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 why market prices and economic data can imply different views of the future. A risk-neutral measure is used to value and hedge traded claims in a pricing model; a physical measure represents real-world probabilities used for…
The document works through the cash-account holdings needed to keep a portfolio self-financing under two choices for the risky-asset holding: the time integral of the asset price, and the asset price itself. It starts from portfolio value as cash holdings…
The document explains why a cap option example presents both a 7% LIBOR or swap zero curve and a 6.9395% continuously compounded zero rate. The rates use different quoting conventions: a 7% annual LIBOR rate with quarterly payments corresponds to four…
The document asks how to estimate historical at-the-money S&P 500 option prices using public data, including VIX or another implied-volatility index, and whether modestly out-of-the-money strikes could also be considered. The answer points to a published…
The document considers whether an exponential stopping-time intensity changes when pricing a prepayment claim under the risk-neutral measure. It explains that a Poisson process used only to define an exogenous redemption time need not change under the…
The document addresses how to compute the second derivative of the logarithm of market discount factors in the Ho–Lee interest-rate model’s calibration function. Since observed discount factors are discrete values rather than a continuous formula, the…
The document describes two approaches to extending binomial or multinomial option pricing to two risky assets over multiple time steps. One approach changes to a stock measure and expresses the pair of asset prices through their ratio, using a common state…
The answer distinguishes a bond’s quoted clean price from the dirty price paid in a secondary-market transaction. The clean quote excludes accrued interest; the dirty proceeds include accrued interest through settlement and may also reflect adjustments for…
The document gives an intuitive account of the Martingale Representation Theorem in a Brownian-motion setting. It describes martingales as stochastic integrals of Brownian increments, with an adapted process controlling the size of each increment. The…
The note clarifies the distinction between unit gamma and dollar gamma for a variance swap. Unit gamma is expressed with an inverse-square dependence on the underlying price, while dollar gamma multiplies gamma by the square of the underlying price. This…
The document clarifies that the VIX is not a measure of protective-option trading volume. It is an options-based estimate of the market-implied variance over a forward horizon, expressed as volatility, and is related to the fair strike of a variance swap.…
The document asks whether an equivalent martingale measure guarantees a replicating portfolio for every derivative, then distinguishes that question from the case of a complete market with a unique equivalent martingale measure. It notes that a trinomial…
The document examines how deterministic interest rates and dividend yields affect the asymptotic behavior of implied-volatility skew as option maturity grows. It starts from the forward price of a dividend-paying asset and notes that the Black–Scholes…
The document considers how to express floating-rate bond sensitivities, including BR01, when discounting and coupon curves are built from different instruments. It proposes representing the input sensitivities as a vector and mapping them into a chosen risk…
The discussion separates how traders use options from how options are priced. Options can provide leverage, insurance, or hedging, but those uses do not by themselves alter an option’s fair value under a risk-neutral pricing framework. The framework is a…
The document explains cheapest collateral in a collateral optimization setting where a party can choose which asset to post. For securities, one view is that the economically cheapest asset is the one with the highest repo funding rate: delivering it avoids…
The document outlines a simulation-based approach to counterparty and own-credit valuation adjustments for an inflation-linked swap. It proposes dividing the valuation horizon into intervals, generating future CPI paths calibrated to a forecast and…
The document explains how to estimate the compounded floating payment on an EONIA swap. The realized rate compounds daily fixings over the accrual period, with the day count for each fixing reflecting how long it applies. Before those fixings are known, the…
The document examines when an American call has the same value as a European call and whether the usual no-dividend Black–Scholes result extends beyond geometric Brownian motion. An answer presents a model-independent argument under stated conditions of…
The document explains why a local volatility surface reconstructed from option prices need not match the implied volatility surface at the same strike and maturity. Implied volatility is the Black–Scholes volatility that reproduces an individual option’s…
The document asks how to obtain LIBOR rates whose reset or maturity dates fall between the model’s predefined dates. It presents two approaches: use an arbitrage-free interpolation scheme designed for the displaced-diffusion LIBOR Market Model, or bootstrap…
The document asks how to differentiate a basket option price with respect to one constituent asset’s volatility. It lays out dependencies among the option price, basket forward, strike, aggregate volatility, and constituent forward, then applies the…
The document describes how to mark an existing vanilla swap to market after time has passed while preserving its original cash-flow dates and maturity. Rather than rebuilding the swap with shifted schedules, the approach is to retain the swap object, advance…
The document discusses choices for a holder of an American International Group warrant with a specified exercise cost and an advance instruction deadline. It explains that the quoted per-warrant amount reflects the cost of receiving 1.05 shares, while the…