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20,364 dokumenter
The document proves a quantile-integral representation for expected shortfall of a continuous random variable. Expected shortfall is defined as the conditional mean below the quantile at probability level one minus the confidence level. The result expresses…
The document explains a sign confusion in a put–call parity arbitrage argument. A trader considers a position involving a call, a put, and the underlying stock, and asks whether the terminal expression represents a debt or a gain when the call is exercised.…
The document studies a European payoff that is zero below a lower threshold, declines linearly between two strikes, and pays a fixed amount above the upper strike. It first expresses the price as discounted risk-neutral expectations over the relevant…
The document examines whether a basic Kalman update can estimate both the evolving mean and the variability of a price series. It presents a recursive mean update using the Kalman gain, with a filtered state variance that shrinks when the gain is below one.…
The document raises a question about two option sensitivities: dual delta, described as the derivative of option price with respect to strike, and epsilon, described as sensitivity to dividend yield. It asks whether these measures have practical uses and…
The document distinguishes a company’s cash position from its legal bankruptcy status. A company with no cash may seek financing to cover a shortfall; insolvency risk becomes acute when it cannot repay or refinance its borrowing. It also notes that treasury…
The document asks which implied volatility surface should serve as the target when calibrating the leverage function in a stochastic-local volatility model. It describes a two-stage setup: first calibrate pure Heston parameters, then fit the leverage…
The document explains an apparent asymmetry in simulated currency prices generated from a GARCH model. The model is fitted to log returns, which may have a symmetric innovation distribution, but the simulation is transformed back into price levels by…
The document distinguishes carry from roll-down for forward-starting interest rate swaps. Before the swap begins, its floating leg has no certain payments over the investor’s holding horizon, so the response describes the position as having no earned carry…
The document addresses how to estimate correlations between company revenues across industries. Its practical approach is to obtain company-level revenue data together with industry classifications, then calculate correlations from those observations. It…
The document explains how to estimate a Treasury futures contract’s modified duration when its cheapest-to-deliver (CTD) bond is known. Under the simplifying assumption that futures track the CTD’s forward price perfectly, the conversion factor cancels from…
The document explains how to value a European option whose payoff is determined at expiry but paid later. It distinguishes the option expiry date from the cash settlement date and expresses the value at expiry as the payoff multiplied by the price of a…
The document describes a request to value a Chilean peso fixed floating swap in QuantLib when the fixed leg pays as a single coupon through the first eighteen months and semiannually afterward. The question includes code for constructing a discount curve…
The document asks how quickly simulated asset paths converge under a Milstein discretization of the Heston stochastic volatility model. It gives the coupled stochastic differential equations for the asset price and variance, including mean reversion in…
The document presents Python code intended to value a European call or put using a time and asset-price grid. It sets the payoff at expiration, then attempts to step backward through the grid while estimating option sensitivities and applying boundary…
The document asks how to reduce a covariance matrix for 100 stocks to a five-by-five matrix after grouping the stocks into five clusters. The intended use is a two-stage asset allocation process: first allocate across clustered returns, then perform a…
The question asks how to obtain a zero-coupon curve for Italian government bonds in order to calculate Z-spreads, including how to treat a bond’s next coupon date. The answer clarifies that the “z” in Z-spread refers to zero volatility, rather than…
The post questions how White’s Reality Check handles strategies that generate different numbers of trades. Its example compares one strategy with two observed returns and another with ten, then describes bootstrapping returns, taking the maximum strategy…
The document presents questions about a continuous-time Kelly allocation derived for a risky asset modeled as a diffusion and a risk-free asset. Under the stated assumptions of self-financing trading, continuous rebalancing, and no market frictions, the…
The discussion describes what makes options strategy backtesting more demanding than testing a simple underlying asset. A credible simulation needs historical option chains, including contract terms and market prices, alongside underlying prices used to…
Money-weighted return is an internal rate of return computed from an investment’s dated cash flows. When those flows change sign multiple times, the return equation can have more than one solution, so the reported rate may not uniquely describe performance.…
A bank deposit creates a liability to the customer and an asset for the bank, initially cash or a central-bank balance. The discussion explains why an idle deposit can still affect bank constraints and costs, while converting cash into loans may generate…
The document discusses generating paired observations from two specified marginal distributions with a target Pearson correlation, as might be needed in Monte Carlo risk assessment. Its central point is that an arbitrary target may be impossible: degenerate…
The document compares Monte Carlo prices for a European call under constant volatility and under volatility sampled once per path from a lognormal distribution. It raises the question of why the random-volatility estimate is slightly below the…