คลังความรู้

This explanation shows how the product rule in Itô calculus creates the discounting term when differentiating an option value divided by a bank account. Set the two factors to the option price and the inverse bank account, then apply the rule, including the…

The document reports a historical data issue in Interactive Brokers requests: weekly and monthly bars for an IBIS-listed stock are labeled one day later than expected, while daily bars for the same contract and bars for NYSE appear correctly dated. The…

The document discusses how market participants price American options on Eurodollar futures and when a European-option approximation may be adequate. It contrasts tree-based models that represent early exercise with the simpler European treatment often used…

This exchange examines a mismatch between QuantLib and Bloomberg pricing for a Czech koruna interest rate swap. The questioner reports matching fixed-leg dates and the par rate but differing floating reset rates, cash flows, and net present value. A…

The discussion explains why equity volatility and credit default swap spreads may move together, focusing on structural models of a firm’s capital structure. In the basic Merton framework, equity behaves like a call option on firm assets, with debt repayment…

This exchange addresses how to retrieve the long-run variance component from a component GARCH model fitted with the rugarch package in R. The questioner can obtain conditional volatility with the package’s standard accessor but needs the time-varying…

The discussion explains why market efficiency does not require an asset’s current price to equal its expected future price under real-world probabilities. Pricing can instead be expressed using a stochastic discount factor, or with expected future prices…

The note clarifies how a replicating portfolio can also function as a hedge. Under risk-neutral pricing, a European option can be offset by a portfolio whose value reproduces the option’s payoff and whose combined position with the option evolves at the…

The note explains why hedging skew exposure in a forward-starting option differs from hedging an ordinary option. A forward-starting put may be analytically short skew, yet during the forward period its strike resets in proportion to the underlying price.…

The note explains why stock price models often require the volatility process to be square integrable so that its stochastic integral with Brownian motion is well defined in the standard Itô framework. It distinguishes the condition that the expected…

This note asks how to interpret a banking risk-capital recommendation that distinguishes gross standalone risk from net enterprise-wide, diversified risk. The question is whether the distinction refers to diversification benefits when a bank aggregates risks…

This note asks whether log differences are an appropriate transformation for a trend-stationary series modeled as a linear trend plus random noise. It contrasts examples where the series has a relatively large baseline and modest trend and noise with cases…

This question frames a market-microstructure research problem: whether intraday adverse selection on a futures or options contract changes systematically as that contract approaches expiry. The focus is the instrument itself, rather than adverse selection in…

This note points readers to a study examining how stop-loss and profit-taking rules affect return distributions. It reports that stop-losses can reduce position volatility, but that hidden costs may offset the perceived benefit. The cited study finds no…

The document asks whether a futures price can fall below spot if interest rates turn negative, starting from the cost-of-carry relation for an asset with no dividends. The response points out that a negative futures basis does not require negative interest…

The note explains how to replicate a zero-coupon structured note that returns its principal at maturity plus an oil-linked payment. The extra payment rises in proportion to oil prices above 25, but is capped at 2,550. The proposed replication combines a…

The document considers whether consensus analyst recommendations and revisions can contribute to trading signals, particularly for holding periods of hours to a few days. It notes the author’s impression from academic research that recommendations may…

The note explains how to calculate a continuously compounded return from index levels observed at different times. It starts from the exponential growth relationship between an initial value and a later value, then rearranges it to express the annualized…

The document addresses how to locate recent US corporate defaults. Its answer points readers to the Credit Derivatives Determinations Committees, which publish decisions on credit events, including bankruptcy determinations for named companies. This provides…

The document considers a claim that pays one unit if default occurs before maturity and seeks to express its value as an integral over possible default times. The proposed representation combines the default-time density, formed from the hazard rate and…

The document raises the claim, attributed to Grinold and Kahn, that relationships between factors and returns may be more stable than relationships between individual stocks and returns. It proposes an intuition: factors capture shared, systematic return…

The document compares three representations of option market information: implied volatility by strike and maturity, raw call or put premiums, and the risk-neutral return distribution. It argues that these are equivalent views of the same information and can…

The document collects questions about calibrating one- and two-factor Hull–White models to cap prices, calculating instantaneous forward rates for the drift function, and obtaining short-rate paths after calibration. The replies distinguish the model’s short…

The document concerns evaluating density forecasts derived from GBP/USD options. The author has estimated a time series of risk-neutral densities nonparametrically and wants to apply the unconditional test described by Christoffersen and Mazzotta. The…