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 a proposed explicit finite-difference method for a nonlinear Hamilton–Jacobi–Bellman equation with a terminal condition. The value function depends on time, a variance-like state, and a Vega state. The proposed grid uses a backward time…
The note asks how to determine the time-dependent drift parameter in the one-factor Hull–White short-rate model when pricing zero-coupon bonds. It states the short-rate process as a mean-reverting rate with a time-varying drift and constant volatility, then…
The note considers a derivative paying an exponential function of a stock’s terminal price and asks whether a static portfolio of stock and a zero-coupon bond can guarantee at least that payoff. Such a portfolio has a payoff linear in the terminal stock…
The document asks whether a weighted mixture of two local-volatility models can provide an implied density for path-dependent options, including barrier and touch products. It presents the mixture as a weighted average of the component models’ vanilla option…
The document explains how to take a short position in a synthetic instrument that can have a negative price, using spreads as examples. It lists calendar spreads, butterflies, and double butterflies, then gives a January–February calendar spread: the long…
The document investigates why a QuantLib USD overnight indexed swap curve built from Bloomberg par rates reproduces Bloomberg discount factors at short maturities but diverges slightly at longer tenors. The example constructs OIS rate helpers and a…
The note explains how the option portfolio’s gamma contribution to price change follows from the second-order term in Itô’s lemma. It distinguishes the instantaneous variance term in the pricing equation from realized movement in the underlying price. Using…
The document gives intuition for the variable changes used to transform the Black–Scholes partial differential equation into the heat equation. The response breaks the spatial transformation into two steps: first express the underlying price in…
The document clarifies an ambiguous claim that spot price and variance have correlation near negative one. One response explains that the leverage effect concerns negative association between stock returns and volatility, rather than between the price level…
The document describes an attempt to build implied volatility smiles for European options from American option chain data. The author calculates implied volatilities with Black–Scholes, selects out-of-the-money options to reduce early-exercise concerns, and…
The document raises two questions about a volatility swap under a flat one-year volatility assumption with no skew: whether the fair volatility equals the quoted volatility when the number of fixings matches the stated annualization factor, and why the fair…
The note explains why an American put on a non-dividend-paying stock has the same value as its European counterpart when interest rates are non-positive. Its key comparison is between the European put’s lower bound, the discounted strike minus the stock…
The discussion explains why a regression intercept used in rough volatility analysis can be interpreted as volatility of volatility. Researchers measure increments in log volatility across sampling intervals, calculate their absolute moments, and regress the…
The document points readers to a practical paper on calibrating the SABR model and to foundational references for interpreting its parameters. It explains that beta is commonly fixed in advance to represent a chosen dynamic, rather than estimated alongside…
The document asks why a drift term obtained after applying Itô's formula to a discounted European option price must vanish in a pricing partial integro-differential equation. The setup models the asset with a Lévy process, so the discounted option value has…
The document examines whether a standard LIBOR floating-rate leg remains worth par when its cash flows are discounted using the OIS curve. It introduces the single-curve bond and forward-rate identity that would imply par value, then asks whether that…
The document explores how carry and delivery optionality can affect the basis between a Treasury futures contract and its cheapest-to-deliver bond near contract expiry. It considers a long basis position under both upward-sloping and downward-sloping yield…
The document asks how to value a European payoff when a stock follows risk-neutral geometric Brownian motion whose volatility depends on its history. It contrasts this setting with the standard Markovian case, where volatility depends only on the current…
The document examines a long call hedged by shorting stock in an amount equal to the option’s initial delta. It considers a sudden underlying-price decline alongside an increase in implied volatility, and asks whether the hedge must make money. A Taylor…
For a European option on the December Brent futures contract that expires earlier, the relevant volatility describes the distribution of that same December contract at the option’s expiry. Under the Black model for futures options, the payoff is determined…
The document explains why buying volatility exposure after a quiet period is not a cost-free way to profit from a future volatility spike. VIX is a spot index rather than a security that investors can hold directly, so traded exposure is typically obtained…
The discussion asks how closely Monte Carlo (MC) and finite-difference methods (FDM) should match exact option prices and Greeks under specified path and grid counts. It describes a delta obtained by bumping an FDM price that differs modestly from the exact…
The discussion explains why a USD three-month LIBOR coupon in a cross-currency swap can accrue over 90 days even when its payment arrives 92 days after the deal date. The trade starts at settlement, two days after the valuation or deal date, and the LIBOR…
The answer considers a price following geometric Brownian motion under a probability measure where its drift is nonzero. It explains that the drift can be absorbed into a shifted Brownian motion: under a new measure, the original Brownian motion plus the…