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.
4,471 documents
The document derives an approximate single implied volatility for a portfolio of options whose components have different implied volatilities. It begins with the condition that the portfolio’s modeled value at the common volatility should equal the sum of…
The document offers historical volatility and correlation estimates as starting points for a foreign currency option model with domestic equities, foreign equities, and an exchange rate. Using weekly observations over five years for the DAX, S&P, and EUR…
The document explains why the delta of a binary call becomes sharply concentrated around its strike as expiry approaches. Under Black–Scholes, the option value is expressed using the normal cumulative distribution function, and differentiating gives a delta…
The document discusses how to calculate p-values for estimated GARCH coefficients and whether the degrees of freedom should account for the model’s parameters. One response recommends using the sample size minus the total number of estimated parameters,…
The document derives a European call pricing representation for an asset whose returns combine continuous Brownian movement with independent Poisson jumps. When jump sizes are lognormally distributed, conditioning on the number of jumps makes the terminal…
An implied volatility surface reflects option prices that vary by strike and maturity, unlike the constant volatility assumption in the basic Black–Scholes model. Looking at one maturity at a time, a steep downside wing means out-of-the-money puts are…
The discussion asks whether manipulation of SPX options or equity and volatility futures caused the February 2018 VIX spike, and what data could help investigate. The response points to volatility-linked exchange-traded products as a possible source of…
The document asks how a short-term VIX futures index’s daily roll weights translate into the holdings and cash flows of an exchange-traded product. It uses a dated example with two adjacent futures prices to question how a roll handles a price difference,…
The document frames a model-selection problem for reinforcement-learning-based dynamic hedging of long-dated swaptions. The proposed application uses 2y2y and 4y2y swaptions, requiring simulated paths that update both a forward swap curve and an implied…
The document raises an econometric modeling question involving a GARCH(1,1) volatility equation and a fourth equation in a simultaneous system. A variable from the fourth equation enters the GARCH specification as an exogenous regressor, while the…
The document examines why the differential of a log price is not the same as the proportional price change for an Itô process, even though their squared differentials agree in quadratic-variation calculations. It applies Itô’s lemma to a price with drift and…
Energy retailers that promise customers fixed prices while buying power or gas at floating wholesale prices face a mismatch between sales revenue and procurement cost. The risk can grow when demand and prices move together, as during cold weather. The…
The thread addresses implementation questions for two-step estimation of a dynamic conditional correlation GARCH model. In the second-stage likelihood, the log of the determinant of the conditional correlation matrix is a scalar, as is the quadratic form…
The discussion distinguishes two research questions that can look similar but require different outcomes. To compare volatility estimators as forecasting inputs, regress a later realized-volatility measure on each estimator available at the forecast date. A…
The document asks how to apply antithetic sampling when simulating the Heston stochastic volatility model with a discretized process. The central issue is whether to reverse the random draws only for the stock price or for both the price and variance…
The document presents a QuantLib Python calibration attempt for a time dependent Heston model that fails with a Boost assertion. The code builds a volatility surface, creates a piecewise time dependent model, attaches an analytic pricing engine, and…
The document considers whether an equity option’s implied volatility should be adjusted when the underlying price moves. It describes alternative ways to hold the volatility surface fixed: sticky strike keeps implied volatility tied to each strike, while…
The document estimates the chance that a stock reaches a buy limit price at least once during a waiting period. It models log prices as Brownian motion with constant volatility, uses the distribution of the running minimum to relate a price threshold to a…
This beginner discussion distinguishes an option’s payoff at expiration from its value before expiration. Changing volatility does not alter the European option’s terminal payoff diagram; it changes the premium beforehand by changing the range of possible…
The document addresses the misconception that volatility is bounded by the largest possible percentage decline in a stock price. In the Black–Scholes framework, volatility scales the standard deviation of the asset’s log return over the option’s life. That…
The document asks why a Black–Scholes option price differs from an expected option payoff calculated from a spreadsheet model. One response identifies a key model mismatch: Black–Scholes assumes lognormal stock prices, while the spreadsheet uses normally…
The discussion points to two practical approaches for hedging volatility swaps. For forward-starting swaps, it cites a method that uses straddles at a particular strike, with hedge notional linked to the volatility skew at that strike. For…
The document considers valuing a European call when its underlying asset cannot be traded, so the continuous-trading replication assumptions behind Black–Scholes are unavailable. Suggested inputs and approaches include estimating the underlying’s value from…
The document contrasts implied volatility from near-expiry, at-the-money S&P 500 options with the VIX. The response characterizes VIX as a discrete approximation to the square root of a theoretical fair variance swap strike, with its calculation window set…