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 concerns numerical evaluation of the integral used to price a call option under the Heston stochastic volatility model. The question asks whether Simpson’s rule or Gauss–Legendre quadrature is suitable and seeks MATLAB or Scilab implementations.…
The post studies option pricing under a time-dependent Heston model in which mean reversion changes across time intervals while other listed parameters are held fixed. It compares prices from an Elice method and two Monte Carlo approaches, Milstein and…
The document considers why a portfolio VaR based on a covariance matrix and normally distributed market factors may exceed its stated confidence bounds more often than expected. It proposes decomposing portfolio risk into component VaR to identify which…
The question derives a replication-error expression in which the difference between assumed local volatility and realized volatility is multiplied by option gamma over time. It interprets the sign: for positive gamma, assuming volatility above realized…
The document presents a time-series modeling problem: an ARFIMA(12,0,12) mean with an eGARCH volatility specification produces plausible one-step forecasts on a sample of 2,000 observations, but extreme mean and variance forecasts after fitting the same…
The discussion asks why equity index implied volatility surfaces often show a pronounced downside skew rather than a smile, and why smiles may have appeared historically. One explanation is that index volatility combines the volatilities of its constituents…
The document investigates why QuantLib’s finite-difference Black–Scholes engine produces American put prices that diverge from a reference spreadsheet when discrete cash dividends are scheduled near expiration. The question reports that call prices are close…
The document asks whether a Hurst exponent near 0.5 in one-second EUR/USD prices supports modeling developed markets as geometric Brownian motion, with constant volatility over short intervals. The author reports estimates around 0.5 from a week of February…
The document explains how to relate daily estimates of drift and volatility to the annual parameters commonly used in geometric Brownian motion. It also corrects a notation error: a Brownian motion increment is random, so it cannot be equated to a…
The document questions whether a standard GARCH model’s constant conditional mean for log returns is appropriate when volatility changes. For normally distributed log returns, it notes that the conditional expectation of the simple gross return depends on…
The document considers fitting an implied-volatility curve to intraday option observations, where data become sparse and variable at extreme out-of-the-money strikes. The question is whether unusual observations can be discounted and whether option-market…
The document explains how to build and plot a Heston model volatility surface using Python QuantLib. The example creates a Heston process from spot, flat risk-free and dividend curves, and model parameters, then wraps it in a Heston model and passes it to a…
The document explains a Monte Carlo check for an implementation of Dupire local volatility. Simulated underlying paths use the local volatility evaluated at the current simulated spot and time, with the process initialized at the market spot. For each…
The note explains a market convention for describing the right side of an implied volatility smile as call skew, even though put-call parity links those prices to in-the-money puts. The answer suggests that traders often build the smile from at-the-money and…
The note compares delta choices for hedging short-dated at-the-money options in an index dispersion trade, which pairs long single-stock variance with short index variance. It explains that using Black–Scholes delta with the option’s initial implied…
The document explains that option traders can seek directional gains as well as profit from volatility. Buying calls can express a bullish view with less upfront capital than buying the underlying or futures, while limiting the buyer’s loss to the premium…
The document asks how to choose volatility when using Black–Scholes deltas to hedge an option, and whether updating the volatility input with each day’s implied volatility changes expected profit and loss or its variance. It contrasts implied volatility,…
The document frames a relative-value trade between American-style options on different futures, potentially quoted in different currencies. The proposed view is to sell volatility in the option with higher implied volatility and buy volatility in the other,…
The document concerns pricing options under the Heston stochastic volatility model with an Euler Monte Carlo scheme. The question reports unstable convergence when using Sobol quasi-random numbers and asks whether a Brownian bridge can address apparent…
The document derives a formula for an asset-or-nothing European call when implied volatility varies with strike. It starts from the Black–Scholes prices for cash-or-nothing and asset-or-nothing payoffs, then applies a tight call-spread argument and the chain…
The document addresses numerical breakdown in SABR normal implied volatility calculations when the forward price equals the strike. In the cited formulation, the intermediate function chi depends on zeta, which becomes zero at this at-the-money point; direct…
The document explains option Greeks in the Heston stochastic volatility model, focusing on delta as the sensitivity of theoretical option value to the underlying price. It also defines gamma, rate sensitivity, theta, sensitivity to variance, vanna, and…
The document asks whether several historical volatility estimators can be ranked from largest to smallest: close-to-close variants and range-based estimators including Parkinson, Garman–Klass, Rogers–Satchell, and Yang–Zhang. The answer says a universal…
The document seeks an intuitive explanation of the integral definition of fractional Brownian motion and asks why its construction includes negative times. The responses describe the Hurst exponent as controlling how increments scale with time and how…