নলেজ লাইব্রেরি

The document addresses pricing a positive-part payoff built from weighted prices of two assets observed at multiple dates. It asks whether a closed-form formula exists when a spread involves more than two prices. The response proposes moment matching:…

The discussion asks whether MACD and its fast and slow exponential moving averages should be calculated from an option’s market price or its underlying. One response argues that smoothing the underlying before using it to calculate an option premium would…

The document explains how least-squares Monte Carlo (LSM) estimates the value of callable derivatives and exposure measures without repeatedly running costly nested simulations. It simulates model states and their discounted future cash flows, then fits a…

The discussion considers whether factor models and momentum strategies used in equities have equivalents in options. It identifies the underlying price, underlying volatility, time to expiration, and interest rates as major influences on option prices. It…

The document addresses whether an option-implied distribution for a stock’s log return must be symmetric because Brownian motion is symmetric. The response clarifies that symmetry is not a general property of option-implied distributions and points to models…

The document examines why principal components extracted from yield curve data may correlate less strongly with familiar level, slope, and curvature measures than a reference study suggests. The questioner fits PCA to par yields and compares the resulting…

The document outlines a way to estimate day-over-day changes in historical simulation VaR without fully revaluing the portfolio. Begin with the historical risk vector, adjust it for new and removed positions using their sensitivities, and update portfolio…

The document examines numerical difficulties in pricing European calls under the stochastic volatility with correlated jumps (SVCJ) model. The original MATLAB implementation produces integration warnings and NaN values while attempting to recover prices from…

The document discusses how to check an option-adjusted spread (OAS) produced by an external calculator. Because OAS results depend on the calculation method and model, verification begins by identifying the stochastic model behind the utility. One can then…

The document considers whether Lévy processes and related academic techniques are used on options market-making desks. Its answer argues that Lévy models are a poor practical choice for pricing derivatives under the risk-neutral measure, warning that using…

The document explains why delta neutrality does not guarantee a break-even result or a profit. Delta measures a portfolio’s local sensitivity to the underlying price; it does not eliminate all sources of return or risk. The response distinguishes the claim…

The document outlines data management issues that can affect backtests using intraday US equity quotes and trades. Beyond missing records, timestamp alignment, and cleaning unusual trades, it highlights changing symbol histories and trading sessions,…

The document derives the instantaneous volatility of the product of two correlated assets modeled with lognormal diffusion dynamics. Applying Itô’s product rule produces a return shock with contributions from both assets, including their correlation.…

The document asks whether principal component analysis (PCA) is appropriate for interest-rate term structures that appear non-stationary, and whether a Kalman filter would be preferable. Its answer recommends applying PCA to changes in yield-curve points,…

The document discusses stopping a Monte Carlo valuation of a European option when the estimate is sufficiently precise. The proposed criterion compares a confidence-interval half-width, estimated as a normal critical value times the sample standard error,…

The document raises a portfolio-construction question about coordinating an alpha model with a statistical risk model. The risk model decomposes returns into factor exposures and factor returns, leaving residual returns. The proposed alpha model uses…

The document examines whether probability belongs in explanations of option Greeks. Its response distinguishes uncertainty in future price paths, given fixed model parameters, from uncertainty in the parameters themselves. Under the fixed-parameter…

The document asks how to find the time horizon at which the expected change in a derivative payoff reaches zero. It models two underlying quantities as drifting diffusion processes, with one carrying Brownian variance, and expresses the expected payoff…

The document assesses a shortcut for obtaining a global minimum-variance portfolio under a no-short-sale constraint. The shortcut first computes the unconstrained closed-form portfolio, sets negative weights to zero, and renormalizes the remaining weights to…

The document derives a condition for a vanilla option’s implied volatility curve to have zero slope with respect to strike at a given maturity. Differentiating the Black–Scholes call price, expressed using strike-dependent implied volatility, and comparing…

The document considers why an investor holding long-dated calls might also buy deep out-of-the-money puts with shorter expirations. Such puts can provide convex protection in a sharp decline: their delta and gamma may increase as the underlying falls, while…

The document examines how to replicate the square of a European call’s value across time. It distinguishes a terminal payoff from a value process: the squared call price does not generally have discounted-martingale dynamics, so a terminal claim alone cannot…

The document asks how futures positions can change a portfolio’s beta, referring to a textbook explanation that reduces beta by cutting short futures contracts and raises it by adding long contracts. The underlying idea is that a futures position contributes…

The document addresses why bank profitability ratios can differ across references, focusing on net profit margin and return on assets. Net profit margin may use net interest income or broader total income as its denominator, while return on assets may use…