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 discussion asks how a trader should decide whether to exercise a physical Bermudan swaption as an exercise date approaches. The accepted answer distinguishes a necessary condition from a sufficient exercise rule. For a receiver swaption, exercising at an…
The post examines a motivation for the SABR model: local volatility models are said to predict implied-volatility smile movements opposite to those observed in markets, whereas the original SABR paper is described as moving the smile in the same direction as…
The document presents a Python implementation of an explicit finite-difference scheme for the Black-Scholes equation, applied to a European call. It lays out a stock-price grid and a time grid, initializes terminal values with the call payoff, and steps…
The document explains the meaning of state-contingent prices in a two-period asset-pricing setup. A security associated with a particular future state pays one unit if that state occurs and nothing in other states; its price today is the price of that…
The document raises a conceptual question about a standard optimal stopping result: for a Markov process, the value function is characterized as the smallest superharmonic function that dominates the payoff. The author questions how this can hold when some…
The document explains the arbitrage implied when a European put's price exceeds its strike, assuming the underlying asset price cannot fall below zero. A put's payoff at maturity is capped at the strike, so a seller's maximum payment is no greater than that…
The question compares a model-free volatility expression based on option prices across strikes with implied volatility obtained by inverting the Black–Scholes pricing formula. The answer clarifies that the two quantities represent different concepts. The…
The note distinguishes option valuation from deciding whether to buy shares. Black–Scholes prices an option under assumptions about the underlying price, volatility, rates, and time to expiry; it does not by itself produce a fundamental value or directional…
The note compares a bond-plus-equity-option approach to valuing convertible bonds with a binomial approach that models both debt and equity features. In the simpler method, the value is treated as the sum of a straight bond and a call option on the…
The note explains how QuantLib’s `growthOnly` setting changes a CPI-linked bond’s principal repayment at maturity. With the setting false, the bond returns the original notional adjusted by the ratio of the maturity inflation index to the initial index. With…
The document presents an identity for forward rates at a given observation time: a forward rate spanning multiple periods is stated to equal the average of the sequence of one-period forward rates over the same horizon. It frames the identity as a…
The document explains why a trader might choose a contract for difference rather than buy shares directly. A CFD provides exposure to changes in an underlying stock’s price without ownership of the stock. Because the trader posts margin rather than paying…
The document distinguishes estimating Vasicek model parameters from historical short-rate observations from estimating the market price of risk. Maximum likelihood estimation on historical data may estimate real-world parameters such as the long-run mean,…
The question seeks free or student-accessible books on stochastic volatility modeling. The answer recommends a book by Lorenzo Bergomi and points readers to sample chapters and presentation materials available from the author's website. It also mentions…
The document considers hedging a USD corporate bond into GBP using either rolling three-month FX forwards or a cross-currency swap, with rates risk hedged separately through interest rate swaps. It asks how to compare the approaches’ costs as an effect on…
The document asks what defines a package trade in rates markets, whether a package must be DV01-neutral, why hedge funds request one, and why it may be hard to price. Its example is a set of instruments traded together to target exposure around a particular…
The document explains why stock index futures are not generally read as forecasts of how much an equity index will rise, even though interest rate futures are often used to infer rate expectations. Index futures can be used to derive a forward curve and…
The note surveys alternatives to the Gaussian distribution for fitting empirical stock returns, emphasizing heavy tails and the distinction between describing returns and pricing derivatives. It discusses stable Paretian distributions, the Heston…
The document considers how to infer the volatility implied by a convertible note’s issue price when the instrument includes early conversion, issuer redemption, and capped calls. A simple decomposition into bond value and option value may be inadequate once…
The note explains why a long European put can have positive theta under Black–Scholes, despite the usual intuition that long options lose value as expiry approaches. A deep in-the-money put can trade below its intrinsic value when interest rates are…
The document examines a Monte Carlo attempt to remove the drift from geometric Brownian motion by multiplying each simulated price path by a Radon–Nikodym derivative. Its central explanation is that this derivative changes the probability weights assigned to…
The document considers how to simulate asset paths under SABR when volatility and vol of volatility are high. It describes a Monte Carlo comparison between a call value obtained from Hagan's implied volatility approximation and an estimate from a discretized…
The note asks whether an American put can be valued by calculating Black-Scholes prices for options with different maturities and selecting the largest. The response explains the key obstacle: an exercise time in the optimal stopping formulation is generally…
The document investigates why a year-on-year inflation swap rate may need a convexity adjustment when inferred from zero-coupon inflation swap rates. It starts with an example using a current index level and market rates at two maturities, then calculates…