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 how to pass parameters to a two-dimensional BB1 copula when running a goodness-of-fit test in R. The reported issue is that the BB1 constructor does not accept a dimension argument in the same way as the normal copula constructor used…
The document derives the present value of a derivative that pays the stock price multiplied by the logarithm of that price at maturity, under standard Black–Scholes assumptions. The response uses a stock-numeraire change of measure: the risk-neutral…
The document considers the expected positive part of a linear combination of a geometric Brownian motion observed at two different times, less a strike. It notes that a sum of lognormal variables generally lacks a closed-form distribution, so treating the…
This document asks how to choose a practical model for smoothing and interpolating implied volatility skews and surfaces. The intended application is short-dated European index options, with a goal of obtaining more usable implied volatilities through…
The document derives expected profit and loss at an intermediate time for a continuously delta-hedged option in a Black–Scholes setting. It separates the option’s mark-to-market value from the cumulative expected gain or loss generated by delta hedging. The…
The document presents a question about replicating an FX volatility-smile construction method, focusing on how to interpret a delta-related quantity defined using call and put deltas at the strike associated with a specified put delta. The questioner is…
The document describes an attempt to revalue a 10-year USD SOFR interest rate swap on consecutive dates using RatesLib curves. The author expects daily mark-to-market changes to relate to swap-rate movements, duration, and carry, but reports noisy results.…
The document compares a Breeden-Litzenberger risk-neutral density estimated from GME options with the option chain’s out-of-the-money prices, implied volatility, and open interest. The author observes that OTM calls appear more expensive than puts at…
The document asks whether equality between historical and risk-neutral expected returns for a zero-beta asset implies that the two probability measures are identical. Its clearest answer is a finite-outcome counterexample: two distinct probability vectors…
The document explains why an FRA whose floating rate is paid after its accrual end date needs a convexity adjustment. When payment occurs at the rate’s end date, the forward rate is a martingale under the matching forward measure, so its curve-implied value…
The document compares the par rates of two LIBOR 3M versus fixed 1Y swaps: one began in the past, and one begins at spot, with both having the same future payment dates and maturity. It asks whether their par rates should match when priced with a common set…
The document describes a proposed validator for a risk-neutral distribution recovered from option prices. It uses the distribution to compute expected discounted put payoffs across strikes, then checks whether each theoretical price lies between the…
The document clarifies an assumption behind the Black–Scholes explanation that higher interest rates can increase a call's value by lowering the present value of its strike payment. The questioner worries that rising rates might also depress the stock price…
The discussion derives call delta by differentiating the Black–Scholes price, giving delta as the standard normal cumulative distribution evaluated at d1. For a spot at-the-money call, this expression generally does not equal one half before expiry; it…
The document addresses how to represent uncertain recovery rates after a credit default when pricing credit derivatives. It identifies random recovery as an extension to Gaussian copula credit models, alongside random factor loadings. The cited discussion…
The document compares one-month forward rates computed by QuantLib with rates recomputed from discount factors on a zero curve. Its manual calculation uses the ratio of the discount factor at the forward period’s start to the factor at maturity, converts…
The note explains the effect of the isInArrears setting on floating-rate coupons in a QuantLib IborLeg. When enabled, the coupon’s fixing date is based on the accrual period’s end date, adjusted backward by the index’s fixing days and calendar rules. When…
The note clarifies which equity measures to use when applying the standard Merton model to a publicly traded company. It recommends market capitalization as the equity value and the stock’s implied volatility as its volatility input, with at-the-money…
The document considers how to value legacy USD LIBOR swaps that fall back to compounded-in-arrears SOFR plus a fixed spread. It distinguishes these fallback cash flows from standard SOFR swaps, whose floating legs compound daily published SOFR. It explains…
The document asks how to set geometric Brownian motion inputs when simulating asset paths to price exotic options under a risk-neutral measure. It distinguishes pricing inputs from estimates drawn directly from historical price data. Its central guidance is…
The document asks which convention Excel uses for YEARFRAC with the ACT/ACT basis. It argues that Excel’s behavior does not match ACT/ACT ISDA or ACT/ACT AFB, and suggests it may be a Microsoft-specific implementation. The response questions whether Excel’s…
The document explains why an option’s implied volatility can move even when that contract has no trading volume. Implied volatility is inferred from a quoted or traded option price, so market makers can revise an option’s bid and ask as their assumptions or…
The document derives the price process of a zero-coupon discount bond from a stochastic process for its continuously compounded yield to maturity. It represents the bond price as the exponential of negative yield times remaining maturity, then applies Itô’s…
The document describes how a cross-currency swap can be used to estimate an FX forward rate and express it as forward points relative to spot. One approach first converts the floating currency leg to a fixed rate using the corresponding single-currency swap…