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20,364 dokumenter
The discussion distinguishes the risk faced by an individual policyholder from the uncertainty faced by an insurer covering many independent customers. An individual’s claim outcome can have substantial standard deviation even when the probability of a claim…
The discussion considers pricing mark-to-market (MtM) basis cross-currency swaps and using their market quotes to derive collateralized discount curves when constant-notional swap data is unavailable. It references a multi-curve framework and an analytical…
The document considers how to identify arbitrage relationships among outright futures and instruments built from them, such as calendar spreads and butterflies. It frames quoted instrument prices as linear combinations of outright prices and asks how to…
The document works through the affine bond-price form for the Ho-Lee short-rate model, where the short rate has a time-dependent drift and constant volatility. Substituting the model’s coefficients into the ordinary differential equations for A and B gives a…
The document discusses combining forecasts from different trading methods, including sentiment measures, signal processing, and neural networks. One recommendation is to express forecasts in comparable units, such as expected returns or event probabilities,…
The document explains why a 10-year receiver and 20-year payer swap with equal and opposite DV01s may not offset under a parallel rate move. Equal DV01s cancel the positions’ first-order sensitivity at the starting curve, but they do not ensure equal…
The document discusses statistical approaches for evaluating whether stock market price changes are consistent with a random walk. It emphasizes testing both randomness and independence, since randomness and dependence are distinct properties and dependence…
The document addresses which date to enter when calculating a Treasury bond’s yield from its clean price, and whether auction prices use the same approach. The answer recommends using the settlement date rather than the trade date or the most recent coupon…
The document describes how to align a QuantLib fixed-rate bond valuation with a Bloomberg clean price. The example concerns a Polish government bond valued on a specified date at a given yield. The initial QuantLib calculation differs from Bloomberg by a…
The document considers how to use parameters estimated from hourly Ornstein–Uhlenbeck (OU) data in a daily simulation. It offers two practical routes: aggregate the observed data to daily frequency and re-estimate the parameters, or simulate at hourly…
The document clarifies naming and interpretation of Actual/Actual day count conventions used in bond and interest rate calculations. It outlines the questioner’s uncertainty about whether the ICMA and Bond definitions differ, particularly around leap days…
The document answers a question about how far an asset price might move over a three-month horizon given its annualized volatility. The response treats the estimate as a static one-standard-deviation range, scaling volatility by the square root of time and…
The document explores how to set asset-level risk contribution budgets while also requiring a portfolio to meet a target volatility. It presents an optimization that minimizes squared differences between each asset’s share of portfolio variance and its…
The document presents a currency and bond arbitrage exercise involving a sterling bond, a dollar loan, spot conversion, and a forward sale of sterling. The question asks why the loan repayment is written as 1.68 times the borrowed dollar amount when the…
The exchange considers why issuing preferred shares does not automatically drive a struggling company's common stock to zero. Preferred holders generally rank ahead of common shareholders in distributions, so the financing changes the common equity's…
The discussion distinguishes forecasting the variance of returns from forecasting their expected direction. A conventional GARCH model updates conditional variance using past squared residuals and earlier variance estimates, making it a framework for…
The document asks how to simulate paths for a mean-reverting diffusion without stepping through its stochastic differential equation directly. It gives the process solution over an interval and its conditional mean and variance, which together specify the…
The document presents an informal argument linking arbitrage to the existence of an investor’s optimal consumption and trading choice. It says that if an optimal strategy exists and utility is strictly increasing, adding an affordable arbitrage that delivers…
The document explains how to obtain a forward discount factor and forward reference rate from discount factors observed from today to two future dates. For dates t1 and t2, it uses the multiplicative relationship between discount factors: the factor from t1…
The document asks how to value a one-year at-the-money European call when volatility is specified as 20% for the first half-year and 90% for the second half-year. The proposed answer combines the two periods’ variances, weighted by their durations, and takes…
The document sets up an arbitrage check for calls on the same underlying with strikes 100, 120, and 130 and prices 8, 5, and 3. It represents a portfolio with signed quantities, requires a negative initial cost, and writes its maturity payoff across regions…
The document studies the stochastic behavior of marginal default density when default intensity follows a lognormal diffusion. It writes default density as intensity multiplied by survival probability, then applies Itô’s product rule to derive a stochastic…
The document explains how to interpret RiskMetrics decay factors in an exponentially weighted moving average volatility model. It uses the half-life formula to connect decay to the time required for an observation’s weight to halve, and describes why a daily…
The document describes an olive plantation scenario-generation problem involving investment costs, delayed revenues, and temperature. The author proposes fitting a four-variable Gaussian copula to ranked observations of costs, revenues, temperature changes,…