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20,364 dokumenter
The document explains why an option skew measure based on volatility differences divided by log-strike distance, with a square-root-of-maturity adjustment, can remain similar across listed expiries. The key comparison uses strikes set at a fixed number of…
The document poses a conceptual question about pricing contingent claims under an equivalent martingale measure. It asks whether taking a conditional expectation requires specifying the underlying stochastic process or terminal distribution, or whether a…
The document discusses how to size the legs of a steepening yield-curve trade using Treasury futures. It clarifies that futures prices are market quotes; the practical sizing question is how many contracts to hold on each side. One common approach is DV01…
The document asks why historical return quantiles can be used for Value-at-Risk when returns are dependent, as in ARCH-type models. The response clarifies that dependence among returns does not prevent modeling their marginal distribution: volatility models…
The document asks how to judge whether an estimated covariance matrix predicts future portfolio risk. It considers comparing a training-period estimate with a later sample covariance using the Frobenius norm, then suggests evaluating whether a mean-variance…
The document asks whether mean-variance optimization research remains worthwhile when expected-return estimates are noisy. It cites a discussion of out-of-sample results in which more accurate volatility forecasts alone did not materially improve the Sharpe…
The document examines integrability conditions for a cumulative income process in a mathematical finance framework. It asks how an expectation under a risk-adjusted measure, involving the finite-variation component divided by a numeraire, relates to an…
The document asks whether forward rates derived from one compounding convention can be used to calculate discount factors under ACT/360. It presents a method for deriving a forward rate from two spot rates and maturities, then proposes a discount-factor…
The document raises implementation questions about valuing an interest rate swap in QuantLib. It asks how a piecewise log-cubic discount curve uses dates and rates supplied through rate helpers, including whether the curve interpolates between those inputs.…
The document asks whether downside deviation, also called semi-deviation, can replace standard deviation in a value-at-risk estimate that accounts for expected return. Its motivating case is a portfolio short an asset whose price is falling: the short…
The document considers whether options can reveal volatility over a specific upcoming interval, such as a trading day containing a scheduled central-bank announcement. It notes that implied volatility is only directly observable for horizons with liquid…
The document asks how to build a forward six-month LIBOR curve in a multi-curve framework from three market inputs: par OIS rates, a fixed six-month LIBOR rate, and par swap rates on swaps with semiannual floating payments and annual fixed payments. It…
The document reviews a call ratio spread designed to start delta-neutral and gamma-neutral, with a short stock position offsetting option delta. Although the structure may collect theta, the answer emphasizes its payoff asymmetry: a credit and frequent small…
The document explains how risk aversion changes with wealth under constant relative risk aversion (CRRA) utility. For the stated power utility function, it distinguishes absolute risk aversion, measured by the Arrow–Pratt ratio of negative second to first…
The document poses a portfolio optimization problem in which asset positions determine portfolio weights, all weights must sum to one, and each weight must remain below a specified cap. It asks whether a standard algorithm can adjust positions to satisfy the…
Co-terminal, or diagonal, swaptions share a common final maturity while their expiries step forward and their underlying swap tenors shorten. The document illustrates the structure with a callable bond that can be redeemed at regular intervals before…
The document considers how machine learning could extend cross-sectional factor models used to explain security returns and estimate portfolio variance. It suggests modeling factor exposures as functions of observable security characteristics, such as size,…
The document explains why a futures contract’s implied repo rate may be higher when the short delivers on the last eligible date rather than the first. The key detail is that the invoice price includes accrued interest in addition to the futures price…
The document compares a portfolio of call options on individual assets with a call option written on a weighted portfolio of those assets. For nonnegative weights summing to one, the payoff of a call is a convex function of its underlying value. Convexity…
The question derives daily log returns under geometric Brownian motion and estimates their sample variance from a month of stock prices. Since the variance of a return over a daily interval is the annual variance scaled by the length of that interval, the…
The question considers a trading range with an equilibrium price where the maximum gains from long and short positions balance. It proposes using the long-side expected log return above equilibrium, the short-side return below it, and zero at equilibrium,…
The document raises an alternative to the common factor backtest that buys the highest-ranked group and shorts the lowest-ranked group. It quotes a research proposal to construct a long-only portfolio with exposure to a chosen factor while targeting a…
The document asks how to choose a moving-average smoothing parameter without relying only on strategy optimization, then presents an example for an exponentially weighted moving average (EWMA) volatility estimate. In the described approach, returns are…
The document asks whether Visual Basic can handle an order-routing calculation budget of about one millisecond, with much greater time expected for communication to and from exchanges. The replies distinguish modern Visual Basic .NET from older Visual Basic…