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 explains how to access values produced by QuantLib’s finite difference engine for an American equity option. The accepted answer describes retrieving a sampled price curve from the instrument’s results under the key “priceCurve.” This provides…
The document considers how to estimate a missing point in a swaption volatility grid indexed by option maturity and swap tenor. The questioner has quoted Black-model volatilities at selected maturities and tenors, and is unsure whether simple linear…
The document explains the distinction between matching an up-and-out call’s terminal payoff and replicating its full path-dependent behavior. If the underlying has not touched the upper barrier, a long call at the lower strike combined with a short call at…
The document explains how to adjust a portfolio with delta 450 and gamma 6,000 using an option with delta 0.6 and gamma 1.5, assuming stock is also available. To offset the portfolio’s gamma, take a short position of 4,000 options. That position contributes…
The document asks how to value options when an asset follows deterministic growth with zero volatility. Its central no-arbitrage point is that a zero-volatility asset is riskless, so in an arbitrage-free market its growth rate must equal the risk-free rate.…
The document considers buying an at-the-money long straddle after an earnings date is announced, then selling before the announcement to capture rising implied volatility. It explains that implied volatility may rise gradually in the weeks before earnings,…
The document explains the instrument used to delta hedge a swaption: an amount of the underlying forward starting swap. For a swaption expiring in one month on a ten-year swap, the hedge is therefore a forward swap that begins at expiry and runs for ten…
The document describes a finite-difference setup for pricing an American–Bermudan Asian option with a fixed strike. The option value depends on time, the underlying price, and the running average, so its pricing equation includes derivatives in both the…
The document asks why a Newton–Raphson solver sometimes returns NaN while estimating implied volatility from option prices. Its code iterates on volatility using the difference between the market price and the Black–Scholes price, divided by vega. The…
The document presents an options parity question involving a call, a put, a strike price, a risk-free rate, and the market price of the underlying stock. It calculates a synthetic long position as long one call, short one put, and holding a discounted amount…
The note distinguishes the Dupire method from the broader concept of local volatility. One answer describes Dupire as a method for deriving a local volatility surface from an implied volatility surface; another says the famous Dupire model is commonly used…
The note explains that directional and non-directional risk do not have one universal definition. The classification depends on which price movements a trading desk treats as the relevant market direction. For options traders, exposure to a change in the…
The note explains why gamma is commonly reported alongside delta, theta, vega, and rho. Its organizing idea is practical hedging: delta indicates the underlying position used to hedge an option, while gamma describes how quickly that hedge needs to change as…
The document poses a mathematical question about whether derivatives of the Black–Scholes price with respect to log spot are bounded when time to maturity is positive. It seeks a bound that depends on remaining time to expiry, with a maximum magnitude…
The document addresses which parameters should define vega in Heston or Bates option pricing. It describes an approach attributed to Zhu (2010): because initial variance and long-run variance both shape the variance level, sensitivity can be reported…
The document asks whether CAPM or the Fama–French model can be applied directly to futures and options, drawing a comparison with their use in analyzing stocks. The answer distinguishes studying an underlying asset from analyzing a derivative contract. These…
The question concerns a forward interest rate that is observed at one date but paid later, creating a convexity adjustment when moving between forward measures with different bond numeraires. The accepted response recommends replication pricing for this…
The discussion distinguishes the risk-neutral expected future payoff of an option from its expected value under the real-world probability measure. Under risk-neutral valuation, the option price is the discounted expected payoff, so the conditional expected…
The discussion considers hedging a payoff that depends on the reciprocal of a stock price, then extends the problem to a payoff proportional to the ratio of a future stock price to its current price. One response uses a static option-replication identity: a…
The document discusses whether an alternative parameter, possibly GARCH alpha, can replace historical volatility in a Black–Scholes option pricing project. It distinguishes realized volatility, estimated from past returns, from implied volatility, which…
The document explains what a calibrated SABR model is used for in interest-rate markets. Its common role is to parameterize volatility surfaces for caps, floors, and swaptions. Because SABR specifies how volatility changes as the underlying forward rate…
This discussion considers the idea that large short positions in out-of-the-money calls and puts could act as resistance and support near their strikes. In the answer's proposed mechanism, dealers holding the other side of those options hedge with the…
The document explains why option volatility surfaces are often indexed by moneyness and expiry rather than raw strike and expiry. It outlines several coordinates: spot minus strike, a spot-to-strike ratio, log forward moneyness, a volatility- and…
The document describes an exotic option in which the holder receives either a call or a put at a specified future time, with the writer choosing which type. Both alternatives share the same strike and expiry. It distinguishes this arrangement from a…