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20,364 dokumentů
The document resolves an apparent paradox: an American put’s value is at least its immediate exercise payoff, yet early exercise can still be optimal. The option value is the greater of immediate exercise value and the best expected discounted payoff from…
The document discusses reducing Monte Carlo pricing variance for a European put under a stochastic volatility simulation. The questioner uses the terminal stock price as a control variate and reports a modest reduction in the estimated standard error after…
The document compares a European call price computed from a binomial model with a Monte Carlo estimate. In a binomial model, the risk-neutral probability is derived from the up and down factors and the risk-free rate. The terminal payoff is then averaged…
The document addresses an attempt to maximize expected portfolio return at a specified volatility using R's optim function. The proposed penalty based on an if statement gives the optimizer a discontinuous objective, and the answer instead describes…
The document considers how to fill gaps in cumulative default probability data across maturities and credit ratings. One proposed framework is to choose a probability matrix that stays close to a target, such as a calibrated estimate or a smoothness…
Yield curve PCA needs observations on a consistent tenor grid, but some markets have quotes at only a few maturities. The note compares running PCA on the sparse observed points with interpolating or extrapolating rates to create a fuller grid. The choice of…
The document asks how to obtain a conditional variance-covariance matrix from an estimated MGARCH-BEKK model fitted to spot and futures price series. It presents a two-asset BEKK-style recursion built from a constant matrix, lagged return residuals, and the…
The document addresses how traders might identify market conditions associated with changes in algorithmic strategy performance. It proposes structural-break analysis as one avenue, naming CUSUM tests on recursive residuals or levels and explosiveness tests…
The answer considers whether market betas and rolling-window beta estimates should be normally distributed when asset and market returns are assumed normal. It distinguishes beta estimated from raw returns from beta estimated using log returns, and argues…
The document discusses whether traders can forecast future option prices directly, then outlines volatility-based approaches. It describes gamma trading as selling options when implied volatility is expected to exceed realized volatility, with delta hedging…
The document asks how a biased random walk converges to a process with nonzero drift as its time step shrinks. It starts from the expected displacement after repeated up-or-down steps, then considers steps of size proportional to the square root of the time…
The document explains the origin and limits of a simple approximation that relates implied variance at a strike and maturity to local variance near the initial spot and the strike at expiry. It places this shortcut alongside short-maturity results: the…
The document describes the challenge of turning SEC filings into readable balance sheets and income statements. Its author retrieves reported facts for thousands of companies, using filing identifiers and fields such as reporting date, accounting tag, period…
The document explains why a bond futures contract may permit delivery of several eligible bonds instead of naming one specific issue. If a particular bond becomes scarce or unusually expensive relative to comparable bonds, restricting delivery to that issue…
The note asks why fixed-income practitioners use duration times credit spread, often called spread duration times spread, while an equivalent duration-times-yield measure is uncommon. It compares the rationale given for spread duration times spread with the…
The document explains how to price a forward between two non-accounting currencies when market basis quotes are available against a common accounting currency. It describes discounting each currency leg using that currency’s risk-free curve plus its basis…
The document derives an inverse covariance matrix for a single-factor CAPM model with a zero risk-free rate. It represents total asset covariance as the sum of a diagonal matrix of idiosyncratic variances and a rank-one market-factor contribution. The…
The document considers whether a Libor Market Model volatility function, built from a maturity-dependent linear term multiplied by an exponential and then shifted by a constant, remains bounded. It assumes the parameters and the rate’s maturity are constants…
The document considers how to obtain long exposure to the VDC ETF with options when its dividend payouts are irregular. It raises a tradeoff between possible option positions and dividend-related price changes around an ex-dividend date. The author is…
The document asks how to interpret a step in a proof involving Gyöngy’s lemma, where an expectation weighted by a Dirac delta at a level is rewritten using an expectation at that level. The response frames the delta as concentrating the contribution on…
The document explains a change of variables used when writing a likelihood for a linear regression with normally distributed errors. In the stated model, the error is the outcome minus the fitted linear expression. When the predictors and regression…
The document describes a simulation problem: a researcher wants to compare a trading model’s behavior on ordinary price paths and paths with jumps, while isolating the effect of increased skewness. They can match the mean of the jump process to a geometric…
The document introduces the interpretation of a longer-tenor overnight indexed swap (OIS) rate. An OIS exchanges a fixed cash flow against a floating leg based on daily overnight rates; the cited answer identifies the Federal Funds Effective Rate and an…
The document explains that volatility skew and statistical skewness are related terms with distinct meanings. Implied volatility skew describes how option-implied volatility varies across strikes for a fixed expiry; it is observable from option prices after…