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.
8,116 documents
The discussion considers how to estimate an option implied volatility surface when the target asset has spot history but no option data, while related assets have observable option surfaces. It presents break-even volatility, or fair skew, as a way to infer…
The document asks how quantitative finance software differs from classroom implementations, using European option pricing as its example. A basic Black–Scholes formula can be coded directly from a few inputs, while a production library such as QuantLib…
The document separates machine learning used to approximate an already computed option pricing function from methods that learn both a claim’s value and its optimal hedge. For fast pricing, a model is trained on examples generated by slower numerical pricing…
The document distinguishes two meanings of volatility in bond option analysis. Price volatility can mean implied volatility from a Black-style option pricing model using the bond price as the underlying. Yield volatility instead treats bond yield as the…
The document asks how to price a quanto option when both the underlying asset and the exchange rate follow calibrated Heston stochastic-volatility models. It specifically questions how to use a constant-volatility quanto formula when volatility varies over…
The note asks why an out-of-the-money natural gas call can have a larger absolute delta than a put whose strike is at a similar percentage distance from the underlying, even though the put has higher implied volatility. It gives example quotes and reports an…
The document asks for the probability that a stock modeled by geometric Brownian motion is at or above a threshold at a later time, given that it was at or below that threshold earlier. The responses explain that taking logarithms converts the stock process…
The document asks whether research on analytic pricing of American options continued after early papers on valuation properties. The response points to work presenting an exact explicit valuation for American put options. It characterizes the approach as an…
The discussion considers how to supply a dividend yield when applying Black–Scholes to an equity option. It distinguishes a known upcoming cash dividend from a continuous yield estimate and describes several ways to form that estimate. Forward-looking…
The question asks whether the lognormal distribution for a stock price can be used to derive the Black–Scholes partial differential equation. The response clarifies that the stated log-price process is an assumption within the Black–Scholes framework, rather…
The document asks where to obtain historical implied volatility rank or percentile data for US equities. The questioner distinguishes those measures from an options data feed that provides implied volatility alongside historical realized volatility, and…
The document asks how to estimate the CEV model’s parameters, which determine the scale and price dependence of stock volatility, for simulations of CPPI and OBPI portfolio strategies. The answer recommends calibrating the model to vanilla equity or index…
The document explains the distinction between clean (quoted) and dirty (cash) bond prices when specifying a bond option. Its answer emphasizes that over-the-counter contracts can define their strike and underlying price according to the parties’ chosen…
The document introduces the skew stickiness ratio (SSR) as a way to describe how at-the-money-forward implied volatility responds when the underlying asset moves. It uses this measure to distinguish two common smile-dynamics assumptions. Under sticky strike,…
The document surveys ways to estimate how an option’s implied volatility may respond to a hypothetical market move, with portfolio risk simulation as the motivation. It describes modeling the joint behavior of forward at-the-money volatility and the first…
The document explains an equivalence between a caplet paying a floating rate above a fixed strike and a put-style payoff on a zero-coupon bond. Its economic interpretation treats the caplet as the right to sell a one-period coupon bond with a predetermined…
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 asks how to extend a concave shape in bid implied volatility data to strikes beyond those observed. It also asks whether bid volatility should approach zero as the strike approaches zero or infinity. These are posed as questions; the document…
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 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…