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The response describes how market makers estimate fair value for a domestic ETF when its international holdings are not trading. Rather than relying on unavailable spot prices, they combine proxies such as American depositary receipts, foreign equity…
The document asks how to convert a recorded purchase price into a value comparable with a stock’s current split-adjusted historical series. The example concerns an older Apple purchase, and the writer notes that splits and other corporate actions can change…
The discussion explains why constant volatility appears in market-making models and how volatility differs from the risk that incoming trades carry adverse information. Volatility estimates the risk that an inventory position will lose value as prices move;…
The document discusses the two-dimensional term structure of lognormal implied volatility for European swaptions, varying by option expiration and underlying swap tenor. It describes a typical pattern in which volatility may rise over the shortest…
The document describes a test of exit rules in short-term foreign exchange data using randomly selected entry points. It compares a trailing stop, which closes a position after gains retrace by a preset amount, with a fixed threshold that exits when either a…
The document considers how to evaluate a simple signal that uses past data to predict a subsequent price move. It proposes comparing the signal with a label based on the next period, but cautions that a single accuracy percentage is an incomplete measure.…
The document explains why a common Bloomberg approximation for the five-year inflation rate beginning five years ahead uses twice the 10-year zero-coupon inflation swap rate minus the 5-year rate. It contrasts that linear calculation with a compounded…
The note discusses how to represent recovery for a bond whose promised solvent-state cash flows have fallen far below its original notional. It cautions against assuming that recovery should simply be a standard fraction of face value: distressed creditors…
The document considers using an FX futures contract to hedge an FX forward, with the question focused on spot-rate exposure while setting aside currency interest-rate sensitivities and cross-currency basis risk. The answer offers a concise market…
The note explains how to translate option sensitivities into approximate dollar gains or losses for specified changes in the underlying price and implied volatility. It defines delta and vega as changes in option value for unit changes in their respective…
The document distinguishes constant-volatility geometric Brownian motion from a model in which returns have time-varying conditional volatility. It explains that a GARCH model is fitted to historical returns, typically by estimating its parameters, and then…
The document explains that QuantLib’s C++ calendar interface provides a holiday-list function, but the Python wrapper does not expose it. Calling that method from a Python calendar therefore raises an attribute error, and calling it as a standalone function…
This note explains a negative-time pricing error when using a QuantLib zero curve to value a credit default swap. The cause is the curve’s first date: the example builds the curve from rates beginning one month after the evaluation date, so discounting or…
The document derives the distribution of the time integral of a deterministic function multiplied by a Brownian motion. It uses integration by parts to rewrite the integral in terms of the Brownian value at the horizon and a stochastic integral whose…
This note explains why manually calculated zero rates for two deposits may differ from a QuantLib piecewise linear zero curve. The key is that the deposits do not share the curve’s valuation date as their start: the overnight transaction runs over one day,…
The document asks how an exchange updates the displayed last price when a market order consumes liquidity at multiple price levels. It distinguishes the time an order finishes executing from the individual matching events that occur as the order fills…
The note explains the theoretical replication of a variance swap using out-of-the-money options across strikes. Its fair variance is expressed as an integral of put prices below the forward and call prices above it, weighted inversely by squared strike.…
The note compares how single-index and multi-index factor models represent the covariance matrix of stock returns. In the single-factor case, covariance is modeled as market variance times the outer product of security betas, plus a diagonal matrix of…
The document explains a simulation framework for comparing Markowitz mean-variance optimization with Michaud’s resampled efficient frontier. A referee treats a specified set of asset means and covariances as the true population values, generates simulated…
The document considers estimating a separate slope coefficient for each intraday time interval when past returns are used to predict subsequent returns. With few days of observations and a weak relationship, independent ordinary least squares estimates may…
The document gives a short derivation for the expectation of the product of two Brownian-related random variables. It represents one variable as a linear combination of an independent Brownian motion and another Brownian motion, then expands the product and…
The document describes a proposed method for turning expiring corn futures contracts into a continuous price or return series. It tracks the nearby and first-deferred contracts and suggests switching between them when open interest in the deferred contract…
The document considers a proposed adjustment for a stock dataset that omits delisted and bankrupt companies. The proposal models bankruptcy likelihood as dependent on volatility, assigns a distribution of losses at bankruptcy, removes subsequent returns, and…
The document discusses why American options on illiquid underlyings are difficult to price: when the underlying share value is poorly known, option valuation is correspondingly uncertain. One answer recommends scenario-based risk and reward analysis, similar…