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 how to relate an option on a delivery-date futures contract to a Black-76 valuation using a different futures contract associated with the option's expiry. Under deterministic rates and basis, it expresses the delivery-date futures…
The document considers two risky assets driven by the same Brownian motion, with different volatilities, alongside a bank account earning the short rate. It constructs a self-financing portfolio from the assets and bank account, then imposes the condition…
In a continuous-time pricing model, the risk-free asset grows at a deterministic rate, expressed as a differential equation with interest rate r. The answer interprets this asset as a bank deposit: its value earns interest without a random return component.…
A call spread that is long a lower-strike call and short a higher-strike call can be priced by subtracting the short call’s value from the long call’s value. Each option is priced separately, then the signed values are combined to obtain the strategy’s…
The document asks how to estimate the expiry stock price at which an option position breaks even after an initial delta hedge that is left unchanged. The reply assumes no stock financing or repo costs and no subsequent trading of the option’s gamma. Under…
This document explains what the iborStartDate argument represents in QuantLib’s FuturesRateHelper. It is the start date of the interest-rate fixing’s underlying accrual period, rather than the futures contract’s expiration date. The fixing itself is for a…
The document explains how to value an American put with a two-step binomial model. Starting from the current underlying price, the tree applies the up and down factors at each step; because their product is the same in either order, the price tree…
The document asks how to compute the expectation of a LIBOR rate over an accrual period under a later forward measure. The answer says the calculation requires a model for rate dynamics between the accrual end date and the forward-measure date; without…
The document asks why a market-convention one-year interest rate swap can involve a final payment date slightly beyond one year from the trade date. The example uses a two-day spot lag and quarterly floating accruals; adjusted dates put the final cash flow…
The document asks how to interpret a condition that arises in Gatheral’s relationship between local variance and the implied total variance surface. In that formula, the local variance is proportional to the maturity derivative of implied total variance…
The discussion concerns how to infer implied volatility from options on VSTOXX. It describes an attempt using Black–Scholes with the corresponding VSTOXX futures as the underlying and an assumption about rates and yield, which produced an unsatisfactory gap…
The discussion explains why a commodity spread option may use variability measured in absolute price changes rather than return volatility. For a spread defined as the difference between two asset prices, the value can cross zero. That makes a geometric…
The note explains why buying a TBA dollar roll should not be treated as simply shorting mortgage-backed securities. A roll combines two linked trades: buying or selling the front-month TBA and taking the opposite position in a later month. The example…
This note derives the risk-neutral up-move probability for a one-period binomial stock model. Under the risk-neutral measure, the expected stock price grows at the risk-free rate over the period. Equating the probability-weighted up and down stock values to…
The document presents an implementation question about numerically solving a Dupire partial differential equation to price vanilla options in log-moneyness and time coordinates. The author uses a fully implicit finite-difference scheme and reports difficulty…
The document explains how to estimate the yield of a floating-rate note issued above par. Its example describes a multi-year note paying LIBOR plus a fixed spread and asks how the investor’s yield compares with that coupon margin. The proposed approach uses…
The document asks how to bootstrap a zero curve from swap quotes when valuation occurs between floating-leg reset dates. It explains why the usual par-at-reset assumption does not directly apply: the floating leg may not be worth par, and the swap may have…
The document asks why a UK bulk annuity provider might adjust bond and swap hedges regularly when another insurer manages similar exposures with mostly static positions. It describes a hedging process that monitors sensitivity measures such as PV01 and IE01…
The document describes a Clenshaw–Curtis quadrature implementation for pricing an American call on a stock that pays multiple discrete dividends. The author compares the computed price with a published result and with a Vellekoop–Nieuwenhuis implementation,…
The document explains how a cash-or-nothing digital call relates to a vanilla call. Its price can be represented as the negative derivative of the call price with respect to strike, and a narrow call spread gives a practical approximation to the digital…
Market incompleteness means the available securities do not span every possible payoff; it does not by itself imply arbitrage. The document tests for arbitrage by seeking a portfolio whose payoff is nonnegative in every state, positive in at least one state,…
The discussion examines how to estimate a cryptocurrency yield curve when perpetual futures are the only obvious derivatives market. One answer emphasizes that a curve describes rates across maturities at a point in time; forecasting future funding rates is…
The discussion considers two vanilla calls written on different, correlated assets under a Black–Scholes framework. For claims driven by correlated geometric Brownian motions, the instantaneous option returns inherit the underlying Brownian correlation,…
The answer challenges the idea that implied volatility (IV) is simply an unbiased forecast of future realized volatility. An option’s IV varies by strike and maturity, forming a smile or skew, while realized volatility is a single measure for a period. IV…