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 author compares a personal implementation of the Kou double-exponential jump-diffusion model with published European option prices. The code aims to price vanilla calls by combining Poisson-weighted jump contributions, normal distribution terms, and…
The discussion concerns the unconditional covariance of a multidimensional Ornstein–Uhlenbeck process, expressed as an integral involving the drift matrix and the diffusion covariance. It asks how to evaluate that integral in a dynamic Nelson–Siegel or…
The question compares expected EUR/USD and USD/EUR exchange rates under a two-outcome scenario. It assigns equal probability to EUR/USD ending at 1.25 or 0.8, then observes that each outcome's reciprocal is the corresponding USD/EUR quote. The apparent…
The note explains how the relationship between the up and down factors determines whether a binomial price tree recombines. When the factors are reciprocals, an up move followed by a down move returns to the same value as the reverse sequence. After seven…
The document examines how to convert tenor-specific parameters in a multi-factor Cheyette, or quasi-Gaussian, interest-rate model into factor parameters while preserving swap-rate variance. It describes a procedure that first matches the variance and…
The document compares the classical mean–variance portfolio objective with an alternative that penalizes return standard deviation directly. The proposed objective may be easier to interpret because volatility is expressed in the same units as returns. The…
The document considers a process with zero drift and proportional Brownian volatility, then asks for the expectation of that process after multiplying it by a deterministic time function and adding another deterministic function. Since the original process…
The document raises questions about generalized method of moments (GMM) in two-pass asset pricing regressions. In the first pass, time-series regressions estimate asset betas; in the second, a cross-sectional regression uses those betas to estimate factor…
The document explains how a zero-coupon bond price can be derived when the short rate follows a stochastic process, and how the bond’s market price of risk relates to pricing. It first applies Itô’s lemma to a bond price that depends on the short rate, then…
The document asks how the size and frequency of bond trades affect subsequent bid–ask spreads. It frames the problem as a market microstructure question: trading can change liquidity, supply and demand, and sentiment, while the size of the effect is…
The document explains the standard time-scaling rule for continuously compounded stock returns. Under a Brownian-motion model with independent return increments, the variance accumulated over a horizon is the sum of the variances of its increments. Variance…
The document compares two ways to value an investment whose expected cash flows grow exponentially. Strict present value discounts each future flow at the risky project rate from its payment date back to today. The alternative first values the stream at the…
The document addresses how to calculate value at risk for a dollar-neutral long-short position in two correlated stocks. Its central correction is that dollar neutrality does not eliminate risk: the long and short positions are exposures to different assets,…
The document asks how the equivalent martingale measure changes when an asset follows an arithmetic Brownian motion with an additive drift, rather than a geometric Brownian motion whose drift multiplies the price. It frames the issue using a bank-account…
The document describes a forecasting problem: applying compound annual growth rates separately to business lines does not necessarily produce the same next-period total as applying a CAGR to their combined value. The reason is that aggregate growth depends…
The document explores why an inversion between three-month and ten-year U.S. Treasury yields has preceded recessions. It offers several proposed mechanisms: risk aversion can shift demand toward government bonds and lower longer-term yields; investors may…
The document asks whether each eigenvector from a principal component analysis of an asset covariance matrix can be interpreted as an eigenportfolio. With no components discarded, it proposes that a portfolio of n assets yields n such portfolios, ordered by…
The author describes an hourly forex classification pipeline using fractional differentiation, CUSUM event sampling, technical features, and XGBoost. Reported test accuracy rises substantially in some configurations, especially when labels are based on…
The document introduces statistical methods for investigating whether one time series tends to lead another. Lagged correlation, also called cross-correlation in this context, measures association after shifting one series relative to the other. Examining…
The document considers how to reconstruct historical forward rate agreement (FRA) levels after a Mexican market moved from a 28-day fixing to an overnight index. With the new OIS index published only from September 2024, a direct history for the new-index…
The document explains why the usual present-value sum of known cash flows and discount factors cannot be applied directly when the cash flows depend on future interest rates. In that case, the cash flows are random variables, so their discounted sum is…
The document interprets the stock return term in the Black–Scholes setting as a proportional, rather than dollar, rate of price change. Dividing the instantaneous price change by the current price expresses movement as a percentage change. The discrete-time…
The document explains why the risk-neutral long-run mean of the state variables in an arbitrage-free Nelson–Siegel term-structure model may be fixed at zero. The answer frames this as an identification restriction: latent factors can be rotated without…
The document explains how to calculate a six-month change from a monthly TED spread series. For each month, subtract the value from six months earlier from the current value. This gives the absolute change in the spread over the six-month interval. The…