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 clarifies that gamma is the local rate of change of an option’s delta with respect to the underlying price. It is a derivative, so multiplying gamma by a relatively large underlying move gives only a linear approximation; delta and gamma…
The document explains a rough way to estimate the price of a high-yield CDX index from its coupon, spread, and duration. The example uses a five percent coupon, a spread near 300 basis points, and duration around four years; applying duration to the…
The document examines whether a continuously monitored Asian call can be bounded by a vanilla call with the same strike and maturity. Under zero rates and dividends, and assuming continuous asset paths, it uses the integral mean-value theorem to represent…
The document outlines how Eurodollar futures can inform the floating-rate projections used to value a plain vanilla interest rate swap. Futures-implied rates need a convexity adjustment before they are treated as forward rates, since futures and forward…
The document explains what happens when an investor sells a European put they previously bought before expiry. Selling the contract to close realizes the change in its market value; it does not leave the investor with an unhedged short put obligation. The…
The document explains the link between the difference in futures and forward prices and the correlation between an underlying asset's price and interest rates. It asks whether negative rate correlation for stocks or bonds would make forwards more expensive…
The document raises an input-selection problem in estimating implied correlation from bivariate option prices. The described approach trains a model on a decade of returns, prices options, and inverts Stulz's formula to infer a correlation coefficient.…
The document explains why Monte Carlo estimates of a European option price can become less precise as volatility rises. The central point is that the estimate averages simulated payoffs, and its sampling error depends on payoff variance and the number of…
The document formulates a contingent claim on an underlying price process that starts between two barriers. The claim pays a specified function of the underlying value at the first time the process exits the interval. This differs from the barrier options…
A cash-settled swaption pays a function of the market swap rate, commonly the intrinsic value multiplied by a cash annuity. The annuity converts the rate payoff into a cash amount. Because the swap rate is observable, this convention can make the payoff…
The document derives the replication error that arises when a trader hedges an option with a Black–Scholes delta while the underlying asset’s realized variance differs from the constant variance assumed by the model. For a one-dimensional diffusion with the…
The document examines the convention of estimating fixed-income roll-down by moving a bond along today’s spot yield curve. It contrasts that practice with using a forward curve, which might seem more suitable as a predictor of yields at the investment…
The document outlines a basis-based method for adapting local-currency swap valuations to discounting on a USD OIS curve. It combines three market relationships: the local currency’s 3-month-versus-OIS basis, the local/USD cross-currency basis, and the USD…
The document derives the risk-neutral version of the Heston stochastic-volatility model from its historical-measure dynamics. It introduces market prices of risk as shifts to the correlated Brownian motions, then applies Girsanov's theorem to express the…
The document raises a question about how changing volatility affects the distribution of option payoffs across simulated underlying-price paths. Its proposed comparison keeps other inputs and the set of paths fixed, then compares payoff histograms produced…
The document asks whether Monte Carlo option-pricing results from different copula models can be compared when antithetic variates are used only for symmetric copula families. The concern is that the variance-reduction technique may not be applicable to…
The document outlines how to infer caplet implied volatilities from a sequence of cap prices and swap rates, as a step toward calibrating a Hull–White interest rate model for swaption pricing. It assumes caps are at the money and explains that the inputs…
The document describes Bloomberg's DLIB suite as a toolkit for pricing and calibrating derivative structures, with templates for some exotic products. It presents BLAN as an option for building bespoke deals from scratch and experimenting with different…
The document introduces Greek surfaces as three-dimensional representations of an option Greek across time to maturity and moneyness, analogous to implied volatility surfaces. Its motivating research question is whether changes in those surfaces, combined…
The document explains why a swap break clause matters and how counterparties may handle an approaching termination date. A contractual break can limit the period used in potential future exposure calculations: where a break allows termination within a…
The document distinguishes contingent claims from forward commitments, two categories of derivative contracts. A contingent claim has a payoff that depends on an underlying asset's value or another uncertain event; an option is the standard example because…
The document corrects an attempted derivation of an option price limit under the Black–Scholes–Merton framework. It explains that an option’s price is an expectation under the risk-neutral measure, where the stock’s drift is the risk-free rate, rather than…
This question asks whether swap rate quantiles in the one-factor Hull-White interest-rate model have a convenient closed-form approximation. The model gives a Gaussian short rate and explicit mean and covariance from calibration inputs. Bond prices are…
The discussion explains why a portfolio valued through a theoretical replicating model may carry more risk than its model-based VaR suggests. Convertible bonds illustrate the issue: their theoretical values depend on factors such as volatility, interest…