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 post investigates why annualized GARCH(1,1) volatility forecasts from Python's ARCH package matched observed volatility for a more volatile futures return series but appeared far too high for a less volatile series. The author initially assumed that…
Option open-interest figures published by financial websites are generally daily snapshots, which limits their direct use in intraday analysis. The post raises the question of whether intraday estimates or suitable vendor data are available, motivated by the…
For European call and put options in a model that includes a continuous dividend yield, the zero-dividend case can be obtained by setting the yield parameter to zero. The response also points to a separate list of formulas, though it does not reproduce those…
The answer outlines a possible explanation for technical patterns: prices may reflect how participants are positioned before news arrives, so a seemingly positive surprise can trigger selling if buyers are already committed and profit takers are ready.…
The note clarifies why a daily volatility formula may use closing prices without dividing by the sample degrees of freedom. In the geometric setting, the relevant price variable is the logarithm of the original price, so the daily change corresponds to a log…
The document explains how the at-the-money level for an interest-rate cap or floor is determined and why volatility quotes are often organized around it. The relevant level is the forward swap rate for a swap with the same maturity, schedule, and other terms…
The document explains the drift term used when simulating a stock price under the risk-neutral measure to price a European call by Monte Carlo. The simulated log return has mean (r − σ²/2)T and a random component scaled by volatility and the square root of…
This question concerns execution after an investor has already decided to buy or sell a particular instrument. The investor has a short window of several days to seek a better price and will use a market order at the deadline if the trade remains unfilled.…
This question asks how to transform implied volatilities indexed by strike and expiry into a surface indexed by delta and expiry. It highlights an apparent ambiguity: two options at the same expiry can appear to have nearly identical deltas while carrying…
This short question raises a central issue in option replication: transaction costs make the market incomplete, and asks what Leland’s modified volatility contributes to pricing and hedging. It also asks whether using that adjusted volatility allows an…
The document considers forecasting returns and volatility from data sampled at intervals of one second or less. It notes a limitation of relying on ARMA and conventional GARCH alone: these time-series models do not directly represent order imbalance or order…
The document addresses how to revalue an options portfolio in a Monte Carlo VaR simulation when the underlying is simulated with a historical stochastic-volatility model such as GARCH. Its central distinction is that historical volatility of the underlying…
The document answers how to select the at-the-money strike when calibrating the volatility level in a shifted SABR model. The shift is added to both the forward and strike in the model’s implied-volatility calculation. Consequently, an option that is at the…
The document presents a simulation of index prices using log returns and a GARCH(1,1) variance recursion. The author selects parameters using the lowest Akaike information criterion and generates repeated paths by drawing innovations from a normal…
The document considers a borrower’s option to choose between a fixed-rate loan, a floating-rate loan, or cancellation after a decision window. It frames the choices as embedded options with value linked to the borrower’s credit spread, interest rates, and…
The document solves an arithmetic Brownian motion with constant drift and volatility over an interval from the current time to a future time. Directly integrating the stochastic differential equation expresses the future state as the current state, plus the…
This discussion examines why longer-dated options can cost more even when implied volatility appears to fall with maturity. It cautions that implied volatility term structures vary: they may rise, fall, or fluctuate, including at the money. In the…
The document compares a one-touch option, which pays when the underlying crosses a threshold at any time through maturity, with a binary option that pays when the underlying is above the threshold at maturity. It reports that the one-touch price is…
The document presents a QuantLib setup for calibrating a one-factor Hull–White short-rate model to a EUR overnight-indexed discount curve and a normal-volatility surface for three-month Euribor swaptions. It describes fitting the model’s mean-reversion and…
The document distinguishes calculating implied volatility from choosing coordinates for interpolation and display. To calculate implied volatility from market prices, supply the actual spot, strike, maturity, rates, and dividend yield required by the pricing…
The document addresses whether the vanilla option portfolio used to replicate a variance swap still applies when the underlying pays dividends and the risk-free rate is nonzero. Its answer says the replication formula remains valid, provided the forward…
The document explains why a long position in a standard European vanilla option generally has positive vega, even when the option is already in the money. Vega measures how an option’s value responds to a change in volatility. The key idea is that a vanilla…
The document derives a one-sided probability threshold for a standardized normal variable, using the inverse error function to obtain a value of about 1.28155 for 90% cumulative probability. It then asks whether this threshold, multiplied by daily volatility…
The document asks how to estimate monthly volatility from a year of five-minute stock prices, including whether to fit a GARCH-family model at the intraday or monthly frequency and how to scale the resulting volatility. Its only suggested procedure is to try…