. The formula advances three months, finds the first Wednesday in the…

The document explains how to estimate the opportunity cost of receiving a cash flow late when the stated annual rate uses an actual/actual day-count basis. For a delay shorter than the annual compounding period, it applies simple interest: multiply the…

The discussion asks how to construct a discrete-time counterpart to a continuous diffusion whose state remains between zero and one. A direct update using normal noise may leave the interval because Gaussian increments are unbounded. One response proposes a…

The document explains the phrase “no shorts left” in a market commentary passage describing an increasingly bullish market. In this context, shorts are investors holding positions that benefit from falling prices, reflecting a negative market outlook. The…

The document clarifies a leverage example involving a home purchase financed partly with a mortgage. The question contrasts a four-to-one ratio based on the loan amount relative to the buyer’s cash contribution with a five-to-one ratio based on the total…

The discussion explains why factor risk contributions may not add up to a portfolio regression’s R-squared when a portfolio contains multiple instruments. Aggregating each instrument’s factor betas by portfolio weight can produce exposures, but the resulting…

The document explains why cointegration among asset prices does not necessarily conflict with market efficiency. Market efficiency concerns whether future returns can be predicted reliably from available information, while cointegration describes a stable…

The document values an option to reroll a fair six-sided die when the player may keep the first result or replace it with a second roll. The decision rule is to reroll when the first outcome is below the expected value of a fresh roll, and otherwise stop.…

The document clarifies a misconception about path dependence in binomial option pricing. Backward induction through time does not itself mean the model represents the full sequence of market states along a path. A tree compresses information into states that…

The document considers a seller of a swaption who delta-hedges once per day and asks what share of daily theta decay remains as profit when the underlying rate move is smaller than a stated breakeven move. The proposed fraction is one minus the squared ratio…

The document asks whether an at-the-money SPX put spread has an edge over a same-width call spread because the put spread's stated reward-to-premium ratio is higher. It frames the comparison as a roulette game with different payouts but supposedly equal…

The document asks whether spot price can be calculated directly from a target option delta when strike, expiry, volatility, rates, and other inputs are known. It discusses Black–Scholes and Bjerksund–Stensland models, which provide option prices and Greeks…

The document presents a failed calibration of the raw SVI total-variance parametrization for a single options maturity. The example converts market implied volatilities to total variance, computes forward log-moneyness, and minimizes squared fitting error…

The document collects several answers to whether the central limit theorem justifies treating asset returns as normally distributed. A core distinction is that the standard theorem describes the distribution of standardized sample means under assumptions…

The document describes an exploratory analysis of one-minute XAUUSD log returns over a long historical sample, compared with fitted normal and Student-t distributions. It raises questions about irregular density peaks, a pronounced concentration near zero,…

The document discusses an interview prompt asking what to do with a large capital allocation over either a multi-year horizon or a few days. One response frames the problem as maximizing expected return over the available horizon, with the idea that a longer…