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.
12,303 documents
The document derives a linear state-space representation for estimating parameters in a futures price model with two latent factors. The state variables follow continuous-time stochastic processes: one mean-reverts, while the other accumulates shocks.…
The document examines whether a covered call can earn a relatively reliable profit by waiting for time decay. Its example sells calls against a large stock holding, but the response points out that the stock’s price movement dominates the small option…
The document explains the popularity of GARCH(1,1) as a volatility model. Its simple structure, connection to established time series methods, and ability to represent volatility clustering and heavy tailed returns help explain its use. The discussion cites…
The document describes a study design for sorting S&P 600 stocks into three portfolios according to historical return volatility. The proposed process estimates each stock’s volatility over a formation year, assigns stocks to terciles at the year end, and…
This note examines an apparent arbitrage in put-call parity when a stock follows a zero-drift Black-Scholes process, with no interest or dividends. For a strike equal to the current stock price, parity makes the call and put prices equal. The apparent puzzle…
The document outlines an Euler–Maruyama simulation for log asset prices under a local volatility model, using volatility that varies with time and the asset level. It asks which drift to use for option valuation versus estimating the real-world chance of an…
The document derives lower and upper bounds for a European call using payoff dominance. A call payoff cannot exceed the underlying asset’s payoff, so its price is at most the asset price. It also dominates both zero and the payoff from holding the asset…
The document asks how the Hayashi–Yoshida estimator for asynchronously sampled asset returns relates to realized variance and Pearson correlation. It describes realized variance as the sum of squared returns and the Hayashi–Yoshida covariance estimator as a…
The document proposes a way to construct model inputs for year-on-year and zero-coupon inflation options when example quotes are unavailable. Comparing yields on Treasury Inflation-Protected Securities with yields on nominal Treasury securities of similar…
The document outlines a first-order and second-order method for assigning daily option profit and loss to delta and gamma. Delta contribution is estimated from delta times the underlying price change, while gamma contribution uses one half of gamma times the…
The document explains why ARMA coefficients estimated together with a GARCH variance model can differ from coefficients estimated in an ARMA model alone. The variance component accounts for changing volatility, which can affect the mean-equation estimates.…
The document asks whether European options can be priced in closed form when the variance gamma model’s drift, volatility, and variance rate are random. It explains that unrestricted random coefficients generally do not yield a closed-form price:…
The document examines how to estimate a stock correlation matrix when securities have different history lengths and those histories may cover different market regimes. It outlines several approaches: truncate all series to a common period, use…
The document discusses what traders mean by spot volatility and how it can be expressed through traded instruments. It presents several interpretations: volatility swaps can provide exposure linked to realized volatility; options can express implied…
The document answers whether an R package is needed to estimate a conditional autoregressive range model. It describes the CARR approach as applying a GARCH-style specification to price ranges rather than to returns. The range is formed from the maximum and…
The document raises a statistical inference problem for a time series of variance risk premia derived from options and realized variance, following Carr and Wu. The author wants to assess whether the series has a statistically significant mean and considers…
The document outlines how to price American options when the underlying pays discrete dividends. Because exercise may be optimal before expiration, the problem is treated as an optimal-stopping problem. A numerical grid method, such as a recombining tree or…
The document considers whether indicators can reliably identify sharp market reversals, including reversals following major market declines. The response lists RSI divergence, MACD crossovers or divergence, and breaks of resistance or trend lines as possible…
The document compares two objective types for calibrating a one-factor Hull–White interest-rate model to caplet or similar market data. A price-based calibration minimizes differences between quoted instrument prices and prices produced by the model. A…
The document addresses an apparent conflict between the Black–Scholes relationship linking spot and forward prices and models that assign different volatility processes to forwards with different maturities. With a constant interest rate and a deterministic,…
The document compares the cost of obtaining leveraged exposure through a leveraged ETF with borrowing to buy a standard ETF. It raises financing rates and fund expenses as relevant costs, then highlights a distinct issue: daily leveraged products can lose…
The document explains why a historical return histogram may compare simple returns with a normal distribution even though geometric Brownian motion implies normally distributed log returns and lognormally distributed prices. For small price changes, the…
The note distinguishes an up-and-in binary call from a down-and-out binary call and explains their payoffs under a constant-strike barrier. For the up-and-in case, a terminal price above the strike implies that the price must have crossed that strike before…
The document sets up a portfolio containing an option, the underlying stock, and a second asset whose value depends on both the stock and variance. The stock and variance follow correlated stochastic differential equations. The question is why the…