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.
8,116 documents
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…
The document explains that an option’s trading currency and venue do not necessarily match those of its underlying. It introduces quanto options, whose payoff is denominated in a different currency, and contrasts them with compo structures that retain…
The document raises a practical question about maintaining a long volatility hedge by rolling spot variance swaps monthly. It describes replicating spot VIX with a portfolio of out-of-the-money calls and puts, weighted by the inverse square of each strike,…
The document separates three tasks that are easy to conflate when constructing an option volatility term structure. Implied volatility is inferred by finding the volatility input at which an option-pricing model, such as Black–Scholes, matches the traded…
The document considers whether signals from a long-only equity momentum system could be used to sell puts. One response suggests choosing a high-momentum stock using a risk-adjusted return measure and selling a near-the-money put with a later expiration,…
The document explains theoretical price bounds for European and American options, focusing on why a European put’s upper bound is the present value of its strike while an American put’s upper bound is the strike itself. It lists lower and upper bounds for…
The document asks how to derive the two risk-free rates used in VIX calculations from a table of Treasury yields when the near-term and next-term SPX option series expire on different days. It describes linear interpolation between the 30-day and 60-day…
The document asks which barrier options can have negative gamma after the questioner finds positive gamma in the knock-in and knock-out options they examined. One response gives a nearby example rather than a barrier structure: a digital call near its…
The document explains why market makers often do not set displayed size through a single theoretical optimization such as a Kelly-style rule. They quote across many strikes, expirations, and sometimes underlyings, while trying to balance incoming flow or…
The note considers whether a more complex SABR Libor Market Model offers an advantage over a simpler SABR model for pricing and hedging plain vanilla interest rate options. Its central point is that if the LMM is calibrated to the same volatility smile…
The note explains the upper bound on a European call’s value: under the stated no-arbitrage assumption, its price cannot exceed the price of the underlying asset. The proposed argument is to sell an overpriced call and buy the underlying, creating a positive…
The document explores why options are studied separately when idealized binomial and Black–Scholes models describe replicating a call with stocks and bonds. The responses explain that exact replication relies on restrictive assumptions, including constant…
The question asks whether Markowitz minimum-variance optimization can choose weights for a basket of call options on different stocks, given fixed strikes, a covariance matrix, and weights summing to one. The answer distinguishes minimizing expected payout…
The document considers how to fit a predicted distribution of future stock log returns using the realized profit and loss of European calls and puts at expiration. It asks how this objective translates mathematically and compares it with likelihood-based…
The document asks how to justify the boundary conditions for the Black–Scholes equation for a European call. It states the pricing PDE and lists a zero call value at zero underlying price, an asymptotic call value matching the underlying price as that price…
The document addresses how to retrieve a changing set of valid security codes from Bloomberg in Excel, especially when option strikes and expirations change. Instead of manually listing possible strikes and building each option code, the accepted answer…
The document addresses whether a flat rate must be constructed from a normal interest-rate term structure to use Black–Scholes for a European option. The answer explains that the relevant discounting rate for an option expiring at time T is the zero-coupon…
The discussion explains that the cover artwork for Guyon and Labordère’s book on nonlinear option pricing was chosen partly for its visual suggestion of nonlinear level sets. The author’s explanation says the artwork has no direct connection to the book’s…
The document derives the probability that a zero-strike spread put finishes in the money. Its payoff is positive when the second asset’s terminal forward price exceeds the first asset’s. Assuming both forwards are lognormally distributed, their log-price…
The document examines Monte Carlo estimation of a European call’s delta under the Heston stochastic-volatility model. Its central correction is that the Malliavin weight should use the Brownian component driving the stock that is orthogonal to the…