คลังความรู้

The document asks why an example of a hedged long-short strategy divides the difference between long and short returns by two when computing net returns. The stated rationale is that the strategy uses twice the capital of the long-only comparison. The author…

The document compares historical daily log-return standard deviations for NASDAQ, gold, and silver with average standard deviations measured across simulated GARCH(1,1) paths. The simulations use rugarch, fit separate models with a zero-mean specification,…

The document asks how to value a perpetual American put in the Black–Scholes–Merton framework when exercise occurs the first time the underlying reaches a chosen threshold below the strike. It sets up the discounted payoff and attempts to transform its…

The document asks how to express the Ho-Lee interest-rate model as a stochastic differential equation after deriving its short rate from the instantaneous forward-rate expression. The central clarification is that the short rate follows a Brownian diffusion…

The document asks how US consolidated market data assigns an equity to a CTA or UTP tape when the same stock trades on several exchanges. It distinguishes a company’s listing venue from the other venues where its shares are traded, and asks whether tape…

The document considers how to adapt a return-prediction neural network from time bars to dollar bars when its features and prediction schedule depend on regular clock times. Dollar bars do not arrive at the same time or count across instruments, so the…

The document asks how to summarize implied volatility and Greeks for a bull put spread, formed by buying a lower-strike put and selling a higher-strike put. It considers averaging each metric across the legs versus taking the long leg’s value minus the short…

The post investigates a persistent difference between simulated returns on an option account and a delta-hedged account when the Black–Scholes model is run at very high volatility. It asks whether the discrepancy comes from confusing the volatility of log…

The document explains how to price currency forwards across different maturities and reconcile a theoretical GBP/USD forward with traded futures. Its central approach expresses the forward as the current exchange rate multiplied by the foreign discount…

The post asks how to manage a short strangle after the underlying rises and the short call develops a large unrealized loss. The trader has been rolling the put to keep the overall position near delta-neutral and wonders whether moving its strike toward or…

The document considers how to assess expected shortfall, also called conditional value at risk, when it is not directly elicitable as a standalone forecast. It discusses a proposal to approximate expected shortfall by averaging several value-at-risk…

The document surveys instruments traders use to infer market expectations for central bank policy rates. For the United States, it describes extracting an implied move from one-month Fed Funds futures under the simplifying assumption that the overnight rate…

The document examines why a basic Black–Scholes calculation may produce theoretical call prices outside observed bid–ask quotes. It points out that the example omits the continuous dividend yield in the pricing formula, but argues that correcting this alone…

The document outlines checks for whether a SABR-fitted option surface is free of static arbitrage. For a fixed maturity, it proposes deriving the risk-neutral density from the second strike derivative of call prices, then checking that the density is…

The document clarifies how leverage and financing apply to a long short strategy whose positions vary during the day and are closed before the next session. It presents a profit and loss accounting framework that combines changes in long and short market…

The document examines whether a cross sectional mean reversion strategy can replicate an equity index using a subset of its components. The proposed signal buys stocks whose returns lag the universe and shorts those that outperform. The response explains…

The document considers whether changing the mean and variance used in a geometric Brownian motion simulation to control how often paths cross a structured product threshold conflicts with arbitrage free pricing. Its answer distinguishes the physical measure,…

The document explores how to represent variance swap exposure using options. It starts from the risk neutral replication identity linking expected squared returns to a log contract and a continuum of calls and puts weighted by inverse strike squared. The…

The document introduces a beta-based long–short idea: short assets with higher market beta and buy assets with lower beta, with the aim of profiting across bullish and bearish markets. The response connects this concept to the betting-against-beta literature…

The document considers Monte Carlo evaluation of conditional expectations involving an integrated Jacobi volatility process, as part of a real-options research problem. The process is bounded, but the questioner worries that Euler discretization may…

The document asks how to obtain a discrete-time form of the Jamshidian–Zhu short-rate model, which combines an Ornstein–Uhlenbeck stochastic driver with principal-component weights for yield-curve movements. The stated application is estimating stressed…

The document discusses how a new risk manager might assess whether VaR, stress-test, and exposure limits are appropriately calibrated and whether they constrain business performance. The suggested approach is to examine which desks or products often approach…

The discussion explains a data-coverage limitation encountered when building a pandas dataset of a US-listed ADR, its foreign ordinary shares, and the exchange rate between them. The questioner finds a London ticker symbol through the provider's symbol…

The document addresses the apparent paradox of a digital call's delta growing without bound as expiration approaches the strike. A payoff capped at one unit may seem unable to have a price sensitivity greater than that amount, but delta measures a local…