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The document describes simulations using the Gibbons–Ross–Shanken test to evaluate a CAPM-style model across multiple test portfolios. With returns generated under the model, the test does not reject the null; adding nonzero portfolio alphas leads to…
The document discusses why Yahoo Finance may report zero implied volatility for some in-the-money options, especially shortly after the market opens. It offers possible explanations rather than a confirmed account of Yahoo’s calculation: missing or unstable…
The document resolves a question about replicating a European call in a zero-interest-rate market where the stock’s diffusion coefficient depends on its price. The key result is that the number of shares in the replicating portfolio is the option’s stock…
The document explains why rising real yields make it more expensive for companies and consumers to borrow. A bond’s coupon divided by price is only a rough running-yield measure; for a zero-coupon bond, the price of a fixed future payment falls as its yield…
The document raises the problem of converting probabilities inferred from stock option prices under a risk-neutral measure into real-world, or physical, probabilities. Its only proposed method is the Recovery Theorem, named in a brief answer. No derivation,…
The document explains how to estimate the probability that an underlying asset reaches an option strike before expiry. It distinguishes this first-passage event from the probability of finishing in the money, noting that option delta is not generally the…
The document asks whether a lender and an equity holder in a simplified collateralized loan obligation should value their claims using the same risk-neutral probability measure. The lender receives an agreed payment ahead of the borrower, who keeps the…
The discussion examines whether theta-to-gamma ratios can guide exits from short at-the-money options paired with long-tail options. It relates the ratio of cash theta to cash gamma to implied variance, and extends this relationship to a portfolio by…
The document proposes combining annualized returns measured over several horizons with a weighted mean and weighted standard deviation. It illustrates assigning each horizon a weight that decays exponentially with its length, controlled by a chosen decay…
The document asks how to compare daily five-day volatility estimates for two countries’ benchmark government bonds. Because both series use rolling windows, adjacent observations share most of their underlying price data and are serially dependent. Simply…
The document addresses whether MATLAB’s one-dimensional interpolation function can produce cubic spline interpolations for yield curve data. The response says that the built-in spline method is suitable for interpolating sampled curve values and identifies…
The document explains the role of the underlying asset position in a variance swap replication strategy. A short variance swap can be hedged with a strip of options across strikes, often represented in practice by an at-the-money straddle together with…
The document distinguishes the fair strike of a plain variance swap from the price of a variance swap whose realized variance is capped. A strip of vanilla options can be used to replicate the uncapped variance exposure under standard assumptions, so…
The document surveys possible developments in quantitative finance that could gain wider use or appear in future textbooks. It describes machine learning as a newer tool applied to established tasks, including risk analysis, risk management, and algorithmic…
The document discusses how to estimate execution slippage for a strategy trading many stocks with orders that are small relative to average daily volume. One proposed starting point is a cross-sectional regression using bid-ask spread and order size relative…
The document asks whether probabilities inferred from derivatives on non-traded variables, such as weather outcomes or central bank rate decisions, represent risk-neutral or real-world beliefs. The responses distinguish pricing measures from objective…
The document examines an apparent performance bias in a simple rolling walk-forward backtest. It uses lagged indicators to predict next-day returns, fits a linear regression on each training window, and evaluates it on the adjacent test window. The accepted…
The document examines a stop-loss style strategy for replicating a call option and asks how its hedging costs relate to the time the underlying spends near the strike. The answer explains the call payoff using the Tanaka-Ito-Meyer decomposition: intrinsic…
The document discusses how much decimal precision trading and portfolio software may need for equity prices and share quantities. It explains that quoting increments depend on the product and venue, and that rules governing displayed quotes do not…
A Bermudan swaption allows exercise on multiple specified dates, giving it more exercise flexibility than a European swaption. The document notes that these products are actively traded rates volatility instruments and are used in callable bond structures: a…
The document asks why a one-year Bitcoin futures contract can trade at a premium whose annualized rate exceeds a comparable government bond yield, despite standard cost-of-carry relationships. It considers whether demand for leveraged exposure may help…
The document raises a regression-design question: whether to exclude a covariate when it has substantially fewer observations than the other variables. The author gives an example in which one variable has 80,000 observations while others have 100,000, and…
The document explains how to revalue a swaption one week after observing its implied volatility in a rates volatility cube. The option retains its underlying forward swap and strike, while its remaining expiry shortens. Its value at the later date is…
The document addresses pricing European options on the ASX 200 index when dividends paid by constituent companies affect the index level. It reports that using a continuous dividend yield in Black–Scholes–Merton produced a price consistent with the observed…