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The document asks how to derive the bid for CAD/CHF from USD/CAD and USD/CHF quotes. It compares a textbook formula, which divides the USD/CHF ask by the USD/CAD bid, with an alternative based on multiplying the USD/CHF bid by the reciprocal of the USD/CAD…

The document notes that market depth has no single official quantitative definition and proposes measuring it through the cost of immediately buying and selling a specified quantity, given the order book at a particular time. This cost varies with both the…

The document explains translation invariance for a risk measure: adding a constant amount to a profit-and-loss position reduces its VaR by that amount. For a continuous P&L distribution, VaR is expressed as the negative of a lower-tail quantile, so shifting…

Realized variance is an estimate of intraday variation, not by itself a model for forecasting volatility across days. To forecast future volatility, a model must specify how information from realized measures relates over time. The document describes…

The document discusses how to infer implied volatility from an option’s bid and ask prices. It compares averaging the prices before solving for implied volatility with solving for each quote’s implied volatility and averaging those values. Although the…

The document raises a conceptual question about the one-factor and multi-factor Hull-White interest rate models. The author understands that the one-factor model has limited ability to represent yield-curve movements, and asks which parameters govern a curve…

The document asks how to express a receiver interest rate swap as a sequence of forward rate agreements. It starts from the swap’s discounted fixed-minus-floating cash flows, then compares those payments with forward-rate terms based on discount factors. The…

The document poses a valuation problem for a software investment whose daily revenues depend on an exchange rate and whose costs depend on a commodity price. The proposed simulation models both underlying prices as geometric Brownian motions estimated from…

The document explains why testing the CAPM by regressing individual stocks’ realized excess returns on estimated betas can produce a very low R-squared. Low fit does not by itself show the model is false: CAPM does not predict a particular R-squared, and a…

The document compares two ways to describe a hedge fund or portfolio’s performance. Cumulative return measures the change in value over a chosen period, while the Sharpe ratio relates returns to the variability of returns, giving a risk-adjusted view. The…

The document considers whether a swap must be hedged with another derivative or can instead be hedged using cash products such as equities or foreign exchange. Its answer is contract dependent: the key issue is whether the swap’s underlying exposures…

The document explains the terminal value of a forward contract that requires its holder to buy one share for a fixed cash price at a specified date. At maturity, the holder receives a share worth the prevailing stock price and pays the contracted amount, so…

The document asks how to interpret a model-independent representation of a twice-differentiable payoff as a combination of terms involving the payoff and its derivative at zero, the underlying stock, and an integral of calls across strikes. The questioner…

The document asks how to read derivative notation in conditions from a theorem on arbitrage-free SVI volatility surfaces. One condition uses a time derivative of a parameter and requires it to be nonnegative. Another bounds the derivative with respect to…

The document presents a question about deriving the dynamics of a process defined as the exponential of a stochastic integral and a quadratic-variation adjustment. The process is parameterized by an integrand and a driving process, in the setting of an…

The document asks how to choose the risk-free rate when calculating a Sharpe ratio over a period in which daily annualized returns and their average and volatility are known. It questions whether using the average one-year Treasury yield over that period is…

The document examines whether scaling a risky portfolio by the ratio of a target volatility to estimated volatility guarantees that realized portfolio volatility converges to the target. The answer first shows that, if next-period conditional volatility were…

The document raises a boundary-condition question about using a finite element method to price an up-and-out call. It refers to an appendix that demonstrates the method for a straddle and focuses on a boundary vector containing the difference between option…

The document asks whether the expected payoff of a multi-leg option position, such as a spread or condor, equals the sum of the expected payoffs of its individual options. It represents each leg’s payoff as a function of the same market value at expiration…

The document reports a proposed intraday pattern in Nike (NKE) NYSE trade data. It compares each day’s highest trade price from 15:06 to 15:11 with the highest trade price from 15:36 to 15:41, asking whether the later interval tends to show a specified…

The document presents a question about the relationship between a long call butterfly and a short iron butterfly. It gives a four-option position consisting of a long lower-strike put, short middle-strike put and call, and long upper-strike call, then…

The discussion separates a stock-price model from the martingale condition. A Brownian-motion-based model can include drift under real-world probabilities; having nonzero drift does not mean the process ceases to be Brownian motion. The first answer connects…

The discussion addresses why an Alpha Vantage intraday query may work for US listings but fail for Indian exchange symbols. One answer describes uncertainty around the provider's underlying sources and exchange coverage, noting that US data was linked to IEX…

The document outlines how Lévy processes can model log stock prices through exponential Lévy models. It explains that these processes combine drift, diffusion, and jumps, and distinguishes finite-activity jump models from models with infinitely many jumps.…