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 asks why some derivatives references express option prices on an undiscounted basis. It contrasts a density formula using the strike derivative of an undiscounted call price with the version using discounted prices, which includes a…
The discussion distinguishes a put diagonal spread from a put calendar spread and explains why a proposed pair of puts with different expirations but the same strike is a calendar spread. The original example uses different strikes, but the answer notes that…
The document asks how to obtain implied volatility for a specific overnight period in foreign exchange, such as the night before a particular trading day. It then asks how to translate an overnight volatility quote into an implied breakeven exchange-rate…
The document asks how option Greeks, especially delta, should be interpreted under Merton and Kou jump diffusion models. Its central explanation is that a continuous hedge cannot offset a discrete price jump instantaneously. A riskless-portfolio argument…
The document asks how to understand and implement calibration of the SABR model for volatility smiles across equity, foreign exchange, and interest rate markets. Its response points readers toward several papers and practitioner resources, and mentions a…
The document gives an intuitive explanation of the Merton model’s representation of risky corporate debt. A lender to a company that cannot default would receive the promised repayment, like holding a risk-free bond. With default risk, however, the lender…
The document examines the tracking error when a trader delta hedges an option using a Black–Scholes volatility that differs from the volatility the asset actually realizes. It presents an integral relating the error to the volatility difference and the…
The document explains that a stock’s quoted implied volatility is inferred from option prices, rather than being a direct forecast of a one-standard-deviation move. Under Black–Scholes with constant volatility, one could estimate historical volatility from…
The document derives the near-expiry approximation for the price of an at-the-money-forward European call under Black–Scholes. It rewrites the call price using the forward price and discounts the resulting payoff expression at the risk-free rate. At the…
The note examines a pricing argument for a replicable option payoff. If a trading portfolio and the derivative have equal terminal values almost surely, their discounted terminal values also agree, so their conditional expectations under a risk-neutral…
The discussion clarifies how a state price density relates to a probability density under the forward measure in a derivation involving Dupire’s formula. The forward-measure density describes the distribution of the underlying state variables at a future…
The document asks whether an individual stock’s historical monthly return frequencies can provide a valid expected return estimate. The proposed method groups observed log returns, treats each frequency as an estimated probability, multiplies returns by…
The document outlines a workflow for representing swaption volatility data in QuantLibXL and using it to price a swaption. First, construct an at-the-money volatility matrix with the QuantLibXL matrix function. Then extend the matrix into a volatility cube…
The discussion considers a foreign-exchange volatility market maker who is long a EURUSD straddle and short a USDJPY straddle, then must quote a EURJPY straddle. It asks whether the existing positions imply an appropriate trading bias for the cross-currency…
The document discusses why out-of-the-money puts may be priced above calls with strikes equally distant from the underlying price, and why this does not necessarily imply an immediate expected decline. It attributes the skew partly to demand from long…
The document explains that whether portfolio Greeks can be combined depends on what each Greek measures and whether positions share a common risk factor. Sensitivities to a shared factor, such as interest rates across equity positions, can be aggregated to…
The explanation shows how to approximate the change in an option’s value as the underlying price and time change. Expand the option price around the current underlying price: the first-order term is delta times the price move, and the second-order term…
The document clarifies that moneyness in the illustrated option pricing context is the ratio of the underlying stock price to the strike price. It addresses confusion about a paper’s graph by reproducing a related set of curves using European call prices…
The document explains how local volatility and jump diffusion models can each produce skew and kurtosis in Black–Scholes implied volatilities. It clarifies that “jump volatility” can refer to randomly varying jump sizes, which are parameters within a general…
The document asks how to fit a cubic spline to observed call option prices for a single maturity while enforcing conditions intended to prevent arbitrage. It outlines a least-squares objective with a smoothing penalty, piecewise cubic segments, continuity…
The document clarifies the payoff sign for a short put in the standard European put–call parity relationship. Selling a put gives the seller the negative of the long put payoff: the short position’s payoff is the negative of the option holder’s payoff. This…
The document compares two instruments that can both be called calendar spreads. A calendar spread in options combines a long option at one maturity with a short option at another maturity on the same underlying and strike. Under that interpretation, pricing…
The document asks how to derive an approximation that maps at-the-money implied volatility to volatility at another strike under a lognormal distribution. The relationship is framed as a strike-dependent scaling rule, using the ratio of the at-the-money…
The document asks why two stated formulas for option vanna appear to differ by a factor of one hundred. It gives expressions involving spot price, volatility, time to maturity, the Black-Scholes variables, and vega, then reports that substituting a…