知識圖書館

The document explains how the time increment in a simulated Heston model relates to the number of steps per year: once the time unit is fixed, choosing one determines the other. Its main example is the Euler–Maruyama discretization of the stock and variance…

The document asks how replication should be understood for an American option in a pricing model under a risk-neutral measure. A self-financing portfolio with an adapted strategy has a martingale value process, while an American option’s payoff process…

The document concerns adapting the Avellaneda–Stoikov market-making model to a longer time horizon. Its question centers on the reservation-price expression, where inventory, risk aversion, volatility, and remaining time shift the indifference price away…

The document describes a simulation question about the Heath–Jarrow–Morton interest-rate framework. The author simulates forward rates with constant volatility and antithetic normal draws, then compares averages of simulated rates with corresponding values…

The document discusses whether exchanges cap the total number of resting orders in an order book. Its main answer is that limits are often applied at the trader or participant level, such as constraints on the number of open orders or the rate at which…

The document explains how to represent dual-curve pricing for caps and caplets in QuantLib Python. The curve handle supplied to the pricing engine is used to discount cash flows, while the curve associated with the Ibor index supplies forward rates.…

The document explains why stock positions remain open overnight even when some day traders prefer to close before the market shuts. Long-horizon investors and institutions—including mutual funds, private individuals, and bank portfolios—may hold shares as…

The document outlines a validation approach for a finite-difference implementation of the Libor Market Model. It recommends comparing European swaption prices across at-the-money and in-the-money or out-of-the-money strikes with prices from a zero-shift SABR…

The discussion examines when at-the-money (ATM) implied volatility can approximate the risk-neutral expectation of average integrated variance. For very short maturities, it motivates the approximation by noting that instantaneous volatility near the start…

The discussion asks whether implied volatility (IV) produces better option prices than historical volatility (HV), noting that the common forward-looking argument for IV is not enough by itself to establish better pricing performance. It cites an experiment…

The Longstaff–Schwartz method prices American options by simulating possible asset paths and using regression to estimate continuation values. The discussion notes that simulation can accommodate options whose value depends on multiple factors, so the method…

The document explains how an out-of-the-money put affects variance-covariance Value at Risk for a portfolio of stocks, bonds, an ETF, and an option. The method begins with market-factor volatilities and correlations, then combines factor sensitivities with…

The document compares two ways of combining the annualized returns of a two-asset portfolio. Weighting each asset’s annualized return assumes the portfolio weights are maintained over time through rebalancing. Weighting the assets’ cumulative returns instead…

The question describes pricing a fixed coupon bond in QuantLib with a flat yield curve built from semiannual zero rates. The user encounters a negative-time error because the curve’s first date comes after the evaluation date. The accepted answer explains…

The document surveys the trade-offs involved in selecting an optimizer for portfolio allocation problems with multiple assets or risk factors, varied objectives, constraints, and simulation noise. It describes numerical search as a balance between…

The document distinguishes the CAPM relation for expected returns from a single-index model for realized returns. It asks whether CAPM alone can support the familiar division between systematic and diversifiable risk, since an expected-return equation does…

The document explains how a portfolio can have lower variance than either of its component assets, even when one asset has higher standalone volatility. It uses a fully invested two-asset portfolio and derives the minimum-variance weight from the assets’…

The document examines how a market maker might manage exposure after buying ETF shares from a customer. Hedging every underlying component immediately can be impractical for a large index basket, especially when fills are small and component share quantities…

The document explains why daily volatility is commonly scaled by the square root of the number of trading days in a year. Under constant daily variance and uncorrelated returns, variances add across trading days, so annual volatility equals daily volatility…

The document discusses how to assess liquidity in commodity futures, noting that stock-market measures such as volume and the Amivest ratio may not transfer directly to every contract. Suggested indicators include trading volume, bid–ask spreads, order-book…

The document considers how to hedge an equity portfolio of acquisition targets when some deals pay part of the consideration in acquirer shares. It proposes estimating the portfolio’s index exposure by multiplying each acquirer’s dollar position by its beta…

The document asks whether the profit or loss of a Black-Scholes delta-hedged option depends only on realized volatility at expiry or also on its path. It references a hedge-error expression involving gamma exposure and the difference between implied variance…

The document examines a density that appears when expressing forward implied variance as an average of local variance. It derives the weighting from the risk-neutral distribution of the underlying and a factor involving spot squared and Black-Scholes gamma.…

The document considers whether high and low prices can improve correlation estimates from OHLC bars. Its central point is that open and close observations have known timing, while the relative timing of each asset’s high and low is unknown. A joint estimator…