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 whether a closed-form barrier-option model for a dividend-paying stock can be adapted to FX and commodity futures. Under Black–Scholes assumptions, it describes forward dynamics with zero drift, so the spot-model input can be repurposed by…
The document explains why a QuantLib Gaussian one-factor swaption engine rejects a Vasicek model: the engine expects a model derived from Gaussian1dModel, while Vasicek does not meet that interface. The accepted answer shows using a GSR model instead,…
The document poses a portfolio-replication problem for a derivative whose terminal payoff is the time average of an underlying asset's price over the contract period, less a fixed strike. It assumes continuously sampled prices and a zero interest rate, then…
The document sets up two Black–Scholes call-pricing equations for options on the same stock with different strikes and a shared maturity. It uses the observed option prices to form a nonlinear system in the continuously compounded interest rate and…
The document raises a derivatives-pricing question about VXTY futures, whose contract specification references options on ten-year Treasury futures. The author distinguishes option selling, which involves receiving an option premium, from entering a futures…
The document examines how changing the shift in a SABR model affects recalibrated parameters and swaption sensitivities. It describes experiments that fit shifted SABR to a constructed volatility set, first freeing correlation and volatility of volatility,…
The document outlines a proposed backtest of a receiver swaption under a one-factor Hull–White or Gaussian Markov HJM framework. It describes forward rates in Musiela form, relates continuously compounded yields to average forward rates, and gives an…
The document clarifies the difference between a portfolio’s payoff at maturity and its price when established. A proposed structure combines European puts at two strikes with a European call at a higher strike. Evaluating the payoff formula at a particular…
The document explains how exercise of a call option on a futures contract creates a futures position whose mark-to-market depends on its entry price. Because futures settle daily, the delivered position is treated as entered at the most recent settlement…
The response clarifies that a forward rate agreement, a caplet or floorlet, and an option on an FRA are different instruments. A caplet and a floorlet on the same future LIBOR fixing have complementary single-period option payoffs and can approximately…
The document presents an attempted trinomial-tree implementation of an uncertain volatility model for pricing European calls between minimum and maximum volatility bounds. It lays out a backward-induction scheme, defines a discrete second-difference term…
The document asks how to model changes in implied volatility when approximating an option portfolio’s profit and loss with delta, gamma, and vega terms. It distinguishes historical VaR, which can reprice a portfolio across observed market scenarios without…
The document asks whether the volatility smile and the volatility-of-volatility smile can both arise from dependence between spot and volatility. It proposes viewing the relationship in two directions: volatility moves affecting spot may help explain the…
The document clarifies an example about a forward-start variance swap and whether a statement about implied volatility contains a typo. It explains that the relevant forward-start swap strike represents today’s expectation of the variance-swap strike for a…
The document explains how Dupire’s formula relates local volatility to the time and strike derivatives of call prices, assuming no dividends. It walks through a small strike-and-maturity table to estimate those derivatives with finite differences and obtain…
The document introduces an approach for inferring a liquidity parameter from market bid and ask prices for a European call. The parameter, denoted by λ, represents a symmetric distortion around the option’s mid price. Rather than deriving liquidity from the…
The document examines why an American call on a stock with one known dividend can be worth more than a European call with the same strike and expiry. It first proposes estimating the difference through European calls around the ex-dividend date, adjusting…
The document explains why digital options can be difficult to hedge near expiry: their payoff changes abruptly at the strike, creating steep or concentrated sensitivities. One practical approach is to approximate a digital with a call spread. A tighter…
The document discusses three probability and option-pricing questions: when to stop drawing from a balanced deck while betting on card color, how to value a call whose underlying payoff is the number of heads in a fixed sequence of flips, and whether equal…
The note presents a way to obtain the probability density of a basket formed by summing two correlated geometric Brownian motion assets. Although each asset is lognormally distributed, their sum is generally not lognormal. The proposed density follows from…
The note explains why an at-the-money short-dated straddle can be approximated using implied volatility. In a Black–Scholes setting, put-call parity reduces the value of an ATM-forward straddle to twice the call value. The ATM call value is approximated as a…
The discussion clarifies whether the VIX is leading or lagging. Because it is calculated from option prices and represents the market’s implied expectation of volatility over the coming period, it is forward-looking in that sense. It does not independently…
Treasury futures allow the short to choose which eligible bond to deliver, creating a quality option for the short and affecting the futures price. If the cheapest-to-deliver bond is already known, pricing can be based on that bond’s forward price adjusted…
The discussion explains why out-of-the-money VIX puts expiring on a given date can lose value even when the spot VIX falls sharply. The key distinction is that VIX options are tied to the VIX futures contract for their expiration, not directly to the spot…