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 derives a European call pricing representation for an asset whose returns combine continuous Brownian movement with independent Poisson jumps. When jump sizes are lognormally distributed, conditioning on the number of jumps makes the terminal…
An implied volatility surface reflects option prices that vary by strike and maturity, unlike the constant volatility assumption in the basic Black–Scholes model. Looking at one maturity at a time, a steep downside wing means out-of-the-money puts are…
The document describes an attempt to estimate value at risk (VaR) and expected shortfall (ES) with a peaks-over-threshold method using a generalized Pareto distribution (GPD). In a rolling sample of Petrobras returns, the author encounters a software error…
The document concerns parametric expected shortfall (ES) when returns are modeled with a four-parameter Paretian stable distribution. It describes a question about implementing a closed-form ES method attributed to Stoyanov, with VaR defined for returns as a…
The document derives the conditions under which the unconstrained minimum-variance portfolio of two assets has no short positions. Starting from the formula for the weight on the first asset, it requires that weight to be nonnegative and no greater than one.…
The document asks whether the conditional expectation of an exponential Brownian increment, given information available at an earlier time, can equal its unconditional expectation. It assumes the earlier time is no later than the endpoint and questions…
The document derives a closed-form price for a European payoff based on the positive part of one minus the strike divided by the terminal stock price, assuming the stock follows geometric Brownian motion under the money-market measure. Its key observation is…
The document explains how to simulate terminal prices for several assets whose returns are correlated, in order to value a multi-asset option by Monte Carlo. In a geometric Brownian motion model, dependence is specified through correlations among Brownian…
The document describes a backward path-integral scheme for pricing an American put on a log-price grid. At each time step, it discounts and integrates the next-step option value against a Gaussian propagator for log prices, then applies the early-exercise…
The document derives an alternate form for the time integral of Brownian motion, a step that arises in the short-rate Merton model. Representing Brownian motion at each time as the accumulation of its increments turns the time integral into an integral over…
The document shows how to rewrite a European put’s discounted expected payoff as an integral of the underlying asset’s cumulative distribution function. Starting from the payoff integral over nonnegative asset prices, it extends the density’s support to the…
The document outlines a property-based method for estimating a REIT’s equity value per share. First calculate net operating income from revenue and expenses before depreciation and interest. Divide that NOI by an assumed capitalization rate to estimate the…
The document considers a weather-linked call whose daily payout depends on maximum temperature mapping to a quantity and a price index average exceeding a strike. The payoff also has daily and contract-wide payout limits, making a direct closed-form…
The document outlines a derivation of the Black–Scholes equation from the Capital Asset Pricing Model rather than from a risk-free portfolio formed by delta hedging. It starts from CAPM’s relation between expected return and covariance-based risk…
The document discusses how to interpret a LIBOR Market Model matrix when constructing discount bond values. It emphasizes that matrix layout must be understood first: under a common convention, columns represent observation times and diagonal entries…
The document examines an option whose payoff and premium are expressed in the underlying asset, using an ETH example to compare conversion from a conventional Black–Scholes value with a direct simulation. The key issue is the payoff definition: converting…
The document asks how to interpret common sell-side analyst ratings on a five-point scale in quantitative terms. It uses a score associated with market-average performance as an example and asks whether ratings above that level correspond to defined ranges…
The document raises an econometric modeling question involving a GARCH(1,1) volatility equation and a fourth equation in a simultaneous system. A variable from the fourth equation enters the GARCH specification as an exogenous regressor, while the…
The document examines why the differential of a log price is not the same as the proportional price change for an Itô process, even though their squared differentials agree in quadratic-variation calculations. It applies Itô’s lemma to a price with drift and…
The document explains how to estimate coefficients in a regression whose intercept and slope depend on a binary state indicator. The proposed method splits observations according to the indicator’s lagged value and fits the same regression separately to each…
The document outlines ways to begin building a machine learning credit scoring model for a thesis, focusing on public datasets, example competitions, and learning materials. It points to credit default prediction tasks as sources of data and published…
The example considers a portfolio value defined as Brownian motion squared minus time. Applying Itô’s lemma to this function produces a drift term from the time derivative and the second derivative with respect to the Brownian state, alongside a stochastic…
A question reports unstable or negative option values when the step count in an FFT-based binomial calculation becomes large. The accepted response suspects numerical precision loss in the terminal stock-price calculation, which raises up and down factors to…
The thread addresses implementation questions for two-step estimation of a dynamic conditional correlation GARCH model. In the second-stage likelihood, the log of the determinant of the conditional correlation matrix is a scalar, as is the quadratic form…