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 question asks why some researchers fit curves to implied volatilities rather than option prices, given that both can vary nonlinearly with strike. The response points out that a standard pricing framework such as Black–Scholes provides a conventional…
The discussion explains carry and roll-down using an interest rate swap whose curve slopes upward. Carry comes from the already fixed floating coupon relative to the swap’s fixed rate; roll-down comes from repricing the remaining cash flows as the swap…
The note decomposes the risk of a USD-denominated Mexican corporate bond into USD interest-rate exposure, the spread of USD-denominated Mexican sovereign debt over the USD risk-free curve, and the issuer’s additional idiosyncratic spread. It suggests hedging…
The note distinguishes the credit exposure of an interest rate swap from the reason overnight rates are used for discounting. Its answer says that swaps referencing LIBOR or another floating rate generally have little counterparty risk when they are subject…
The note explains how the strike derivative of a call price relates to the probability that the underlying finishes above that strike. For a discounted call, the derivative must be adjusted for the discount factor; for an undiscounted forward call price, its…
The document distinguishes a currency’s convertibility from whether an FX contract delivers the currency. A currency may be difficult or restricted to convert because of capital controls or limited market access, while a non-deliverable forward settles its…
The document explains why a local volatility model can be useful after fitting an implied volatility surface to vanilla option prices. Under Dupire’s approach, the surface is converted into a local volatility function that can be used to model the underlying…
The document outlines how to build a curve from an index instrument and a sequence of forward rate agreement quotes, including overlapping FRAs. It frames the task as choosing curve parameters, interpolation, and discount factor node dates so the setup can…
The document concerns adding principal redemptions that fall between coupon dates to an amortizing floating-rate bond in QuantLib. Assigning a redemption directly to the bond’s redemption list did not make the cash flow appear in the reported schedule. The…
The document explains how to derive the value at an intermediate time of an FX forward whose underlying spot rate is simulated in a Monte Carlo model. It rewrites the value as the difference between the current forward exchange rate for maturity and the…
The document addresses whether the tenor of a LIBOR rate used for discounting should match a swap leg’s payment frequency. Its answer says that LIBOR is generally not the preferred discount curve for uncollateralized trades. Because LIBOR includes a credit…
The document considers pricing options on an illiquid currency pair when only one bank provides option quotes. It asks whether historical realized volatility can support implied volatility estimates, how a market maker might account for a risk premium, and…
The discussion explains why calibrating a Bermudan swaption model only to coterminal European swaptions may miss important market drivers. A Bermudan’s exercise value can depend on swap rates and swaption prices across many expiries and tenors, including…
The document discusses pricing single- and double-window barrier options, whose barriers are monitored only during a specified interval within the option’s life. It cautions that closed-form formulas are generally limited to Black–Scholes settings with…
The document raises a curve-construction question about combining SOFR futures at the front end with SOFR swaps at the longer end. It notes that centrally cleared swaps require daily cash variation margin and asks whether that feature makes their economics…
The document explains that the discount curve used to value a swap is connected to the collateral terms agreed by the counterparties. Those terms are set out in the Credit Support Annex, which forms part of the contractual arrangement governing collateral…
The document explains how option Greeks can help attribute changes in a delta-hedged position. Gamma captures the effect of underlying price movement and realized variance relative to the volatility assumption; vega measures sensitivity to changes in the…
The discussion considers a bullish investor choosing how to gain exposure to a forward, with position size capped at a stated maximum. The response explains that an optimal position cannot be determined from the expected direction alone: it depends on the…
The document explains how to construct a portfolio of stock and a risk-free bond that matches an option's payoff in a one-period, two-outcome binomial model. In the up state, the portfolio's stock and bond values must equal the option value; the same…
The document considers whether a stock’s expected future value under the risk-neutral measure equals its current price when the risk-free rate is zero. One answer connects the stock payoff to a forward contract: arbitrage pricing relates the forward price to…
The document explains how to infer a later-dated option’s implied volatility from a calendar put spread when the earlier straddle’s fair value is known. It first compares the trade price with model values to estimate the spread’s edge, then uses put-call…
The document examines how the change in value of a Black–Scholes hedging portfolio is derived when it holds an option and a short position in the underlying stock. It distinguishes applying Itô’s lemma to the option value, viewed as a function of time and…
The document discusses why Itô calculus is common in finance and how it relates to the Stratonovich convention. It presents the view that, with appropriate treatment, both conventions can lead to the same Black–Scholes equation. The choice of stochastic…
The document clarifies the meaning of the Poisson rate in Merton’s jump-diffusion model. The rate λ is an intensity measured as expected jumps per unit of time. Over a short interval of length dt, the expected number of jumps is λdt, which corresponds to the…