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 discussion explains a possible meaning of the phrase “variance swap volatility.” It interprets the quantity as the volatility level associated with a variance-swap strike that makes the contract have zero value at the relevant time. This is a concise…
The document presents an exercise involving prices of calls across strikes and asks how to derive prices for two other terminal-payoff claims: a digital that pays when the underlying exceeds a strike, and a squared call payoff. It defines the call value as…
The document considers whether a holder of bitcoin can mimic put-option protection by shorting CME bitcoin futures above a chosen price and returning to a neutral position when the price crosses that threshold. The motivation is concern that a rising market…
The note clarifies how to interpret year labels and short-rate nodes in a Black-Derman-Toy bond tree. It explains that the initial rate, r₀, discounts the bond over the period from now to one year, while the up and down rates at the next tree level apply…
The document distinguishes forward variance swap volatility from the future implied volatility smile used to value forward-start options. Under idealized assumptions of a pure diffusion and continuously measured variance, the forward variance swap rate can…
The document raises a notation issue in Fourier option pricing with the Heston model: some characteristic functions include a term for the current log-price, while others show only terms involving the model’s variance state. The distinction is whether the…
The document examines two Black–Scholes sensitivities for an at-the-money European option: how Vega changes as time to expiry grows, and how option price changes as implied volatility rises. For the expiry question, it considers the derivative of Vega with…
The document considers a cash-or-nothing claim that pays when one of two risky assets exceeds the other at maturity. Both assets are modeled with geometric Brownian motion driven by the same Wiener process, alongside a risk-free asset. The proposed pricing…
The document proposes estimating a Treasury bond futures price from a selected Treasury bond’s cash price and the conversion factor for the cheapest-to-deliver bond. It suggests dividing the bond price by that factor, then comparing the estimate with the…
The document explains why a forward contract with zero value at inception generally has a delivery price different from today’s spot price. It uses replication: hold the underlying asset and finance the delivery payment with a riskless bond position.…
The discussion asks whether an unhedgeable option should be valued using real-world probabilities rather than risk-neutral pricing. Its central point is that risk-neutral valuation relies on relationships supported by trading and hedging in the underlying.…
Lévy processes do not necessarily have probability densities, and even when a density exists it may not have a closed-form expression. The document contrasts this with familiar exponential Lévy examples, including geometric Brownian motion and a…
The explanation distinguishes the volatility parameter in a geometric Brownian motion model from the standard deviation of the asset price itself. For an Ito process with proportional diffusion, the price is lognormally distributed, so its variance is shaped…
This discussion addresses whether SABR should be calibrated directly to cap quotes or to the individual caplets that compose those caps. Its proposed workflow is to first strip market cap quotes into a caplet volatility surface, then calibrate SABR…
This exchange explains how to represent an FRA whose start date does not fall an integer number of months after the valuation date when constructing a yield curve with QuantLib. The suggested approach is to calculate the interval from the valuation date to…
The document gives simple bounds for American calls and puts on an underlying with continuous dividend yield. Because an American option can be exercised at maturity, its value is at least that of the corresponding European option, so the European lower…
The document distinguishes real-world probability estimates from risk-neutral derivative pricing. It explains that using expected returns in place of the risk-free rate changes the underlying dynamics, while option prices also depend on the market price of…
The document describes a simulation question for a SABR-LMM model under a selected numeraire. Forward LIBOR rates have shifted SABR dynamics, stochastic lognormal volatilities, and correlated Brownian drivers. The author already uses Euler discretization…
The document asks whether two stocks driven by the same Brownian motion can have different physical drift terms and still admit a risk-neutral measure. Its answer distinguishes between processes that are tradable assets and related return series that are not…
The document explains why repricing a live swap at a later evaluation date can fail when an earlier floating-rate coupon needs a fixing that has become historical. QuantLib can forecast fixings from a yield curve for current or future dates, but a curve does…
The document explains how to approach pricing a barrier option on a basket when the available QuantLib Monte Carlo engines do not support both features together. It uses a worst-of down-and-in put as an example of the unsupported combination. The suggested…
The discussion asks why higher-order Greeks are not seen more often in practice. The answer distinguishes Black–Scholes use for quoting implied volatility from more complex models used to price products and measure their risks. Exotic options may require…
The discussion explains how cross-currency swaps and local overnight-indexed swap markets can help construct discount curves for cash flows collateralized in another currency. In a two-currency setup, the response describes fitting a foreign-currency curve…
The discussion considers whether Monte Carlo simulation can calibrate the Heston stochastic volatility model and which discretization to use. One answer recommends calibrating vanilla European options with the model’s known characteristic function and…