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 surveys tools and references for constructing an options volatility surface from strike prices and bid–ask quotes. It mentions QuantLib, NAG, Intermark toolkits, an empirical study with source code, OpenGamma Strata, and research on consistent…
The document compares two descriptions of implied-volatility smile dynamics under local volatility. Derman’s account focuses on a negatively skewed equity market: as the index rises, local volatility is lower, and as it falls, local volatility is higher.…
The document investigates why a Monte Carlo estimate for a European call differs from a binomial-tree value. The accepted explanation identifies the simulation’s use of first-order Euler steps for geometric Brownian motion as a source of bias, especially at…
The document discusses why a delta-hedged option portfolio is assigned the risk-free return in no-arbitrage pricing. It describes a short call hedged with stock and considers the portfolio value as the stock hedge minus the call liability. One answer…
The document explains how a vanilla option’s price changes when the underlying price and strike are both rescaled by the same factor, with implied volatility, time to expiry, and other pricing inputs held constant. In its example, reducing both the…
The document explains intuitive bounds for a dual digital payoff that pays when two digital option conditions are both met. If the individual event probabilities are 0.7 and 0.8, the joint probability cannot exceed the smaller probability: the less likely…
The document asks how to extend an Excel Monte Carlo pricer to value American options, which allow exercise before expiration. It mentions least-squares methods associated with Longstaff and Schwartz, but the questioner finds that approach difficult to…
The document asks how to value the bond-return leg of a total return swap and how that valuation differs from a bond forward. It focuses on coupon treatment: the TRS receiver gets the bond’s return, including coupons, while the forward buyer does not receive…
The document examines how to apply a Vanna-Volga adjustment to an up-and-in put. The question proposes starting with a flat-volatility Black-Scholes barrier price and adding a hedge-cost adjustment based on market prices of vanilla options, with hedge…
The document works through a two-period binomial example in which a company’s value can rise or fall, shareholders own a stated fraction, and debt holders own the remainder. It first derives the risk-neutral probability of an up move from the up and down…
The document compares two ways to discount semiannual bond coupons: applying an annual rate over fractional-year periods, or converting the quoted annual rate to a semiannual rate and compounding for the number of half-year periods. These produce different…
The document asks about an asymptotic expansion used in a paper on convergence of European option prices under binomial trees. It presents an expression for the inverse function used in the Leisen–Reimer construction, followed by a claimed large-step…
The document addresses how to label nodes in a binomial price tree with more than one step. It compares a conventional two-step representation associated with John Hull’s presentation to an alternative notation proposed by the questioner. The response…
The document describes an attempt to infer credit default swap spreads from end-of-day prices using QuantLib. The workflow builds currency-specific interest rate curves from swap data, derives a flat hazard rate from each quoted price and tenor, creates a…
The document surveys sources for identifying derivatives by ISIN and explains why coverage is uneven. In the European Union, ESMA's FIRDS database provides a large, downloadable collection of instruments reported under applicable rules, including…
The document explains how banks may price and hedge target redemption forwards (TARFs), emphasizing that the approach resembles hedging other derivatives but becomes complex because TARFs have many structural variations. Pricing commonly relies on stochastic…
The document distinguishes option vanna from the broader relationship between equity prices and implied volatility. Vanna measures how delta changes with implied volatility, equivalently how vega changes with spot. Its sign depends on strike relative to…
The document raises a numerical-methods question about the relationship between binomial option-pricing trees and explicit finite-difference schemes. It asks how a choice of time and space steps can make the finite-difference update correspond to a binomial…
The document describes how a US-based investor could hedge the currency exposure of a euro-denominated bond while also holding a dollar bond. Its example matches the foreign bond’s coupon dates and principal repayment with euro payments surrendered under a…
The document poses a valuation question for a cash flow paid at a future date and resetting earlier. The expression combines a floating rate and a discount bond price in one currency with a discount bond price denominated in another, under a forward measure…
The document explains why standard mathematical finance models generally treat stock prices as nominal amounts. Derivative contracts such as fixed-strike options are specified in nominal currency, so modeling a stock in inflation-adjusted terms would require…
The document explains why a portfolio value written as holdings in a stock and a risk-free asset can be modeled using only the gains from those assets under a self-financing strategy. Applying the product rule to each holding reveals additional terms…
The document explains that retail investors may be able to sell exchange-traded calls and puts directly, subject to broker access, margin requirements, and local rules. Selling an option creates a short position in that contract; it does not require…
The document examines the at-the-money-forward straddle approximation under a Black–Scholes geometric Brownian motion model. It starts from the straddle payoff’s risk-neutral expectation, expresses the terminal price using a lognormal density, and changes…