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 presents Black-76 formulas for European payer and receiver swaptions, scaling the option payoff by the present value of the underlying swap’s fixed-leg annuity. It defines the forward swap rate, strike, expiry, volatility, compounding frequency,…
The document explains the value of a receive-floating, pay-fixed interest rate swap by separating it into floating and fixed legs. The fixed leg is a sequence of discounted coupon payments, while the floating leg can be replicated by buying a zero-coupon…
The document asks whether the stock-and-bond portfolio used to interpret the Black–Scholes call formula remains self-financing as time passes. The proposed hedge holds a quantity of stock linked to the call’s delta and finances part of that position by…
The document clarifies that a forward premium is not an option premium paid for a right to exercise. It describes the annualized forward premium as the continuously compounded rate implied by the ratio of the forward price to the current spot price over the…
The document considers whether futures options volatility behaves as sticky strike or sticky delta, and why intraday tick data can make the distinction difficult. Options and futures quotes may update at different times, while illiquid markets may not…
The document asks how to bootstrap zero rates from Australian bank bill swap rates and interest rate swap quotes, including how coupon frequency conventions affect the bootstrap and whether the transition from short to longer maturities requires special…
The document considers whether two call options can hedge a short call so that the resulting portfolio is both gamma-neutral and vega-neutral. It expresses the hedge as a two-equation linear system, with the other options’ vegas and gammas forming a…
This exchange examines whether implied volatility can be used to estimate the range of future stock prices. The question raises three concerns: log returns may be modeled as normal while prices are lognormal, the expected return affects longer-horizon…
The question asks how to model daily SPX implied volatilities across several maturities and moneyness levels, preserving their correlations and incorporating jumps linked to recurring events such as economic releases and dividends. The proposed goal is to…
The document asks why ISDA uses different assumed recovery rates for senior unsecured, subordinated, and emerging-market debt in credit default swap conventions. The answers clarify that these standardized rates are conventions used in quoting and pricing…
The document explains how to obtain the terminal asset-price density from the second derivative of a European call price with respect to strike. It starts from the discounted payoff integral and its first strike derivative, which is minus the discounted…
The document considers filling missing market-maker bid and ask values across strikes and maturities when historical option prices are available for all liquid contracts and fair quotes exist for only some. It covers both European options, for which the…
The document distinguishes Brazilian domestic debt indexed to the dollar from debt that provides investors with actual USD. For the historical NTN series D, it describes a USD notional with a fixed coupon: investors paid BRL at the spot exchange rate, and…
The document explains that a floating-rate note’s yield to maturity is an internal rate of return based on its coupons and principal repayment. Because future coupon amounts have not yet been set, the calculated yield depends on the method used to project…
The document explains why co-terminal European swaptions are often used to calibrate the Hull–White interest-rate model when the intended application is pricing Bermudan swaptions. Each Bermudan exercise date is associated with a European swaption whose swap…
The document asks whether interest rate swap returns can be decomposed in a manner similar to bond attribution. The response recommends organizing the analysis around risk factors that explain changes in value. For yield curves, it highlights movements in…
The document investigates an apparent increase in call-option gamma when a Black-Scholes routine is used to represent options on futures. The setup discounts the futures price before passing it as the underlying, then compares options with the same spot and…
The document explains why hedging an option on one asset with a correlated second asset can require a sensitivity that differs from the ordinary OLS slope between their price levels. Under a bivariate geometric Brownian motion, the instantaneous changes in…
The document distinguishes two corporate bond spread measures by the benchmark curves used to calculate them. A G-spread compares a bond’s yield with a government Treasury curve, while an I-spread compares it with a swap curve. The question asks what extra…
The document asks how to price an option on a long-duration coupon bond whose payoff depends on the bond’s value at option maturity relative to its initial value. It proposes simulating short-rate paths with a model such as Hull–White, deriving discount…
The question compares a stated reference value for SPY with a lower quoted value for deeply in-the-money FLEX calls and asks why the contracts appear to have been purchased at a discount. One answer offers expected dividends as an explanation: when a call…
The document addresses fitting SABR to market volatility smiles quoted in normal and lognormal conventions. It distinguishes the volatility convention used to translate SABR prices into implied volatility: normal market quotes should be compared with normal…
The document explains why a continuously monitored knock-out option’s value approaches zero as the underlying price reaches its barrier. For driftless Brownian motion, the reflection principle relates the probability of crossing a nearby barrier before…
The document raises a pricing question about autocallable products: why their value can depend on volatility of volatility and the forward smile, and why a local stochastic volatility model may be appropriate. The questioner offers a hedging intuition for…