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 discussion describes what makes options strategy backtesting more demanding than testing a simple underlying asset. A credible simulation needs historical option chains, including contract terms and market prices, alongside underlying prices used to…
The document compares Monte Carlo prices for a European call under constant volatility and under volatility sampled once per path from a lognormal distribution. It raises the question of why the random-volatility estimate is slightly below the…
The document asks how to estimate a stochastic volatility model from historical daily returns without using an implied volatility surface or computationally intensive MCMC. It specifies a latent log variance that follows an autoregressive process with…
The document raises a model-validation question: whether stochastic-volatility option models produce more accurate market-price estimates than the standard Black–Scholes–Merton model. It highlights two practical costs of more complex models: greater…
The note raises two implementation questions about the time-series momentum method described by Moskowitz, Ooi, and Pedersen. First, it asks how to interpret the paper’s ex-ante volatility estimate when the strategy uses a twelve-month return signal: whether…
The document asks whether Black–Scholes call valuation should use a point estimate of variance from historical returns or average option values across the sampling distribution of that estimate. It describes treating the sample variance as uncertain, mapping…
The document considers how to estimate and plot volatility from a long history of FTSE closing prices. Its code calculates log returns, but the questioner’s approach appears to treat the deviation of each individual return from the overall mean as a…
The document considers whether measuring geometric Brownian motion at weekly rather than daily intervals lowers annualized volatility. Under the stated assumption of independent, normally distributed returns, variance grows linearly with time. Scaling the…
The document raises a pricing question about bonds with constant-maturity swap (CMS) coupons in euros, where interest rates may be negative. It asks whether the convexity adjustment from Hull, which assumes lognormal rates, can be adapted to a normal-rate…
The document examines how a rise in implied volatility for a short-expiry option may affect a longer-expiry option with the same strike, assuming the event driving the move occurs within the shorter option’s life. The answer models volatility across time…
The document explores estimating daily volatility for government bonds from open, high, low, and close prices. It notes that a daily high-low range can distinguish sessions with larger and smaller intraday fluctuations, then identifies the Garman-Klass…
The note distinguishes fitting an implied volatility surface at the current time from specifying how that surface changes as time passes and the underlying price moves. A cross section indexed by maturity and strike can be fitted to current market data, but…
The document asks what it means to say Black–Scholes overprices or underprices options when the option’s true value is not directly known. It presents research claims that the model can price deep in-the-money calls too high and deep out-of-the-money calls…
The document compares the simple exponentially weighted moving average used in legacy RiskMetrics volatility estimates with the more involved RiskMetrics 2006 approach. The response characterizes the later methodology as combining an ARCH-like process with…
The document asks why Ljung–Box tests on squared returns can report very high p-values even when their autocorrelation plots appear to show dependence. It presents test results for returns and squared returns at several lag lengths, then asks whether the…
The document explains why converting an FX option delta into a strike requires the market’s quoting conventions and the correct definition of at-the-money. In the example, the pair uses unadjusted deltas, and the at-the-money strike is delta-neutral: the…
The document explains how to obtain one-step-ahead conditional mean and volatility forecasts across a time series after fitting an sGARCH model with rugarch. A standard call to the forecast function returns a forecast at the end of the fitted sample, which…
The note asks how power-law distributed pauses would change the first-passage-time density of Brownian motion with drift. It frames the process as motion that advances according to a drifted Brownian model but intermittently waits, and proposes convolving…
The document considers an exchange-traded product combining a butterfly payoff with a double no-touch condition: the payoff follows a butterfly profile if the underlying stays between two barriers until maturity, and becomes zero if either barrier is…
The discussion examines option price changes near expiration that appear larger than delta and theta alone would suggest. It explains that gamma exposure is most pronounced near at-the-money strikes and presents gamma scalping as a way to manage a long gamma…
The document clarifies what a mid-curve swaption measures and how it can help infer forward volatility. A mid-curve swaption measures volatility of a forward-starting swap rate, but that is not itself the forward volatility of an option whose strike will be…
The document addresses how to value American options on SPY when dividends are present. It challenges the proposed shortcut of taking the maximum of two European option values, one tied to the ex-dividend date and one to final expiry. An American option can…
The document considers how to assess long-volatility strategies with frequent small losses and occasional large gains, where mean return, Sharpe ratio, and hit rate may not capture the payoff pattern. The response recommends beginning with a long history of…
The document poses an implied-volatility problem for an American call when a known dividend is paid before expiration and interest rates are zero. Because early exercise may be optimal immediately before the ex-dividend date, the contract can be viewed as…