คลังความรู้

The document explains how Fourier pricing formulas for European options can be adapted from spot assets to futures. It focuses on the Variance Gamma model and notes that its raw process characteristic function needs a drift adjustment so the exponentiated…

The discussion compares price-to-earnings and price/earnings-to-growth ratios for valuing companies with different growth profiles. It notes that a low P/E can reflect declining revenue, while PEG may be unsuitable for businesses with very stable growth. The…

Underlying stock return correlation does not directly determine the correlation between two option positions. The document illustrates this with perfectly correlated stocks and options whose exposures point in opposite directions: a deep in-the-money call on…

In a GARCH model, returns are represented as conditional volatility multiplied by an innovation. The document explains that the innovation is standardized to have zero mean and unit variance, even when its underlying distribution is non-normal. This…

The document describes how to encode an index-tracking portfolio in a genetic algorithm. The proposed chromosome represents which benchmark securities are selected, rather than their portfolio weights. For each selected subset, a separate quadratic…

The document asks what information the filtration represents when defining a risk-neutral measure for the Heston stochastic volatility model. A filtration describes the information available up to each time, and the response gives a market-oriented example:…

The document explains a no-arbitrage trade when a European call costs less than its intrinsic value, defined here as the underlying price minus the strike. The described position buys the call and shorts the underlying. At expiration, if the underlying is…

The document examines whether a Federal Reserve rate cut is simply the result of bond purchases that raise bond prices and lower yields. The responses explain that the Fed announces a target for interest rates and uses its operations to steer prices and…

The document introduces variance swaps as instruments for taking a view on an underlying asset’s volatility, described in the question as historical volatility. It asks whether a variance swap can practically hedge vega or volga exposure, and in what market…

The document asks how to choose weights in a weighted Frobenius norm when using alternating projections to adjust an equity correlation matrix that is not positive definite. It raises the possibility of weighting entries according to portfolio exposures, so…

The document considers whether cryptocurrency market conditions such as low volume, high volatility, or market immaturity might allow intra-exchange triangular arbitrage gaps to persist long enough for an API-based strategy. It asks whether traders can…

The document explains how a near at-the-money payer and receiver swaption pair behaves as the underlying forward swap rate moves. Its initial delta is approximately zero, though the exact value depends on the pricing setup; spot-premium treatment can also…

The document considers how to simulate a passive buy order using trade prints and snapshots of the best bid and ask, while assuming the simulated order has no market impact. The proposed simple approach is to use changes in bid and ask prices as a rough…

The document works through finding a probability measure under which a process formed from Brownian motion and time is a martingale. The accepted solution applies the product rule to separate the process into two factors, then rewrites its differential so…

The document asks whether the carry of a short bond futures position can be estimated by subtracting the cheapest-to-deliver bond's conventional yield from the futures implied repo rate. The answer explains why the direct subtraction is not generally valid:…

The document shows a QuantLib workflow for bootstrapping a yield curve from deposit rates, futures, and swap rates, then asks why some curve node dates do not match the apparent swap tenor dates. The example uses a U.S. calendar, modified-following…

The document examines a backtest of a collar formed with shares, a long put, and a short call, with both options struck at the current stock price. Its payoff expression simplifies the option payoff terms at expiration, leaving the initial call-put premium…

The document describes estimating an event-related move from options by separating variance expected across ordinary time from the extra variance attributed to the event. It uses at-the-money implied volatilities for the first two expirations after the event…

The document considers the usual estimate that annualized volatility equals monthly return standard deviation multiplied by the square root of twelve, and asks whether different month lengths should change the calculation. It explains that the relevant…

The document explains what it means for SPY to track the S&P 500. The fund seeks to hold component weights close to those in the index, so its net asset value changes with the weighted returns of its holdings, after fees and expenses. The difference between…

The document explains why missing-value checks can fail when financial data is arranged in rows or arrays rather than a one-dimensional list. Comparing a value directly with NaN does not work reliably; a NaN-aware check is needed. When a check produces…

The document explains ways to estimate how AAPL’s trading volume is split across exchanges. It describes using a financial data vendor’s volume-weighted average price view, where exchange names and their reported volumes can be displayed as a breakdown. It…

The document considers how to estimate a Basel long-run average default rate when exposures enter and leave a portfolio during the year. It describes a simple estimator: at each year end, count the exposures still active, measure defaults among them over the…

The document explains why implied volatility can still be useful even though it is calculated from an option’s market price. It presents Black–Scholes as a way to transform observed prices into volatility values, which can then be used to estimate prices for…