คลังความรู้

The question asks whether a CME futures order book consists of aggregated stop and limit orders, using a hypothetical book to illustrate how consuming displayed offers can change the cost of executing a buy order. It also asks how the spread could narrow…

The note examines an undefined function, F_X, in a theorem associated with the Longstaff–Schwartz method for valuing American options. It compares the theorem’s notation with the paper’s discussion of approximating the continuation value F using M basis…

The document explains why early exercise does not add value to an American call when there are no dividends or repo costs and interest rates are nonnegative. Put-call parity implies that a European call is worth at least its intrinsic value under these…

The document gives a standard-error approach to estimating how many observations are needed to assess a strategy’s returns. It relates sample size to measured return variability, a chosen confidence level, and the desired width of the confidence interval.…

The note explains a maximal curve as a way to estimate the probability that price reaches a specified distance up or down within a given time. It describes converting a volatility estimate, expressed as price movement per hour, into probabilities with a…

The document shows how to compute the second moment of a stochastic integral against a compensated Poisson process. Its method defines the integral as a martingale, applies the product rule for jump processes to its square, and separates the jump quadratic…

The document poses a stochastic-calculus problem for a price process whose relative changes are driven by a compensated jump measure. It also specifies a state variable and a jump intensity that depends on that state. The requested quantity is the…

The document explains why otherwise identical call options should not become more expensive as their strike prices rise. If a lower-strike call costs no more than a higher-strike call, an investor can buy the lower-strike option and sell the higher-strike…

The document describes a practitioner’s attempt to extend univariate GARCH risk analysis to a three-series DCC-GARCH model. The workflow fits separate conditional volatility models, combines them through a dynamic conditional correlation specification, and…

The document addresses valuation of a cross-currency basis swap whose two currency legs are collateralized in a third currency. Its example uses Indian rupee and South African rand cash flows with US dollar collateral. The stated procedure is to convert each…

The document explains why the coupon required to price a callable bond at par can vary non-monotonically with the call date. The coupon spread over a comparable non-callable bond reflects the value of the issuer’s call option. That value depends on time to…

The document describes a one-minute foreign-exchange backtest that chooses a trade direction using the next bar’s close. Because that information is unavailable at entry time, the apparent advantage is a look-ahead bias rather than a usable signal. It also…

This response recommends a focused path for learning interest rate risk in the banking book (IRRBB). It suggests beginning with Basel Committee materials that set out the regulatory framework, then consulting jurisdiction-specific guidance such as a recent…

The document examines why CAPM assigns an asset with zero market beta an expected return equal to the risk-free rate, even though a single zero-beta asset can still carry substantial risk. It explains diversification using the variance of an equally weighted…

The question concerns a spot forex system that uses digital filters and behaves poorly around news releases. Rejecting signals generated within two hours of an announcement has not resolved the issue, because signals shortly afterward can still react to…

The document examines why daily returns on a leveraged forex trade can become misleading when calculated as daily profit or loss divided by a small account balance. Its example starts with $40 of capital and shows losses pushing the balance close to and then…

A self-financing portfolio changes value only through changes in the assets it holds, with no external deposits or withdrawals. For holdings phi_i in assets priced S_i, its infinitesimal value change is the sum of each holding multiplied by that asset’s…

This note traces the use of q for continuous dividend yield in derivative pricing. It contrasts Merton’s use of D in an early treatment of continuous dividends with later use of q in work by Hull and White and in Hull’s textbook. Other papers used d or the…

The question asks whether quantitative finance has a counterpart to complex economics, focusing on markets as dynamic systems in which participants’ forecasts and trading can influence future prices. It contrasts the usual emphasis on option pricing and…

The answer addresses whether time can be divided by a Brownian motion differential and whether one can interpret a quotient such as dV/dS for Itô processes. It warns that manipulating formal differentials as ordinary algebra can produce misleading results.…

The discussion considers how an issuer might hedge an ETN linked to a VIX strategy, especially when replicating an index with VIX futures could involve trading costs and limited liquidity in deferred contracts. The answers emphasize that a hedge need not…

The document explains how to locate historical CAD–USD cross-currency basis data for converting USD short-term yields into Canadian equivalents. The question proposes combining CORRA, the spread between a US yield and SOFR, and the CAD–USD basis, but reports…

The document considers a Brownian bridge defined by an SDE with drift pulling the process toward a terminal value. Its solution contains a stochastic integral whose contribution must vanish as time approaches the endpoint for the process to converge to that…

The document sets out proposed formulas for Bitcoin’s Pi Cycle top and bottom indicators and asks whether the inequalities are stated correctly. The top condition compares a 111-day simple moving average with twice a 350-day simple moving average. The bottom…