Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
21,023 documents
The document describes a question about fitting an Asymmetric Laplace Distribution (ALD) to daily NIFTY 50 log returns and determining whether the fitted distribution has finite variance. The post gives fitted location, scale, and asymmetry parameters and…
The discussion outlines ways to study high-frequency quotes and trades when observations arrive at uneven intervals. It recommends first defining the target, such as volatility or correlation, and accounting for how measurement intervals affect the…
This document considers how to interpret significant cross-correlations with opposite signs at adjacent lags in two time series. Its example frames interest rate data as sound signals and reports a strong positive correlation at zero lag alongside a stronger…
Bond yields are generally quoted using a compounding frequency that matches the coupon payment schedule. Some markets instead standardize yields to the frequency used for local government bonds, which makes comparisons with benchmarks and across issuers…
The document considers how to estimate volatility when a return series contains complete monthly observations plus a final observation covering only part of a month. It proposes a weighted variance calculation: first scale the partial-period return to an…
The document explains how to calculate a portfolio’s cumulative return across several periods and why the calculation depends on whether the portfolio is rebalanced. For buy-and-hold, multiply each asset’s returns across periods, apply its initial portfolio…
The document explains a formula for estimating a one-period total return on a ten-year Treasury note using its yield at the start and end of the period. The formula values the note’s coupon stream as an annuity discounted at the ending yield, adds the…
Mean-variance optimization is a general portfolio framework that evaluates portfolios by expected return and variance or standard deviation of returns. Under suitable distributional assumptions, it identifies efficient portfolios: those offering the best…
The document examines a structural default model in which a firm's unobserved assets follow a geometric Brownian motion and default is linked to a debt threshold. It contrasts measuring default at a fixed horizon by checking whether assets finish below the…
The document discusses numerical instability when optimizing a custom GARCH quasi-maximum-likelihood objective in R. Its proposed safeguard is to clamp each filtered conditional variance to a chosen lower and upper limit, preventing extreme parameter values…
The document asks how to apply multidimensional Itô’s lemma when a function maps a vector of stochastic processes to another vector. It illustrates the question with a vector of assets divided by a stochastic numeraire, a transformation that can arise when…
The document asks whether methods besides principal component analysis are standard for decomposing interest-rate term structures. The response names the Nelson–Siegel model as another commonly used approach. This points readers toward a parametric way to…
The discussion explains why an arbitrage-free call price curve should be convex in strike. A butterfly spread combines calls at neighboring strikes so that its payoff is nonnegative across terminal prices and positive over an intermediate range. If the call…
The document explains an ACT/365 deposit-interest calculation when settlement timing and a business-day convention affect the maturity date. In the example, a deposit is quoted for seven days, but T+2 settlement falls on a weekend, so the answer treats the…
The discussion considers what mathematical background can help a reader understand and implement models in Brigo and Mercurio, including HJM, LMM, and local volatility models. The questioner has studied introductory stochastic calculus and is working through…
The discussion distinguishes two simple price differences over a bar or other observation period. The high–low range is the period’s highest price minus its lowest price, so it is nonnegative and describes the span of observed prices. The open–close…
The discussion explains why corporate actions can distort daily returns when a price series is adjusted incorrectly. A stock split should be reflected consistently across historical prices; a discontinuity caused by a mismatched close and adjusted close can…
The document addresses whether an exchange rate and its reciprocal, such as a currency pair and the inverted pair, should have the same at-the-money implied volatility. It models one exchange rate as a diffusion with proportional volatility and applies Itô's…
The document explains how to calculate portfolio drawdowns from cumulative returns and find both the deepest decline from a prior peak and the longest period spent below a peak. It identifies a common pandas indexing error: integer access can fail when a…
The document describes an R workflow for estimating a CARMA(2,1) model with the yuima package from daily market price data. The initial attempt passes a price column directly into the package and produces an error while constructing the model data. The…
The document asks which representation of interest rates should be used when applying principal component analysis or other stress tests to interest rate swaps: par swap rates, spot rates, or forward rates. It notes that the studies the author has…
The document examines a change-of-measure density for an asset with constant dividend yield, whose price follows a geometric Brownian motion under the physical measure. It solves the price process and substitutes that expression into a proposed density,…
The document explains dual delta as the sensitivity of an option’s value to its strike, distinguishing it from ordinary delta, which measures sensitivity to the underlying price. In the Black–Scholes–Merton framework, call dual delta is negative and relates…
The document asks whether annualized Sharpe ratios for separate years are enough to calculate a Sharpe ratio across the full period. It explains that, in general, they are not: the ratios alone do not specify the return means, volatilities, or dependence…