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 compares pricing an at-the-money European call on a two-stock basket with a multivariate local volatility model using constant correlation and a Gaussian copula using the same correlation. It reports a result for models calibrated to each…
The document concerns a numerical issue in the Longstaff–Schwartz least-squares Monte Carlo method for valuing early-exercise options. At each exercise date, the continuation value is estimated by regressing future cash flows on basis functions using only…
The document compares two ways to value a fixed-for-fixed FX swap under multiple curves. One approach discounts the foreign-currency leg using a curve adjusted for cross-currency basis, then converts its present value at spot. The other converts each foreign…
The document poses a relative valuation problem: comparing callable bonds from the same issuer when their call schedules differ. It asks whether option-adjusted spread can be compared directly across those bonds, given that OAS accounts for embedded option…
The document describes an observed inverse relationship between strike and Black–Scholes implied volatility for Ibex 35 options. The author says the option prices and strikes came from daily exchange data, plots spot alongside the volatility curve, and…
The document explains how to create an implied-volatility curve from option prices generated by a Heston model. For each strike, first evaluate the Heston call price using the chosen model parameters and maturity. Then find the Black-Scholes implied…
The document asks how a continuous-time price and variance process relates to a discrete-time stochastic volatility model. Applying Itô’s lemma to log price and log variance gives a mean-reverting log-variance process and a log-return process whose…
The document compares SOFR curve construction and cash-flow projection with legacy IBOR approaches. One answer says curve building still depends on the available liquid market inputs and chosen interpolation, while projecting cash flows follows the rate’s…
The document derives the value and duration of a semiannual floating-rate note with coupons reset to the prevailing six-month rate. Working backward from maturity, the answer shows that each reset-date value equals par: the principal and next coupon…
The document explains why an RQuantLib valuation of an American option can return a price while showing missing values for delta, gamma, vega, theta, rho, and dividend rho. The accepted answer attributes this to the selected pricing engine: the simplified…
The document examines why Monte Carlo estimates of a European call option vary when the random-number seed changes. A seed determines a reproducible pseudorandom sequence, so changing it changes the simulated terminal prices and the resulting sample-average…
The document describes problems backing out implied volatility from 30-minute options bars, especially for in-the-money contracts near expiration. The question uses a numerical root-finding approach with a short-term Treasury yield as the risk-free rate…
The document explains why a currency call option payoff can be calculated by subtracting a strike exchange rate from the market exchange rate. In the example, both values are quoted in euros per dollar, so their difference is also an exchange-rate amount,…
The question concerns pricing an American put when the underlying follows a square-root diffusion, and asks whether QuantLib-Python can use its SquareRootProcess class. The author proposes parameter values for mapping the stated process to that class, but…
The document explains the sign of convexity for payer and receiver swaptions by starting with the underlying interest rate swap. A payer swap pays fixed and receives floating, so it benefits when rates rise. However, the gains from higher rates are…
The document explains how traders summarize the shape of an implied volatility smile or skew. It defines the risk reversal as the difference between 25 delta call and put volatilities, and the butterfly as their average relative to at-the-money volatility.…
The document compares ways to estimate value at risk for a call option. If historical prices for the option are available, an analyst can calculate returns over the chosen horizon and estimate VaR from a tail percentile. For a current option without a usable…
The document clarifies the interpretation of a calibration described for the one-factor Hull–White interest-rate model. The question asks whether the optimization produces a mean-reversion rate and diffusion parameter shared across all curve tenors, rather…
The discussion compares ways to fit implied volatility skew across strikes for a single option maturity. A quadratic polynomial is raised as a simple alternative to higher-order polynomial fits, but the responses focus on parametric distribution approaches…
The document considers why bump-and-reprice calculations can assign substantial duration to an interest rate swap’s floating leg, even though a common bond-style approximation treats that leg as having near-zero duration. Shifting the forward curve changes…
The document works through building discount and projection curves in QuantLib to price a five-year EUR receiver interest rate swap. The setup uses an ESTR-linked overnight curve for discounting, a six-month Euribor curve for forecasting, and Bloomberg swap…
The answer explains a route from stochastic future volatility to strike-dependent implied volatility. It writes a vanilla option value as an expectation over possible future realized volatilities, or equivalently as an average of Black–Scholes prices…
The document poses an apparent contradiction in the Black–Scholes model. As volatility rises without bound, the probability that a geometric Brownian motion finishes above the strike tends toward zero, which seems to imply a worthless call. Yet the…
The document examines an FX option whose payoff is settled in the currency of the underlying rather than the usual domestic currency. It first sketches a Black–Scholes setup for an exchange rate, then changes the payoff through the currency conversion and…