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 explanation changes from the foreign risk-neutral measure to the domestic measure using a Radon–Nikodym density tied to the exchange rate and money market accounts. Girsanov’s theorem shifts the correlated Brownian motions, producing domestic-measure…
A single-currency basis swap exchanges cash flows linked to two floating interest rate indices. The document points to QuantLib’s FloatFloatSwap instrument as the class for representing this structure in Python, contrasting it with a vanilla interest rate…
The document asks how to price structured products that depend on three-month EURIBOR, including constant-maturity swap spreads, range accruals, and target redemption notes, when discounting uses €STR. It proposes modeling the €STR short rate with a…
The document asks how to set the contingent payment for a pay-later option whose holder receives the call payoff when the underlying finishes above the strike and then pays a fixed amount. Because the holder pays nothing at inception, the answer treats the…
The document gives a simple way to estimate the fixed rate on a forward starting interest rate swap from spot starting swap rates. It treats the longer term as a combination of an initial period, or head, and a later period, or tail. Under a chosen fixed-leg…
The document derives a positive exponent that makes the discounted negative power of a Black–Scholes stock price a martingale, as a step toward bounding the value of an American put. It rewrites the stock process using geometric Brownian motion and separates…
The document explains why the Black–Scholes delta hedge can have gains or losses when volatility changes, despite the model’s claim of a riskless hedge. The key distinction is that the theoretical result assumes geometric Brownian motion and continuous…
The document addresses which implied volatility to use when converting a quoted option delta into a strike. Its guidance is to use the volatility associated with that particular delta, together with the other inputs required by the option-pricing…
The document distinguishes a pricing kernel, a stochastic discount factor (SDF), and an SDF process. A pricing kernel is described as a time-indexed stochastic process that makes the price-weighted asset value satisfy a conditional martingale relation.…
The document explains why interest rate models often focus on short rates or forward rates rather than introducing a single model for an isolated long rate. The meaning of a long rate depends on the chosen maturity: rates at two, five, or ten years could…
The document explains the intuition behind buying an option when its implied volatility appears lower than a forecast of realized volatility. A long option position has positive gamma: as the underlying rises, its delta increases and a trader can sell some…
CDS index series begin with constituent default swaps set to a five-year tenor. As time passes, the series’ remaining maturity declines, so a contract entered into later has the time left on that series rather than a fresh five-year term. This is the key…
The document distinguishes implied-volatility skew across option strikes from skewness in the underlying asset’s return distribution. It presents model-free implied skewness as a measure connected to realized skewness, and describes research finding a…
The document raises a question about changing from the physical probability measure to a risk-neutral measure for a lognormal asset process. It describes the usual setup in which the market price of risk depends on the asset’s physical drift, risk-free rate,…
The document examines how to quote an FX swap when the near and far legs have different notionals. It presents a proposed shortcut based on net spot exposure and far-leg swap points, then compares it with pricing each leg separately. A worked EUR/USD example…
This explanation shows how the product rule in Itô calculus creates the discounting term when differentiating an option value divided by a bank account. Set the two factors to the option price and the inverse bank account, then apply the rule, including the…
The document discusses how market participants price American options on Eurodollar futures and when a European-option approximation may be adequate. It contrasts tree-based models that represent early exercise with the simpler European treatment often used…
This exchange examines a mismatch between QuantLib and Bloomberg pricing for a Czech koruna interest rate swap. The questioner reports matching fixed-leg dates and the par rate but differing floating reset rates, cash flows, and net present value. A…
The note clarifies how a replicating portfolio can also function as a hedge. Under risk-neutral pricing, a European option can be offset by a portfolio whose value reproduces the option’s payoff and whose combined position with the option evolves at the…
The note explains why hedging skew exposure in a forward-starting option differs from hedging an ordinary option. A forward-starting put may be analytically short skew, yet during the forward period its strike resets in proportion to the underlying price.…
The note explains how to replicate a zero-coupon structured note that returns its principal at maturity plus an oil-linked payment. The extra payment rises in proportion to oil prices above 25, but is capped at 2,550. The proposed replication combines a…
The document considers a claim that pays one unit if default occurs before maturity and seeks to express its value as an integral over possible default times. The proposed representation combines the default-time density, formed from the hazard rate and…
The document compares three representations of option market information: implied volatility by strike and maturity, raw call or put premiums, and the risk-neutral return distribution. It argues that these are equivalent views of the same information and can…
The document collects questions about calibrating one- and two-factor Hull–White models to cap prices, calculating instantaneous forward rates for the drift function, and obtaining short-rate paths after calibration. The replies distinguish the model’s short…