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 frames a calibration problem for a one-period stock-price binomial model. The two possible next-period prices are represented as multiplicative up and down moves from the current price, with continuously compounded risk-free growth over the…
The document raises practical questions about building a forward curve for non-deliverable forwards when swap points and outright forward quotes are available. It asks whether curve construction should use swap points or outright forwards, how to derive…
The document considers how to estimate the probability that a forward swap rate finishes above or below a swaption strike. A simple approximation uses the cumulative normal distribution of a standardized forward-minus-strike distance under a Bachelier model,…
The discussion explains how to calculate the probability that a call finishes in the money in a discrete-time binomial model. First determine the minimum number of upward moves needed for the terminal stock price to exceed the strike. For a recombining tree,…
The document addresses whether QuantLib can model option value changes at finer than daily time intervals on the final trading day before expiry. It says intraday date resolution is possible, but requires rebuilding both the C++ library and its Python…
The document examines why a simplified Treynor–Black weighting expression appears to favor a call option over its underlying stock. In the example, the option’s alpha is scaled by delta while its variance is scaled by delta squared, which can make the…
The discussion explains why geometric Brownian motion (GBM) remains common despite unrealistic assumptions about returns. Its appeal comes from simplicity, intuitive results, and closed-form Black–Scholes pricing. Practitioners often use Black–Scholes as a…
An amortising swap’s declining payment notionals can be decomposed into a stack of constant-notional swaps with different maturities. Each component starts with part of the total notional and remains active through its own maturity; adding their notionals…
The document describes how to extend conditional sampling from a bivariate Clayton copula to an n-dimensional one. Starting with independent uniform draws, it uses successive conditional distributions derived from the copula generator and its derivatives.…
The document contrasts maximum-likelihood fitting of a Student-t model for future log returns with fitting the same model to realized option payoffs. In the first approach, parameters determine the conditional mean and volatility from current variance and…
The document asks how to price options on stocks when the premium is settled daily rather than paid upfront. It proposes adapting standard Black–Scholes pricing by multiplying the ordinary option value by the growth factor for the risk-free rate over the…
The document considers an option whose terminal payoff is the positive part of a constant multiple of the underlying asset price minus a strike. It shows that when the multiplier is positive, the multiplier can be factored outside the positive-part…
The document asks how to estimate the price impact on a convertible bond when its underlying stock falls sharply. It describes a second-order approximation using the bond’s delta for the linear component and gamma for the curvature component, then questions…
The document raises a model-risk question: when a trading desk uses the Heston stochastic-volatility model to generate a volatility surface, why might risk management use other models to produce adjustments? It names interest-rate mean reversion and other…
The document asks how Arrow–Debreu prices relate intuitively to Green’s functions, especially in the Black–Derman–Toy interest-rate model. It notes that some model discussions use “Green’s function” or “pricing kernel” without explaining the connection to…
The document examines why a called corporate bond may still show market prices after its effective call date and asks how to treat accrued interest during the gap before settlement. It explains that call notice periods and call schedules vary, and…
The document frames a derivatives-pricing question about which traded instruments are hardest or infeasible to value. Its concrete example is a best-of or other rainbow option with early exercise. A rainbow payoff depends on multiple underlying assets,…
The document discusses the Cox–Ingersoll–Ross short-rate process, which combines mean-reverting drift with volatility that scales with the square root of the rate. It responds to a question about converting that process to standard Brownian motion and notes…
The document asks whether a European swaption can be priced equivalently under the risk-neutral measure and the forward swap measure, using the swap annuity as numeraire. The key correction is that the annuity at expiry is stochastic because it depends on…
The discussion explains why holding a Treasury futures contract to expiration does not imply a loss equal to a simple difference between a quoted yield and a repo rate. Under the stated assumption that rates and market prices do not move, the futures price…
The document explains the link between gamma and realized volatility for a delta-hedged option position. An option’s value is curved with respect to the underlying price, so a hedge that offsets its current delta removes the local linear exposure but leaves…
The document explains why observed prices and implied volatilities need not match a pricing model perfectly, using SABR and interest rate swaptions as context. Its central point is that market prices arise from trading among participants; models are…
The document describes a researcher’s search for continuous-time stochastic volatility models suitable for simulation and estimation through indirect inference. The stated preferences are models that are reasonably easy to simulate and have relatively few…
The document asks which computer algebra system can help reproduce financial pricing formulas, using a year-on-year inflation swap under the Jarrow–Yildirim model as an example. The motivation is to check mathematical derivations against code and avoid…