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.
10,263 documents
The document explains why a delta-gamma-theta estimate can differ from an option’s actual price change when the underlying price moves substantially. The approximation combines the first-order delta effect and second-order gamma effect of a stock-price move…
The document asks whether a one-factor Hull–White interest-rate model can price a European swaption that includes a floor on its floating leg while matching both swaption volatility and LIBOR volatility. The response says that fitting the floor or cap market…
The document explains why a Treasury futures conversion factor should not be treated as a general estimate of a deliverable bond’s current price. The factor is based on a standardized 6% yield convention, while the question’s proposed alternative would vary…
The note explains how practitioners should choose finite-difference bumps when calculating time-sensitive option Greeks and related risk measures. A bump should be large enough to avoid numerical noise yet small enough to represent the sensitivity of…
The discussion considers whether tree and finite-difference methods can price convertible bonds whose call, put, or conversion-reset rules depend on past stock prices and allow early exercise. The central method is to add auxiliary state variables that…
The document asks why formulas connecting local volatility to implied volatility appear to give zero volatility when the underlying price equals the strike. That apparent result would make the equations seem unusable for at-the-money options, and values near…
The document addresses the sign of interest rate sensitivity, or rho, for call and put options. It identifies a likely typographical mistake in a cited book: under the standard setup discussed, call rho is positive and put rho is negative. The explanation…
The document compares a six-month Eurodollar futures contract with a forward contract at the same quoted rate. Its main pricing distinction is daily marking to market: futures gains and losses must be invested or funded as rates move, while a forward…
The answer shows how to price a European average-price call option using QuantLib’s continuous geometric averaging Asian option class. It sets up a call payoff and European exercise date, then supplies an initial asset value, constant volatility, and flat…
The document reconciles two expressions for estimating the present value of dividends from option prices. It states European put-call parity in terms of the spot price, strike, discount factor, call price, and put price, then rearranges the relationship to…
The problem describes a European call that must be sold if an independent event occurs, at the lower of its current value and its original purchase price. One response reframes the contract as a standard call minus the value of a compound call written on…
The discussion surveys products outside plain-vanilla swaps, swaptions, caps, and floors, while noting that the examples are not all specific to interest rates. It briefly defines Asian, Bermudan, digital, barrier, and window-barrier options, then describes…
The discussion considers why option-pricing models commonly use stock-return processes with finite variance, even when heavier tails are desired. It gives several explanations: the historical influence of Black–Scholes, mathematical and computational…
The discussion examines how to estimate the six-month roll-down of a five-year interest rate swap. It challenges simply subtracting a five-year spot rate and a four-and-a-half-year spot rate, then explains how to represent the original swap after time…
The discussion asks whether historical stock returns can be used to estimate volatility skew across option strikes. It distinguishes estimating at-the-money volatility from determining how implied volatility varies for out-of-the-money puts and calls, and…
The document asks how to price options quickly during model calibration, comparing the Carr–Madan and COS methods. It highlights Variance Gamma models with stochastic arrivals and related models where cumulants may not be available in closed form. The…
The document investigates why a VIX-like volatility estimate calculated from option prices can fall below the volatility used to generate synthetic options. The example uses Black–Scholes prices with constant volatility, zero interest rate, and zero cost of…
The document discusses numerical pricing accuracy in the Heston stochastic volatility model, especially for very far out-of-the-money options near expiry. It contrasts a reported Gaussian quadrature error with option prices smaller than that error, raising…
The document compares the time values of equally deep in-the-money European calls and puts with no dividends, using strikes the same dollar distance from spot. It applies put-call parity to split the difference in spot-based time values into a discounting…
The document defines option open interest as the number of contracts that remain open, rather than the net difference between long and short positions. A contract is counted when one party holds a long position and another a short position; open interest…
The document explains why a Black–Scholes theta estimate can exceed an option’s current value without implying that the option will actually become negative. The closed-form theta is an instantaneous derivative, commonly stated per year; multiplying it by a…
The answer explains how a weekend-adjusted payment date usually affects the timing of a bond coupon without changing its amount. For a regular semiannual period, the coupon is generally based on the scheduled coupon period and remains the regular half-year…
The discussion considers pricing mark-to-market (MtM) basis cross-currency swaps and using their market quotes to derive collateralized discount curves when constant-notional swap data is unavailable. It references a multi-curve framework and an analytical…
The document works through the affine bond-price form for the Ho-Lee short-rate model, where the short rate has a time-dependent drift and constant volatility. Substituting the model’s coefficients into the ordinary differential equations for A and B gives a…