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 asks why volatility models used to estimate Value at Risk may pass a backtest at a 5% confidence tail while failing at a 1% tail. The response says this pattern is common: as the tail becomes more extreme, the assumed return distribution matters…
The document presents an implementation question about fitting a Heston–Nandi GARCH model by maximum likelihood. The author scales log returns, recursively computes conditional variance and standardized residuals, and uses differential evolution to search…
The document asks how Markit defines spot dates for several currencies and how intermediate discount factors enter swap-curve bootstrapping. Its central example is a two-year EUR swap: the coupon schedule needs an 18-month discount factor, while quoted LIBOR…
The document examines how to reproduce the stress performance scenario in a PRIIPs key information document example for a category 2 product. The questioner reports being able to match the other scenarios from the stated return dataset but finding…
The document discusses how to estimate continuous-time credit rating migration dynamics from observed rating histories. It contrasts discrete-time cohort transition matrices, formed from beginning-to-end rating changes over a period, with a continuous-time…
The document asks how to price two claims under Black–Scholes: one paying the time integral of the asset price and another paying the squared log of its terminal price. For the integral claim, the answers use discounted risk-neutral expectation and…
The note addresses where to find historical corporate bond yield series, especially across credit ratings and maturities. It identifies FRED as a free source for some ICE Bank of America credit index data, including a high-yield index series. Such index data…
The note examines why the Fama–French model is often described as a risk model and how that differs from an alpha model. It presents a factor-pricing view in which expected excess returns are related to assets’ factor exposures and the premia associated with…
The document examines whether a European call butterfly, formed from three strikes, must have a strictly positive price under no arbitrage. It warns that subtracting separate lower-bound inequalities does not establish the desired result. One argument uses…
The document asks how to interpret the Black–Scholes price of a European equity call. It focuses on the formula’s two normal cumulative distribution terms, the stock price, and the discounted strike, and proposes reading the distribution terms as…
The document considers principal component analysis for estimating risk in an international equity portfolio whose stocks are denominated in several local currencies. It asks whether PCA can be applied to local stock returns separately from exchange-rate…
The document derives the stochastic dynamics of a reverse exchange rate. If the quoted rate gives domestic currency per unit of foreign currency and follows geometric Brownian motion, the reverse rate is its reciprocal, representing foreign currency per unit…
The document considers storage for real-time stock ticks and aggregation into volume clusters by time period, price, and trade side. The desired output groups buy and sell volume at each price over intervals ranging from minutes to hours. It asks which…
This note outlines a transformation of the Black-Scholes option-pricing equation into a diffusion equation, then asks how to simulate the transformed PDE numerically. It gives the variable substitutions, the resulting heat-equation form, and a transformed…
The note addresses how to find aggregate market-size figures for structured products across product categories. The answerer says they do not know of a global estimate and points instead to European industry data compiled from national market figures. This…
The discussion considers what risk information can be inferred from a portfolio snapshot containing prices, position values, share counts, and stock betas, but no time series. One response suggests using beta to approximate a stock’s volatility if market…
The document identifies a stochastic volatility specification in which the asset follows geometric Brownian motion while volatility is the exponential of an Ornstein–Uhlenbeck process. The log volatility mean-reverts, and its driving Brownian motion may be…
The document addresses whether a Student’s t distribution can represent the fat tails often observed in stock returns and how that choice relates to risk measures. It concludes that the distribution’s degrees of freedom can be used to model heavier tails…
The document explains why annualized volatility is commonly calculated by multiplying monthly return volatility by the square root of twelve. Under independent, identically distributed monthly log returns with finite variance, annual log return is the sum of…
The document explains why an attempted R calculation returned zeros: it subtracts the logarithm of each price from the logarithm of that same price. Log returns instead compare prices at different observations, commonly by taking the difference between…
The document describes a direct way to interpret a finite set of equally probable portfolio-return scenarios for Value at Risk. With 250 scenarios, sorting the outcomes from worst to best makes the 25th-worst outcome the 10% VaR under the convention…
The document explains how the stochastic discount factor prices a payoff through its expected value and its covariance with that payoff. When covariance is zero, the payoff has no exposure to the priced source of risk represented by the discount factor. Its…
The document explains why changing interest-rate or dividend-yield inputs can make an option implied-volatility smile appear unusual, especially for in-the-money options. Under Black–Scholes intuition, a higher interest rate raises a call’s modeled value; if…
The question investigates why a USD zero-coupon inflation swap’s fixed-leg payment can remain unchanged when its maturity date moves by a few days, then jump to the next annual compounding amount. The answer proposes interpreting the 1/1 convention through a…