知識圖書館

The document explains how to relate an option on a delivery-date futures contract to a Black-76 valuation using a different futures contract associated with the option's expiry. Under deterministic rates and basis, it expresses the delivery-date futures…

The document considers two risky assets driven by the same Brownian motion, with different volatilities, alongside a bank account earning the short rate. It constructs a self-financing portfolio from the assets and bank account, then imposes the condition…

The document presents ways to assess how the number of Monte Carlo scenarios affects an estimated value at risk. One approach repeats the VaR calculation many times at a fixed scenario count, then uses the sample standard deviation of those estimates as an…

The document asks how much capital or trading volume is needed to move the 10-year Treasury yield by 10 basis points. It frames the question around a recent period of Federal Reserve rate hikes, noting that the 3-month to 10-year yield curve stayed inverted…

The document explains how to interpret the sample count in the two-scale realized variance estimator (TSRV) and why the estimate can be negative. It treats n as the number of intraday observations over the interval being studied, rather than as a fixed count…

The document clarifies why log returns and simple returns can appear nearly identical in a price series. A log return is the logarithm of the ratio between consecutive prices, while a simple return is the price change divided by the previous price. Expanding…

In a continuous-time pricing model, the risk-free asset grows at a deterministic rate, expressed as a differential equation with interest rate r. The answer interprets this asset as a bank deposit: its value earns interest without a random return component.…

A call spread that is long a lower-strike call and short a higher-strike call can be priced by subtracting the short call’s value from the long call’s value. Each option is priced separately, then the signed values are combined to obtain the strategy’s…

The document asks about statistical properties of a sample estimator for average value at risk, also called conditional value at risk. It presents the population objective as a minimization over a threshold parameter, with expected tail loss beyond that…

The document asks how to estimate the expiry stock price at which an option position breaks even after an initial delta hedge that is left unchanged. The reply assumes no stock financing or repo costs and no subsequent trading of the option’s gamma. Under…

This document explains what the iborStartDate argument represents in QuantLib’s FuturesRateHelper. It is the start date of the interest-rate fixing’s underlying accrual period, rather than the futures contract’s expiration date. The fixing itself is for a…

The document considers how to estimate partial or full fills for a limit order placed at the best bid or ask in a FIFO order book. It recommends using historical data to examine whether and when simulated orders would have executed, while cautioning that a…

The document distinguishes futures contracts whose prices are constrained by arbitrage from those whose prices are harder to model. For a storable commodity with an observable spot price and no convenience yield, the cost-of-carry relationship can determine…

The document discusses extreme forward-rate paths in a lognormal Libor Market Model simulated under the spot measure. It notes that reducing the time step or switching from ordinary Euler to log-Euler discretization may fail to eliminate the problem. One…

The document explains how to value an American put with a two-step binomial model. Starting from the current underlying price, the tree applies the up and down factors at each step; because their product is the same in either order, the price tree…

The document asks how to compute the expectation of a LIBOR rate over an accrual period under a later forward measure. The answer says the calculation requires a model for rate dynamics between the accrual end date and the forward-measure date; without…

The document asks why a market-convention one-year interest rate swap can involve a final payment date slightly beyond one year from the trade date. The example uses a two-day spot lag and quarterly floating accruals; adjusted dates put the final cash flow…

The discussion explains why the Sharpe ratio is commonly annualized by multiplying by the square root of the number of periods, under an assumption of independent, identically distributed returns. Over longer horizons, random return components may offset one…

The document poses a quadratic minimization problem with a positive-definite matrix and constraints requiring each linear form in the decision vector to have magnitude greater than one. Although the objective is convex, the feasible set is non-convex because…

The document asks how to determine whether a factor such as size changes a strategy’s performance, using backtests on large- and small-cap stock groups as an example. Comparing returns or Sharpe ratios alone does not establish that the difference reflects a…

The document asks how to interpret a condition that arises in Gatheral’s relationship between local variance and the implied total variance surface. In that formula, the local variance is proportional to the maturity derivative of implied total variance…

The discussion concerns how to infer implied volatility from options on VSTOXX. It describes an attempt using Black–Scholes with the corresponding VSTOXX futures as the underlying and an assumption about rates and yield, which produced an unsatisfactory gap…

A portfolio’s dollar volatility is unchanged when every position is reversed: variance is sign-insensitive, so a short portfolio with the same absolute value as a long portfolio has the same standard deviation. The discussion distinguishes this total risk…

The discussion examines whether a long-only strategy designed for rising markets can be backtested using only historical periods that rose, while excluding declines and joining selected price segments into a synthetic series. Its central distinction is…