คลังความรู้

The document clarifies how tick imbalance bars are formed from transaction data. Each tick receives a direction of plus or minus one based on the change from the prior trade price; unchanged prices inherit the previous direction. The running sum of these…

The document raises a practical question about applying triangular arbitrage to CFDs. It describes a supposed mispricing across EUR/USD, USD/GBP, and GBP/EUR, then asks how to account for opening three long positions, keeping them open, and closing them into…

The note examines why an equity option’s annualized at-the-money implied volatility can be higher for a shorter expiry than for a longer one. It distinguishes a downward-sloping volatility term structure from negative forward variance: comparing two implied…

The document raises a question about using a non-flat term structure when pricing options on bonds with a normal short-rate model. The author describes a proposed mapping for a ten-year bond: at each future point before maturity, use a zero-coupon yield…

The note asks how to estimate whether options trades were initiated by buyers or sellers, ideally for individual strikes and maturities. It identifies two approaches. A specialized exchange dataset used in published research classified daily call and put…

The note explains how regular expiration cycles affect which monthly expirations appear for an individual equity option. Its central point is that the traditional January, February, and March cycles describe the pattern of farther-out standard monthly…

The document explains the economic reason bid and ask sides may appear reversed when deriving implied interest rates from an FX forward. A long AUD forward is described as a sequence: borrow USD, exchange USD for AUD at spot, and lend AUD. Each leg has its…

The document compares two ways to estimate the price of a European call at a strike and maturity absent from the market: interpolate neighboring option prices directly, or interpolate model inputs such as implied volatility and then reprice with…

The document explains where practitioners can obtain dividend and repo assumptions when pricing vanilla equity options. It identifies broker quotes or contract terms as sources for repo rates, noting that the standard rate may apply when the underlying is…

This brief exchange asks what price to charge for an option whose expected payoff is zero. The reply gives a minimal market-based answer: a seller would accept the smallest positive amount buyers are willing to pay. It treats the question as one of…

This exchange asks why a German government bond future can have a quoted price far above the price of a cash government bond. The question considers yield-curve expectations, quotation conventions, and carry, and wonders whether coupon payments should make…

This post asks whether a proposed Average Directional Index calculator produces plausible values across several example price sequences. The examples include steadily rising and falling prices, an accelerating rise, a constant series, and a repeating…

This post raises two practical challenges when using QuantLib from Python: inspecting the market inputs inside a Black–Scholes–Merton process and determining the conventions used to calculate a vanilla option’s Greeks. The author says the library’s C++…

The response offers several theoretical research areas for someone seeking mathematical finance problems grounded in analysis, probability, and optimization rather than statistical modeling. It suggests investigating convergence questions in simulation-based…

The discussion explains how price alignment interest (PAI), paid on variation margin, changes the funding interpretation of cleared interest rate swaps. With perfect collateralization, where collateral tracks the derivative’s net present value, the…

This discussion concerns the timestamps attached to historical intraday equity data from Yahoo’s chart endpoint. The sample rows contain Unix epoch values, but converting them appears to produce times offset by varying seconds from the expected minute…

The discussion identifies potential benchmarks for US corporate and Treasury bond strategies over a historical daily sample. It distinguishes an investable exchange-traded fund from the index it tracks: the fund’s price history begins later, while the…

The document explains a common return on invested capital calculation: after-tax operating profit divided by invested capital, with invested capital defined as equity plus debt minus cash. It uses quarterly financial statement fields to illustrate the…

The discussion addresses portfolio analysis when stocks have different listing dates and incomplete monthly return histories. It warns that interpolating irregular observations to create an even time series, often by linear interpolation, can introduce…

The answer interprets “near choice” as dealer jargon for a spread whose midpoint is close to zero. For a risk reversal, the proposed meaning is that buying one direction of the spread or the reverse direction costs roughly the same, with the trader…

The document compares several ways to annualize returns from a bet costing one unit today, with an equal chance of receiving either two units after one year or half a unit after two years. It contrasts averaging the two annualized outcomes, using an average…

The discussion explains why delta neutrality is common in options trading while emphasizing that it depends on the trader’s objective. A market maker who earns spreads may hedge directional exposure to focus on volatility and pricing, whereas a risk taker…

The document explains that differencing and detrending address different sources of nonstationarity, so the appropriate choice depends on the data-generating process. A trend-stationary series has a deterministic time trend around a stationary error…

The document considers the expected maximum drawdown of a Brownian motion with constant drift and volatility over a fixed horizon. Drawdown is defined as the gap between the running peak and the process value, and the maximum drawdown is the largest such gap…