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 considers a European call that the holder may sell back to its writer at its Black–Scholes value before a specified time. At that time, the writer imposes a fee by reducing the holder's option value by a percentage. The question asks whether the…
The document investigates why QuantLib can return different European option prices when using a forward volatility surface with a Black process versus a Black–Scholes–Merton process or a flat volatility curve. Although the queried implied volatilities can…
The document examines whether a straddle, strangle, iron condor, or other collection of options on one underlying can be assigned a single implied volatility. Implied volatility depends on a chosen pricing model and the market price of the payoff. Where the…
The document asks whether the VVIX, which measures volatility of the VIX, can be tracked through tradable instruments despite having no directly tradable index, futures, or options. It presents two replication perspectives: variance exposure can be…
The discussion examines why Pearson correlation between two correlated geometric Brownian motion price processes can move toward zero over time, even when the underlying Brownian shocks are highly correlated. The explanation is that Pearson correlation is…
This brief explanation answers whether adding a holding in the underlying asset changes the gamma of a portfolio containing options. It defines portfolio gamma as the second derivative of the portfolio’s value with respect to the underlying price. A position…
The discussion asks whether Black–Scholes models are weakened by representing only a few risky assets. It explains that pricing a portfolio of options on different underlyings together can require their correlations: a basket option generally has a different…
The document asks how to calculate the Black-Scholes delta of a knock-in or knock-out barrier option. It lists the inputs the questioner has available, including barrier and strike levels, spot price, time to expiry, option type, implied volatility, and the…
The document asks whether OTC derivatives markets use standard moneyness buckets, such as percentage ranges around the underlying price, and whether suitable bands vary by asset class. It also asks whether bucketed activity can serve as a proxy for changes…
The document poses a pricing problem for a call whose terminal strike depends on the average stock price over a future interval. The average is a continuous-time arithmetic average, and the strike is formed by scaling that average before applying lower and…
The document compares Sobol quasi-random sequences with ordinary pseudo-random sampling for Monte Carlo pricing of path-dependent options. It recommends pairing Sobol points with Brownian bridge path construction, which reduces effective dimensionality by…
The document outlines a way to derive the European call lower bound directly from the Black–Scholes formula, without relying on put–call parity. Hold the spot price, strike, interest rate, and maturity fixed, and view the call price as a function of…
The document asks how to judge whether buying calls can be profitable when a trader has estimates for the probability and size of short-term stock moves. It frames the problem in terms of expected gains and losses, noting that a high win rate alone may not…
The document asks how to adapt the Carr–Madan Fourier transform method for European call options when the initial asset price is not normalized to one. It presents the damped Fourier pricing integral and its characteristic-function term, then describes…
The document clarifies how a call option’s delta determines the hedge for a written position. Delta approximates how much the option price changes for a small change in the underlying stock price. In the example, the option price rises by about $0.60 when…
The document compares a portfolio consisting of a call minus a put with a position in the underlying asset financed by a discounted strike payment. If the options share a strike and maturity, their terminal payoff matches the financed underlying position.…
The document discusses how to infer caplet volatilities from normal volatility quotes for caps on compounded, backward-looking overnight rates. It distinguishes an expiry adjustment used when transferring assumptions from forward-looking LIBOR caplets—where…
The document asks why an integration-by-parts boundary term vanishes when deriving Dupire’s local volatility formula from European call prices. The proposed explanation is that the transition density of the terminal stock price tends to zero as the price…
The document explores how Black–Scholes delta hedging relates to option gamma, time decay, and the risk-neutral pricing argument. The questioner begins with the idea that an infinitesimally delta-hedged portfolio is locally risk-free and should grow at the…
The document asks whether raw SVI parameters must be calibrated separately for each option expiry or whether one parameterization can describe the full implied volatility surface. Raw SVI fits total implied variance on each log-moneyness slice with five…
The discussion explains why FX forwards may depart from the relationship implied by two quoted money-market rates. In practice, banks cannot necessarily borrow and lend independently at those rates; they often transact through the currency basis swap market.…
The discussion explains why an American put is modeled with different conditions in its exercise and continuation regions. The holder chooses an exercise time to maximize expected discounted payoff, so the valuation is an optimal stopping problem. The option…
The discussion examines a delta-hedged, initially gamma-neutral options risk reversal intended to benefit when realized spot-volatility behavior differs from implied skew dynamics. Its P&L is separated into skew-related, vega, and model-marking effects. The…
The discussion examines whether buying out-of-the-money puts and then shorting stock, or buying calls and then purchasing stock, could move prices enough to make the options profitable. Its main explanation is that large trades incur costs: a substantial…