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 question examines whether the ratio of two zero-coupon bond prices, with one price evaluated at a later date, equals the price of a bond maturing on that date when interest rates are stochastic. It challenges an argument that treats a later-date amount…
The document distinguishes a caplet written on a forward Libor rate from one whose payoff uses the spot Libor rate observed at the option’s reset date. The forward-rate caplet can be expressed under the relevant forward measure as an option on a martingale…
The document asks how quickly the value of a Bermudan option approaches the value of an American option as exercise dates become more frequent. It describes the practical setting in which numerical methods use discrete exercise opportunities, and proposes…
The answer explains an intuitive link between a probability and the price of a binary claim. If an event pays one unit when it occurs and nothing otherwise, its expected payoff under the relevant pricing assumptions is the event probability. On that basis,…
The document poses a pricing problem for a path-dependent option on a geometric Brownian motion asset. Its European payoff depends on the running maximum and a time-averaged quantity formed from the integral of the squared asset price. The question asks how…
The document asks for the variance of the time average of the exponential of standard Brownian motion. The questioner applies Itô’s formula to the exponential process and tries to derive the variance from an endpoint term, a stochastic integral, and their…
The document considers choosing a call option when a stock’s terminal price is forecast to be uniformly distributed over a specified range. Assuming the available calls are priced with the Black–Scholes model, the answer recommends the lowest available…
The document asks whether a claim’s price, computed as an expectation under the risk-neutral measure, can be used directly to construct a replicating strategy by holding its derivative with respect to the stock price. The claim pays the larger of a fixed…
The example explains why a QuantLib price for a fixed-rate bond can differ from a hand calculation. It first checks the generated cash flows and finds that the semiannual coupon schedule is as intended. The initial zero curve, however, interpolates from a…
The discussion considers an open term loan that pays monthly interest and returns principal when closed. Because either the lender or borrower can end the loan, its remaining cash flows depend on interest rates and on each party’s decision to call or repay.…
The question considers an option that pays the difference between two stock prices at maturity only if stock A has remained above stock B throughout the contract. The accepted response reframes the condition by using stock B as the numeraire. In units of B,…
The discussion compares ways to set floating cash flows for interest rate swaps after LIBOR, whose fixing was known at the start of an accrual period. It distinguishes forward-looking term rates from backward-looking overnight risk-free rates compounded over…
The document explains how to value a European put that knocks in at a lower barrier and knocks out at an upper barrier. It expresses the payoff using the terminal put payoff and indicators for whether the underlying has crossed the lower barrier and remained…
The document asks whether the effective parameters in a time-decay SABR model can be expressed by one closed-form formula across all values of the decay start time. It presents two results from Sander Willems’s backward-looking SABR work: one for decay…
The document explains that there is no standard rule for how many past days to use when estimating historical volatility. It distinguishes historical, or realized, volatility from implied volatility: option prices reflect the market’s view of future…
The note explains that options on volatility control indexes exist, even though they may not appear as exchange-listed contracts. It says these options are generally embedded in structured notes and are mainly traded over the counter. This provides a reason…
The note asks whether portfolio gamma and vega, like delta, can be calculated by summing the Greeks of each position. The answer says that in linear valuation models, prices and their Greeks add across positions. It specifically identifies Black–Scholes as a…
The note discusses numerical instability when using the Bjerksund–Stensland 2006 option pricing model at very low volatility, especially when solving for implied volatility on out-of-the-money options. It offers a practical parameter choice: use a minimum…
The document describes calculating Black–Scholes delta and vega in R for a sample of executive compensation contracts containing multiple options. The author derives the Black–Scholes call sensitivities and reports that computed vega values are zero,…
The document asks how practitioners estimate equity volatility surfaces when listed option prices are scarce or unavailable. The answer describes a market-based approach rather than a formal model: index volatility is informed by active interdealer markets,…
The document examines an attempted derivation of a European put's upper price bound using a portfolio that shorts the put and invests the proceeds. The key correction is to distinguish present value from terminal value: with continuous compounding at a…
The document raises a notation question about up-and-out and down-and-out call payoffs. It defines the terminal call payoff using the strike and multiplies it by an indicator based on whether the price path remains on the permitted side of a barrier. The…
The document shows how to price a call in a one-period binomial model by applying CAPM, then compares the result with the standard replicating-portfolio calculation. It specifies a stock’s up and down outcomes, probabilities, and risk-free rate, computes the…
The document examines why a convertible bond model might show a higher fair value when the issuer’s CDS spread rises, even though wider spreads imply greater default risk. One explanation uses a delta hedged position: a convertible bond paired with a short…