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.
8,116 documents
The document raises a numerical issue in Monte Carlo valuation of European calls and puts on the same stock. Under standard simulation, each option value is estimated by averaging its payoff over simulated underlying paths. With a finite sample, the…
The document asks how to classify the direction of option trades using tick-level trade and quote data. The proposed workflow is to align trade records with contemporaneous call and put quote panels by option symbol and timestamp, then compare each trade…
The document explains why a vanilla option’s implied volatility is not, by itself, a reliable way to price a knock-out barrier option with a rebate. Market implied volatility is defined through the Black–Scholes formula for a vanilla contract. A volatility…
The document surveys developments beyond the classic Black–Scholes and binomial option-pricing models. It describes extensions that add stochastic volatility, stochastic interest rates, credit risk, dividends, local volatility, jumps, or GARCH dynamics. It…
The document asks how to calibrate a SABR volatility surface for S&P 500 index calls when the beta parameter is fixed in advance. The choice is between fitting alpha, rho, and nu separately for each expiration or fitting one parameter set across the full…
The response gives practical guidance for building an implied volatility curve when calls and puts with the same delta show different volatility estimates. It recommends averaging call and put implied volatilities for at-the-money options, while using…
The document shows how to model a private equity clawback when the value relevant to limited partners consists of a risky net asset value component and a fixed amount of past distributions. It represents the net asset value as a geometric Brownian motion and…
The document explains how no-arbitrage reasoning bounds the price and strike sensitivity of a vertical call spread. For strikes K1 < K2, the spread formed by buying the lower-strike call and selling the higher-strike call has a payoff between zero and K2 −…
The document raises questions about local volatility models used for equity derivatives. It asks why forward smiles under local volatility are said to become flatter and higher, whether the model’s calibration to an initial volatility surface makes its…
The document derives the self-financing portfolio interpretation of a vanilla call when the stock is used as numeraire. Starting from a martingale representation for the call price divided by the stock, it applies Itô's formula to relate changes in the…
The document considers buying a call and selling a higher-strike call below the spread’s theoretical value, then delta-hedging through expiry. One response says that under Black–Scholes dynamics, with the hedge using the true volatility, the initial pricing…
The document poses a derivatives-pricing question: how to value a maturity payoff equal to the inverse of a non-dividend-paying stock price assumed to follow geometric Brownian motion. The proposed approach starts with the stock’s risk-neutral dynamics,…
The note addresses an apparent funding gap when rebalancing a short call hedge as time passes and the underlying price stays unchanged. Its answer uses the Black–Scholes pricing equation with zero interest and dividends, where theta offsets the gamma…
The document asks how VIX futures can keep trading when a circuit breaker halts SPX options and prevents the VIX index from being calculated, especially if the halt overlaps the March contract’s valuation date. It raises the possibility of estimating…
The document collects book recommendations for an algorithmic trading programmer who wants to connect basic options theory with the language and practice of volatility trading. Recommendations include introductory treatments that emphasize intuitive option…
The document explains why vanilla calls and puts can show the same asymmetric volga profile, with larger values for in-the-money calls and out-of-the-money puts. It uses the Black–Scholes expression for volga, which combines vega with a term based on d1 and…
The document addresses which option maturities to use when replicating a variance swap whose observation period runs from the next day through a later end date. It says the option strip used for static replication should expire on the same date as the…
The document asks whether the conditional expectation of a payoff process’s maximum over stopping times equals the Snell envelope, which takes the supremum of conditional expected payoffs. It highlights a key distinction: admissible stopping times depend…
The discussion explains why adding the vegas of all options in a portfolio can misstate total volatility exposure. A simple sum assumes implied volatility moves in parallel across strikes and maturities, an assumption that may not hold when the volatility…
The document introduces raw SVI, natural SVI, and SVI Jump-Wings parameterizations for a single implied-volatility slice, using log-moneyness and total implied variance. It then asks how these choices relate to direct volatility fitting, what maturity…
The document considers a swap that receives three-month Libor plus a spread and pays a rate that depends on whether Libor is above a strike. The proposed simplification applies when Libor is fixed at the beginning of each three-month accrual period. Under…
The document asks whether the difference in delta between two options with otherwise identical Black model inputs can be represented by the delta of another option. Its answer gives a first-order approximation instead: treat the option price as a function of…
The document explains why portfolio managers might buy calls or take long exposure to options on a volatility-target index. Such exposure can provide gains in turbulent markets, which may help offset losses in portfolios with a long equity bias when…
The document examines a Heston stochastic volatility implementation that uses Fourier integration to price a European call. It lays out the characteristic function’s Riccati solution, including alternative algebraic forms intended to handle complex…