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 outlines a probabilistic route from the Black–Scholes terminal-value problem for a European call to its familiar closed-form price. Feynman–Kac represents the solution as a discounted expected payoff under a diffusion. The derivation then…
The document explains why the DV01 of a fixed income swap is not constant across interest rate levels. A simplified rule of thumb discounts each future annual payment using a single rate, then sums the discounted sensitivities. Under that approximation, a…
This discussion explains why a fixed rate bond’s net present value can differ from its dirty price in QuantLib. The key distinction is the discounting date: NPV uses the discount curve’s reference date, while dirty price is expressed at the bond’s settlement…
The document investigates why an implied volatility calculation for a long-dated S&P 500 index call returns zero. The response checks whether the observed option price is consistent with intrinsic value under the selected interest rate. Using the supplied…
The document explains the theoretical cost of hedging a written call by repeatedly adjusting a stock position to match the option’s delta. Under the Black–Scholes assumptions, dynamic hedging replicates the option payoff, but the hedge trades generate a…
The document explores why barrier options in the Black-Scholes framework can be priced with the usual pricing PDE while incorporating barrier behavior through boundary conditions. Unlike path-dependent products such as Asian options, the barrier feature can…
The document considers how to price term interest-rate exposure in Poland as contracts move away from WIBOR, asking whether WIRON can support forward-looking term rates. Its answer argues that a term rate generally depends on a sufficiently active…
The document distinguishes using a bootstrapped interest rate curve from using a stochastic model of rate dynamics. A market curve built from instruments such as forward rate agreements and swaps is sufficient to price simpler contracts through no-arbitrage…
The document addresses a Python QuantLib error encountered while pricing a European credit default swap option with a Black-style option engine. The reported constructor error indicates that the engine expects its volatility input as a quote handle rather…
The document explains how to estimate 95% value at risk for long and short European calls when simulated terminal stock prices and their option payoffs are already available. Rather than applying a stock-return standard deviation and z-score through a delta…
The document examines a SABR calibration on Ethereum option data where the fitted alpha parameter changes substantially when strikes and the forward are expressed at a different scale, even though the implied volatilities are unchanged. The questioner…
The document clarifies how to approach an implicit finite-difference exercise for a European call when volatility varies over time. The stated example uses a linear volatility function, while the exercise also provides a Black–Scholes approximation that…
The document explains the Carr–Madan formula as a way to represent a sufficiently smooth payoff as a linear position in the underlying, a cash amount, and integrals of European put and call payoffs across strikes. The decomposition expands the payoff around…
The document shows how put–call parity can identify an arbitrage across European options with two different strikes, even when the current stock price is unknown. Applying parity separately at each strike and subtracting the equations removes the stock-price…
The document discusses extracting implied volatility from American option prices using a Cox–Ross–Rubinstein binomial tree. The tree prices the option by working backward from terminal payoffs, comparing continuation value with early exercise value at each…
The document explains how to simulate stock paths when periodic log returns are modeled with a Normal Inverse Gaussian (NIG) distribution, with the aim of pricing options by Monte Carlo. It warns that an NIG random variable cannot simply replace the normal…
The document questions a boundary condition for a travel-time option whose state includes a mean-reverting process with additive Brownian noise and its time integral. In the familiar geometric Brownian motion example, zero is absorbing: once the underlying…
The document explains how to compare spreads on fixed-coupon bonds and loans or floating-rate notes. Its answer says that the fixed bond’s additional interest-rate exposure need not justify a separate spread adjustment, since that exposure can be hedged at…
The document presents two parametric ways to describe equity implied volatility across strikes and maturities. One uses ATM forward volatility plus linear skew and quadratic curvature on a log-moneyness scale normalized by volatility and the square root of…
The document addresses whether a martingale-corrected Andersen discretization for the Heston model needs adjustment when the model has a nonzero constant interest rate. The answer endorses adding the risk-free accrual over each time step to the exponent…
The document explains why a foreign exchange forward is not generally the conditional expectation of the future spot rate under the domestic risk-neutral measure when interest rates are stochastic. The forward price instead comes from discounting the payoff…
The document asks whether vanilla options on two assets, together with the assets themselves, can create insurance that costs money when correlation is high and pays when correlation falls. The motivation is to hedge a strategy that benefits from the assets…
The document frames the rate sensitivity of a pay-fixed, receive-floating interest rate swap as three contributions: discounting floating coupons, discounting fixed coupons, and projecting floating cash flows. It asks how the magnitudes of those components…
The document compares three ideas used to explain why the Black–Scholes–Merton option-pricing formula can hold: profitable trading opportunities, market efficiency, and market equilibrium. It asks why equilibrium might be considered the most important of…