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20,364 documente
The document explains why a bank can find low-credit-risk lending or securities consuming under a leverage ratio. Traditional risk-based capital rules assign different capital charges according to credit risk, while the leverage ratio described here compares…
The document presents a method for analyzing whether a stochastic process is a martingale: apply Itô’s formula to obtain its differential, then inspect the coefficient of the time increment, or drift. A zero drift makes the process a local martingale under…
The document distinguishes running basis points from upfront basis points in bond risk and carry calculations. Upfront basis points translate a running spread into a price-risk amount using DV01, the dollar value of a one-basis-point yield move; the…
The document addresses how to identify a particular financial index when providers publish many strategy, currency, or other variants under similar names. Its example is a family of hedge fund indexes whose labels differ by strategy and currency, making…
The document explains how minimum-variance and minimum-tracking-error portfolio problems relate to quadratic programming and second-order cone programming. It clarifies that expressing a continuous convex risk constraint as a cone constraint does not remove…
The document asks how the residual income valuation model should change when the cost of equity varies over time. It begins from the constant-rate formulation, where discounting and the residual income adjustment use the same rate, and considers why the…
The document compares error assumptions in simple ARIMA models with those used in ARIMA-GARCH estimation. It explains that some ARIMA or ARMA models can be fitted with ordinary or iterative least squares, while maximum likelihood estimation is often used…
The document explains how a prospective hedge fund employer or investor may evaluate a person’s claimed Sharpe ratio. The usual evidence is a return time series, preferably from live trading and at daily frequency. Some reviewers may accept a combination of…
The document poses an optimal stopping problem for a firm's profit modeled as a Brownian process with drift and volatility. The value is expressed as accumulated discounted profit up to a stopping time, then rearranged into a term involving an expected…
The document explains how to test whether a signal predicts returns by sorting securities into portfolios according to the signal, then comparing high-signal and low-signal groups. A spread portfolio is formed by going long the high group and short the low…
The document considers whether the yield difference between on-the-run and off-the-run bonds of similar maturity could support a mean-reversion trade. It explains why the spread may reflect persistent differences in liquidity and investor demand: new issues…
The document shows a QuantLib setup for pricing European call options with the analytic Black–Scholes engine. It compares outputs for several strikes with an online calculator and asks whether QuantLib supports Black ’76. The response identifies two inputs…
The document explains why cumulative delta readings in the E-mini S&P 500 futures contract (ES) can differ sharply from those in its micro contract (MES). Cumulative delta records executed buying versus selling volume in a particular contract. Although the…
The document asks how to assess correlations between one stock’s returns and another stock’s returns shifted across different lags. It distinguishes this cross-series question from the usual use of the Ljung–Box test for autocorrelation within one series.…
The document describes a static replication result for a European payoff using calls and puts across a range of strikes. For a twice continuously differentiable payoff function, the second derivative determines the weights applied to vanilla options. The…
The document derives bounds on the derivative of a call price with respect to strike. It compares calls with nearby strikes and uses the fact that, at maturity, the difference between their payoffs is bounded by zero and the negative of the strike gap.…
The document asks how to price equity quanto options with a local-stochastic volatility model, building on a proposed Heston approach that adjusts equity and variance dynamics for quanto effects. The supplied answer recommends modeling both the equity and…
The document asks how the long-run mean, often denoted theta, in an Ornstein–Uhlenbeck model should relate to the initial mispricing of a mean-reverting pair spread. It refers to a paper on optimal profit-taking and stop-loss boundaries, which describes…
The document explains how forward rates relate to the dates in an interest rate swap's floating leg. It distinguishes payment dates, accrual dates, reset or fixing dates, and rate valuation dates. The rate being estimated is associated with the period over…
The document asks how to use estimated betas and risk premia from a Fama–MacBeth regression to predict returns. Its answer draws a distinction between testing an asset pricing model and building a forecasting model: Fama–MacBeth regression is presented as a…
The document compares Monte Carlo Value at Risk with a parametric approach. Monte Carlo methods can be useful when a portfolio contains nonlinear or path-dependent positions, such as options, mortgage-backed securities, or convertible bonds. The method…
The document considers how to size three long and short currency positions to target a specified annual portfolio volatility while allocating risk equally. The proposed procedure first scales each currency position separately so that each standalone position…
The document describes a learner's attempt to estimate a GARCH(1,1) volatility model by hand after fitting an AR(1) model to a return or time series. The AR(1) residuals supply the lagged squared innovations used in the conditional variance equation, while…
The document asks how to price American options in QuantLib when the contract is specified by a time to maturity rather than fixed calendar dates. Its suggested approach is to choose a start date, such as today, and add a period representing the duration in…