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 why forward prices can matter to option valuation even when a Black–Scholes formulation is written using spot and an interest rate. For equities, no-arbitrage cash-and-carry reasoning connects spot, funding, dividends, and the forward…
When calibrating an option pricing model across several maturities, the risk-free input should come from securities whose prices primarily reflect interest rates, rather than being chosen to fit the options themselves. The answer recommends building a…
The document asks why a multi-curve framework remains necessary after the transition from LIBOR to overnight risk-free rates. It outlines a common intuition: an OIS curve built from SOFR swaps can serve as the discount curve, and the quoted swap rates might…
The document values an option to reroll a fair six-sided die when the player may keep the first result or replace it with a second roll. The decision rule is to reroll when the first outcome is below the expected value of a fresh roll, and otherwise stop.…
The document clarifies a misconception about path dependence in binomial option pricing. Backward induction through time does not itself mean the model represents the full sequence of market states along a path. A tree compresses information into states that…
The document considers a seller of a swaption who delta-hedges once per day and asks what share of daily theta decay remains as profit when the underlying rate move is smaller than a stated breakeven move. The proposed fraction is one minus the squared ratio…
The document asks whether an at-the-money SPX put spread has an edge over a same-width call spread because the put spread's stated reward-to-premium ratio is higher. It frames the comparison as a roulette game with different payouts but supposedly equal…
The document asks whether spot price can be calculated directly from a target option delta when strike, expiry, volatility, rates, and other inputs are known. It discusses Black–Scholes and Bjerksund–Stensland models, which provide option prices and Greeks…
The document presents a failed calibration of the raw SVI total-variance parametrization for a single options maturity. The example converts market implied volatilities to total variance, computes forward log-moneyness, and minimizes squared fitting error…
The document explains how covariance between two currency-rate returns can be inferred when a third rate is related to them through a currency triangle. In log terms, the cross rate is represented as the sum or difference of the two component rates,…
The document explains why a simple unilateral credit valuation adjustment for an option must combine the option’s future value with the counterparty’s probability of default. The suggested discretized calculation averages discounted expected exposure at…
The document discusses hedging a known future expense of 2,500 USD when the home currency is euros. Using the stated spot and six-month forward rates, the answer calculates the euro amount fixed by the forward contract: dividing the dollar expense by the…
The document clarifies how a volatility surface indexed by moneyness can remain consistent with put-call parity. Although the question assumes calls and puts use opposite moneyness ratios, the answer explains that moneyness is generally defined the same way…
The document describes diagnosing weak convergence in Monte Carlo simulations of an option-pricing model with state-dependent volatility. The original comparison estimates expectations at two time-step sizes, but uses independent simulated paths. Sampling…
This note addresses a Python type error when calculating a bond’s z-spread with QuantLib. The example passes a RelinkableYieldTermStructureHandle into BondFunctions.zSpread, but the available overloads expect a yield-curve object, producing an argument-type…
The document presents Gyöngy’s theorem as a way to construct a local volatility process whose one-time probability distributions match those of a given stochastic process. In the stated result, the local drift and variance are conditional expectations of the…
The document addresses how to infer forward rate or caplet volatilities from cap prices or quoted cap volatilities. Its central method is volatility stripping: order caps by maturity, take price differences between consecutive maturities, associate each…
The document examines claims that artificial neural networks outperform Black–Scholes in option pricing. The cited study generates Black–Scholes estimates using simplified inputs, including a closing spot price, fixed volatility and interest rate, no…
The document asks how the return of a function of an asset changes when the underlying asset’s drift rises by a constant, assuming the asset follows geometric Brownian motion. It applies Itô’s lemma to the function, separating the stochastic term from the…
The document examines whether negative forward variance inferred from at-the-money-forward implied volatility across two maturities signals an arbitrage. It defines forward variance from the difference in total implied variance over the two time intervals.…
The document compares shorting borrowed shares with constructing a synthetic short using a long put and short call at the same strike and expiry. Its example uses a hard-to-borrow stock and reports that the option combination produces a credit and an…
The document outlines a scenario-based approach to assessing the richness or cheapness of a government bond futures basis and asks how to value the end-of-month switch option. The described steps estimate historical betas for yield changes, apply directional…
The document asks which partial differential equation is satisfied by an expectation of a function evaluated at a Wiener-driven, exponentially transformed variable. The proposed derivation differentiates the expectation and applies Itô’s rule to the…
The document explains why a bond forward’s impliedYield method does not directly return the yield of a forward-starting bond. In the example, applying it to the spot bond price and clean forward price produces a curve zero rate, because the forward price…