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 distinguishes estimating mean reversion from historical rate observations from calibrating a pricing model to market instruments. Under the historical measure, it describes representing rates with a discrete autoregression: regress the next rate…
The document asks how to calculate beta-weighted delta and gamma for a portfolio of options on different stocks. Its answer gives a relationship for an individual option’s beta: multiply the underlying price by the option’s delta and the underlying asset’s…
The document asks how options volume, dollar volume, and open interest across strikes and expirations might inform implied sentiment, volatility surfaces, option premiums, or Greeks. It contrasts modeling each contract on its own with measuring activity…
The document investigates whether discount factors calculated from a Nelson–Siegel–Svensson yield curve are implausibly small. It applies the model to maturities from six to thirty months, converts the fitted zero-coupon rates into discount factors, and uses…
The document asks why an American put’s value approaches zero near expiration in a specified region above its optimal exercise boundary, even though its terminal payoff is the positive part of strike minus stock price. It introduces time remaining to…
The document asks whether a risky asset modeled as an exponential of a Lévy process is well defined and has finite first and second moments. Its Lévy measure combines negative jumps at integer sizes, weighted by a geometric sequence, with positive jumps…
The document asks how to express a callable bond’s payoff and relate its value to a straight bond and an embedded call option. It presents a proposed payoff formula for a bond callable at a specified date and strike, but does not validate the formula; the…
The document surveys ways sine, cosine, and related functions appear in financial calculations. Fourier methods use trigonometric components in applications such as option valuation, value-at-risk, and time-series analysis. Trigonometric functions can also…
The document explains why Black–Scholes implied volatility can vary with an option’s strike, forming a smile or skew. It begins from the model’s assumptions of constant volatility and continuous price paths, then frames implied volatility as the…
The document explains the stochastic-calculus shorthand that the square of a Brownian motion increment behaves like a time increment. It identifies this rule as a lemma associated with Itô calculus, rather than an arbitrary definition, and connects it to…
The document explains how two expressions for the conditional short-rate distribution in the Hull–White model are related. Starting from the model’s stochastic differential equation, it gives the conditional mean and variance when the drift parameter is…
The document asks whether a currency-conversion identity used in pricing an option with a currency exchange feature holds generally. It describes two valuation routes for a payoff denominated in one currency: convert the payoff at maturity and discount in…
The document gathers several starting points for learning to price options on weighted combinations of assets. Suggestions include studying a method that approximates basket, spread, and Asian options through sums of Black-Scholes-Merton models, which is…
The document considers the expected time integral of a stock price under a zero-drift geometric Brownian motion, conditional on its terminal price. It corrects an attempted approach that treats the intermediate price as a simple function of the terminal…
The document asks how to interpret one-, two-, and three-month US Treasury Constant Maturity (CMT) par yields when converting them into discount factors. It contrasts treating each quote as a discount bond with treating it as a hypothetical coupon security,…
The document explains why a continuously delta-hedged option has zero net P&L in the idealized Black–Scholes setting. Applying Itô’s formula splits the option’s change into theta, delta, and gamma contributions. Once the delta hedge removes the underlying…
The document asks whether the Brownian motions in the SABR stochastic differential equations are specified under the physical measure or a risk-neutral measure. Its answer explains that a forward rate is modeled as a martingale under the measure associated…
The document describes a Monte Carlo exercise procedure sometimes called hindsight overhedge for path-dependent options. At an exercise date, it examines the simulated path through a later maturity and uses that future information to decide retrospectively…
The document explains how to value a floating-rate bond when both interest rates and future coupon amounts are uncertain. For a coupon period, it defines the rate using the price of a zero-coupon bond at the rate-setting date, then changes to a forward…
The document clarifies how a Black–Scholes put can be replicated when interest rates are zero. The put has a negative delta, so the hedge involves shorting shares and placing the corresponding funds in bonds. The bond holding can exceed the put’s price…
The document explains how to choose among QuantLib’s deposit, FRA, and swap rate helpers when constructing an interest-rate term structure. The key rule is to match a helper to the instrument represented by the market quote, rather than selecting it solely…
The document asks which EURIBOR rates to use when projecting future interest income on a bank’s loans: zero coupon rates or forward rates. The response recommends zero rates for this purpose, reasoning that they relate to investment over a period ending at…
The document considers whether a dealer can charge a client a fee when the parties add cash collateralization to an existing, uncleared derivatives relationship. Its setup assumes a master agreement and a single-currency collateral agreement with zero…
The document explains how to estimate an option price at an unquoted strike or expiration by first converting observed option prices into implied volatilities, fitting or interpolating a volatility surface, and then pricing the target contract with an option…