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 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 considers a no-dividend Black–Scholes stock and the power process Z(t)=(S(t)/H)^p, where H is positive and p is set by the interest rate and volatility. It shows how to apply Itô’s formula: differentiate the power function, include the quadratic…
The document explains how to estimate tenor-specific DV01, or key-rate risk, for a swap in QuantLib. Instead of shifting the entire yield curve to obtain aggregate sensitivity, it reprices the swap after increasing each market par-rate quote individually,…
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 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 explains how to think about a rolling foreign exchange carry trade and why an implied yield is not itself the trade’s return. The forward rate embeds the interest differential under covered interest parity, which links spot, forward, and…
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 asks how default affects the nondefaulting party in a plain interest rate swap. Party A pays floating and receives fixed from B; if A defaults, the question is why B’s position appears to benefit when rates rise but not when rates fall. It…
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 explains how issuer-level CDS contracts relate to the bonds and loans underlying an issuer’s credit risk. A CDS is not tied exclusively to one bond: its terms identify one or more reference obligations, while the contract generally covers a…
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 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 discussion distinguishes margin approaches for uncleared over-the-counter derivatives from those used by central counterparties. It identifies ISDA’s Standard Initial Margin Model (SIMM) as a common methodology for calculating initial margin on uncleared…
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…
The document explains why a distressed bond’s market price is not captured by simply discounting its promised payments at a risk-free rate or adding a credit spread. A more complete valuation separates coupon and principal cash flows received if the issuer…
The discussion addresses the futures–forward price difference when interest rates and the underlying price move together. It attributes the difference to daily futures settlement: gains and losses arrive over time and can be reinvested or financed at rates…
The document proposes simulating equity prices under a constant elasticity of variance model, then pricing European and American options across strikes and maturities. It asks whether implied volatilities inferred from those prices would form the same…