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 clarifies what it means to complete pricing by integrating a modeled future swap rate. The target is not to integrate the rate merely to recover its current value, which follows from its martingale property under the swap measure. Instead, the…
The document discusses ways to reduce runtime when calibrating a Heston model with Monte Carlo simulations in MATLAB. The author reports using a four-core computer, 10,000 scenarios, 1,000 time steps, and `fminsearch`, with a run taking roughly half an hour…
The document considers how to combine coefficient arrays from repeated wavelet decompositions of a time series. The stated aim is to represent the frequency component while leaving residual noise with the smallest standard deviation. The question notes that…
The document explains why integrating a Wiener process over time does not produce zero, even though a naive sum of variances for partition terms may appear to vanish. The error is treating the sampled process values as independent: Brownian motion at…
The discussion explains how to include control variables in both the conditional mean and conditional variance of a GARCH model using the rugarch package in R. The example specifies one external regressor for the mean equation and another for the variance…
The document explores modifying a depth-weighted midpoint so that distant quotes with little chance of execution contribute less. The proposed approach is to weight bid and ask levels by the probability that prices reach those levels, estimated from…
The document describes calibrating a Heston stochastic volatility model to market prices by minimizing weighted squared pricing errors with a Levenberg–Marquardt optimizer. It lists the model parameters and their natural constraints: correlation must lie…
This explanation gives an intuitive account of why a longer-dated option can have greater sensitivity to implied volatility than a short-dated option. It compares two far out-of-the-money calls with the same strike and underlying price, one expiring the next…
The document addresses two inputs needed when calibrating a swaption model with QuantLib: the volatility convention and the interest-rate term structure. It notes that QuantLib’s cited calibration example expects Black, or lognormal, volatilities by default,…
The document asks whether Dupire’s formula can be understood through the same replicating-portfolio framework used to explain Black–Scholes. The answer distinguishes the purpose of the two frameworks: Dupire’s formula is presented as a calibration…
The document explains a rule of thumb that relates an option's bid-ask spread to its vega. Vega measures how much the option price changes when implied volatility changes. Because of that sensitivity, a volatility bid-ask interval can be translated into a…
The document discusses ways to estimate a reference implied volatility (IV) for options at different moneyness levels, with the aim of identifying contracts whose market IV appears mispriced. For forward-looking average volatility, it points to variance swap…
The question asks whether daily returns across asset classes have measurable differences in time-series behavior, distributions, trader composition, and relationships with macroeconomic variables. It gives examples of possible contrasts, such as whether an…
The note distinguishes the inventory-sensitive reservation prices in the Avellaneda–Stoikov market-making framework from the optimal bid and ask quotes. Reservation prices define an idealized center for quoting: they shift with the market maker’s inventory…
The document discusses how to obtain the two risk-free rates used in the CBOE VIX calculation for its near and next expirations. The cited methodology uses U.S. Treasury Constant Maturity Treasury yields and applies a cubic spline to estimate yields at the…
The document explains why a long put can sometimes have positive theta, meaning its value can rise as time passes. The sign depends on the relationship among the option price, intrinsic value, interest rates, and remaining maturity; it is not determined…
The document considers pricing an autocap, a cap-like contract that automatically exercises in-the-money caplets but limits how many can be exercised. Since its value depends on correlations among LIBOR rates, the author proposes calibrating a LIBOR Market…
The document considers a ten-day, 99 percent value-at-risk estimate for a portfolio of options on the USD/GBP exchange rate. It presents a delta-equivalent position and a daily-volatility-based calculation that scales daily risk by the square root of the…
The document clarifies the role of GARCH in forecasting a time series such as a gas price. GARCH models changing conditional variance, so it is useful for describing and forecasting volatility rather than directly supplying the expected level of a series. A…
The discussion asks whether Asian option prices reveal information about a stock’s stochastic process beyond what can be inferred from European options. In an idealized setting, a full set of European call prices across strikes can be differentiated with…
The document examines how to specify cross-correlations among Brownian drivers for two equity spots and their volatility processes. The question challenges an assumed cross-correlation between the first spot driver and the second volatility driver, proposing…
The document describes an attempt to model intraday price changes in SPX options that expire the same day. The goal is educational: to explore how option values respond to movements in the underlying index and volatility, especially near expiration, rather…
The document discusses why an implied volatility computed with a European Black-Scholes model may differ from a quoted estimate for Microsoft options. The response points out that these options are American style, so they can be exercised before expiration,…
The document explains why implied volatility and historical realized volatility can move in opposite directions when a scheduled event occurs. Before the event, implied volatility for a fixed expiry can reflect uncertainty from that event as well as other…