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 asks whether an asset is equally likely to trend or range and whether that likelihood can be calculated. The answer distinguishes trend from volatility and suggests that expected return, implied volatility, and the Sharpe ratio can help…
The document describes a calibration question for the eSSVI implied volatility surface, where parameters are fitted slice by slice across maturities. It focuses on a calendar-consistency inequality that links the current slice parameters to those of the…
The document explores when early exercise can be optimal for American put options in zero or negative interest rate settings. It contrasts the familiar positive-rate intuition for calls with the corresponding conditions for puts, noting that early exercise…
The document discusses how traders might estimate volatility for option analysis when the appropriate historical lookback is unclear. It describes two choices in historical volatility calculation: the length of the past period being measured and the spacing…
The document distinguishes historical volatility, calculated from past stock returns, from Black–Scholes implied volatility, inferred from traded option prices. Historical volatility summarizes observed movements, while implied volatility reflects the option…
The document raises a backtesting problem for a systematic strategy that repeatedly buys one-year, 90% strike equity index puts and rolls them shortly before expiry. It proposes repricing the option each month with Black–Scholes using the current spot,…
The document asks how much a short straddle could earn in the long run under an efficient market and Black–Scholes assumptions. It assumes the implied volatility used to price options matches future realized volatility, which remains constant over the…
The document compares historical daily log-return standard deviations for NASDAQ, gold, and silver with average standard deviations measured across simulated GARCH(1,1) paths. The simulations use rugarch, fit separate models with a zero-mean specification,…
The document asks how to summarize implied volatility and Greeks for a bull put spread, formed by buying a lower-strike put and selling a higher-strike put. It considers averaging each metric across the legs versus taking the long leg’s value minus the short…
The post investigates a persistent difference between simulated returns on an option account and a delta-hedged account when the Black–Scholes model is run at very high volatility. It asks whether the discrepancy comes from confusing the volatility of log…
The document examines why a basic Black–Scholes calculation may produce theoretical call prices outside observed bid–ask quotes. It points out that the example omits the continuous dividend yield in the pricing formula, but argues that correcting this alone…
The document outlines checks for whether a SABR-fitted option surface is free of static arbitrage. For a fixed maturity, it proposes deriving the risk-neutral density from the second strike derivative of call prices, then checking that the density is…
The document considers whether changing the mean and variance used in a geometric Brownian motion simulation to control how often paths cross a structured product threshold conflicts with arbitrage free pricing. Its answer distinguishes the physical measure,…
The document explores how to represent variance swap exposure using options. It starts from the risk neutral replication identity linking expected squared returns to a log contract and a continuum of calls and puts weighted by inverse strike squared. The…
The document considers Monte Carlo evaluation of conditional expectations involving an integrated Jacobi volatility process, as part of a real-options research problem. The process is bounded, but the questioner worries that Euler discretization may…
The document addresses the apparent paradox of a digital call's delta growing without bound as expiration approaches the strike. A payoff capped at one unit may seem unable to have a price sensitivity greater than that amount, but delta measures a local…
The document asks whether TA-Lib can speed up calculation of an exponentially weighted moving standard deviation. It distinguishes TA-Lib’s rolling standard deviation from the exponentially weighted statistic provided by pandas. The proposed custom Numba…
The document asks how a positively skewed stock-price distribution affects Black–Scholes–Merton option valuations across strikes. It includes two brief responses: one links right-skewed outcomes to greater probability of high terminal prices and a higher…
The document considers how to calculate option deltas across strikes when implied volatility varies with strike. It frames the key issue as selecting the implied volatility input to Black–Scholes when the volatility surface is skewed, especially for hedging…
The document addresses the intuition behind the Black-Scholes call price as volatility grows without bound. An accepted explanation states that the call approaches the discounted value of the underlying forward, which is the spot price when dividends and…
The document explains why the estimated constant in a GARCH return model may differ from the ordinary sample mean. The sample mean gives every observation equal weight. Under a GARCH model, observations have different conditional volatility, so…
The document corrects a claim about the delta of a down-and-out call as the underlying approaches its lower barrier. It explains that delta generally falls toward zero near the barrier, since reaching the barrier knocks out the option. For options close to…
The document sets out the risk-neutral Heston dynamics for an asset price and its stochastic variance, then asks how to value a European put by discounting its terminal payoff. The author is interested in transforming the put valuation into a form related to…
The document compares Monte Carlo estimates for discretely monitored variance and volatility swaps under a Variance-Gamma model. It defines the variance swap value as the square root of expected realized variance, while the volatility swap value is the…