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The document concerns hybrid models that combine Heston stochastic volatility with Hull–White interest rates. The question is how to approximate European option prices for model calibration, particularly when the pricing approach uses Monte Carlo simulation.…
The document poses a modeling question about whether local volatility derived from an observed implied volatility surface reproduces that surface or changes its skew. It outlines a workflow: obtain market implied volatilities, fit a model such as SVI, use…
The document examines why a derivative’s price should not depend on which other derivative is chosen to hedge volatility risk in a stochastic-volatility model. The proposed replication argument uses the underlying and a second derivative to span two Brownian…
The document describes how to express an unhedged US investment’s performance in euros. First, turn the dollar return series into a total-return price index, using an arbitrary starting value such as 100. Next, convert each index value into euros using the…
The document poses a fixed-income immunization question involving a mortgage asset with fixed payments, prepayment and option-adjusted spread models, and calculated price, duration, and convexity. The asset and a blend of liabilities are assumed to trade at…
The document explains what the ACT/360 day-count convention means when calculating interest. A year is treated as 360 units for the calculation, while elapsed time is counted in actual calendar days. As a result, a 365-day period accrues interest for 365/360…
The document explains a linear approximation for implied volatility in Emanuel Derman’s sticky implied tree model. The answer starts with local volatility modeled as a linear function of the underlying price, with slope determined by a parameter describing…
The document asks which risk-free rate to use when constructing a maximum Sharpe ratio portfolio from a rolling estimation window of monthly returns. It frames the problem within mean-variance portfolio theory, where the Sharpe ratio measures expected…
The document considers how to recover the risk-neutral density of an underlying at a given expiry from call option implied volatilities across strikes. It describes converting each implied volatility into a Black–Scholes call price, then applying the…
The document asks why a project option valued with real-world probabilities and the project’s required return differs from a risk-neutral valuation. Its binomial example has a successful project value of $10 million, an unsuccessful value of $2.7 million, an…
The note explains how a conditional expectation at a specific asset level can be expressed as a ratio of expectations weighted by the Dirac delta function. For a terminal asset value and a random variance, the numerator weights variance by the event density…
The document asks why a generalized linear model’s design matrix is assumed to have full column rank and whether maximum-likelihood estimation can proceed when it does not. The response connects rank deficiency to non-identifiability: if columns are linearly…
The document describes a reported pattern of month-end declines in the Effective Federal Funds Rate and asks why it weakened from mid-2018 through mid-2021 before appearing again. It presents bank balance-sheet window dressing to improve reported liquidity…
The document explores reducing a large ETF or equity universe before portfolio optimization. Suggested approaches include clustering return series using correlation-based distances, examining PCA loadings to group assets with similar behavior, and using…
The document asks how to evaluate a Laspeyres index built from five oil and energy stocks, intended for use in mean-reversion allocation across asset classes. The central suggestion is to measure tracking error or tracking efficiency: compare the index’s…
The document asks whether an anomaly detector can be trained on normal gift-card activation transactions and then evaluated on anomalous cases. It also describes a setting with no reliable fraud labels and transaction-level fields such as merchant, location,…
The document considers a heterogeneous portfolio in which inverse-volatility risk parity can assign very large weights to instruments whose estimated volatility has fallen relative to the rest. It describes a proposed cap that compares risk-parity weights…
The document works through an Itô-calculus exercise involving two independent Brownian motions. It defines a process as their product minus one half of the time integral of the sum of their squared values, then differentiates that process using the product…
The document asks how to interpret specialness in bond futures when holding a long-only cash bond portfolio. It contrasts a cash bond’s implied forward price, determined by its carry, with the futures-implied forward price. When the futures-implied carry is…
The document explains how borrowing and financing support ETF market making, creation and redemption, and arbitrage when ETF prices diverge from their underlying holdings. Market makers may finance temporary inventory, borrow securities, use repo, or provide…
The document describes a market practice for estimating cross-currency basis between quoted maturity dates. Rather than interpolating the quoted basis or outright FX forwards directly, it presents a representation of the FX forward using spot, domestic and…
The document examines a security paying one dollar if IBM reaches a specified price, with the stock initially below that level and no dividends or transaction costs. It contrasts a risk-neutral probability argument, which would imply a payoff value of one…
The document asks how to discount the legs of a fixed-to-fixed cross-currency swap when its collateral currency changes at a mandatory break date. Without a break, its proposed setup discounts euro cash flows using the euro collateral curve and uses a…
The document addresses how trade and investment payments can be handled when a country’s currency is not freely convertible, using Brazil as an example. Its answer gives a high-level principle: transactions may require approval from the relevant authorities…