Βιβλιοθήκη γνώσης

The discussion explains how a contract combining one touch barrier with one no-touch barrier can pay, using upper and lower barriers as an example. A one-touch feature generally triggers a payout when its barrier is reached, while a no-touch feature can…

The document clarifies the dividend-yield convention used in the Goyal and Welch stock return predictability data. The dataset’s dividend yield is computed as aggregate dividends paid by all stocks divided by total stock market capitalization measured at the…

The document explains how prices of European receiver swaptions relate to the risk-neutral distribution of the underlying swap rate. It corrects the idea that an out-of-the-money premium, compared directly with an at-the-money premium, gives the probability…

The document addresses whether value at risk remains useful despite shortcomings in how it is sometimes interpreted and its failure to satisfy coherence. It explains that financial institutions use VaR as one component of risk management, often with models…

The document outlines maximum-likelihood estimation for a GARCH(1,1)-M return model under the physical measure, then discusses an implementation problem in an R optimizer. The model specifies conditional returns using a known risk-free rate, an estimated…

The document concerns noisy, incomplete one-minute price and volume data for several stocks, with the goal of forecasting volatility for the month after the sample ends and investigating whether volatility is related to liquidity. The response recommends an…

The document asks how investors’ target risk might be chosen in light of wealth, future income, savings, housing, and expected expenses. It contrasts this problem with broad allocation rules and age-based target-date strategies, then proposes a questionnaire…

The document considers whether borrowing at a low nominal rate and buying goods whose prices rise with inflation creates an arbitrage. The answer explains that a consumer price basket is not a readily tradable investment: it includes perishable goods and…

The document poses a one-period binomial market problem with a risk-free asset and a stock that can finish in either an up or down state. It asks how to establish no arbitrage, replicate a claim whose payoff is the squared terminal stock price, calculate the…

The document asks whether adding a derivative that depends on an otherwise unspanned source of risk makes an incomplete market complete. It sets up a continuous-time market with fewer traded risky assets than Brownian risk sources, including an example where…

The document examines a covered interest parity example involving Australian and US interest rates and a spot exchange rate quoted in US dollars per Australian dollar. The example applies the rate differential over the contract term to derive a forward…

The document asks how to translate a 90-day SOFR market rate into a comparable three-month LIBOR rate. It highlights a key timing distinction: SOFR for the accrual period is compounded in arrears, so the realized period rate is not known until the period…

The document distinguishes implied volatility from historical volatility. Implied volatility is the volatility parameter that makes an option pricing model reproduce the market price of an option; it is inferred from current prices rather than calculated…

The document asks whether a one-period market is arbitrage-free whenever the asset’s log return has a continuous distribution over the real line, and whether such a distribution guarantees a martingale measure. The motivating comparison is with a…

The document considers how to infer whether a trade was buyer or seller initiated when a feed omits the aggressor-side field. A basic quote test labels trades at or above the best ask as buys and those at or below the best bid as sells, leaving trades inside…

The document discusses Hull’s formula for estimating a portfolio’s high-confidence default rate over a fixed horizon. It applies the inverse normal distribution to the probability of default and confidence level, with asset correlation entering through a…

The explanation links negative correlation between an asset’s spot price and its instantaneous volatility to a downward implied-volatility skew. It contrasts the result with the standard Black–Scholes assumption of constant volatility, under which…

The note explains a discrepancy between manually interpolated annual-compounded zero rates and rates returned between curve pillars by QuantLib. The key point is that the curve interpolates continuously compounded zero rates, even when its configured…

The document frames a portfolio stress test for zero-coupon bonds using key-rate DV01 exposures. Each maturity bucket has minimum and maximum allowed DV01 bounds, and the sum of the bucket exposures is subject to an overall limit. Given a stress vector…

The answer uses the martingale concept to explain why, under a simplified random-walk model, an increase in portfolio wealth has the same expected value at a later time. A martingale is defined by the condition that the conditional expectation of a future…

The document asks whether the size at the best bid and ask in a limit order book can be modeled to predict when the current top price level will disappear. It clarifies that quote entries have size, while volume refers to executed trades. One suggested…

The discussion explains why an index does not itself have a single gamma position and how market commentary may instead estimate the aggregate gamma exposure of option dealers. A simplified calculation assigns dealers the opposite side of customer put and…

The document presents several uses of the term microstructure noise. In high-frequency econometrics, it can mean disturbances that make estimates such as realized volatility unstable. In market microstructure, it can refer to observed price deviations from…

The document outlines a Monte Carlo procedure for generating joint price paths for several stocks. First, draw a matrix of returns whose asset-level observations at each time step follow a specified multivariate distribution, using a covariance structure to…