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 document discusses potential drawbacks of using deep learning to calibrate and price a full implied-volatility surface. It notes that neural methods can produce very fast calibration at application time, while training may involve substantial…
The document addresses why an at-the-money call’s familiar delta of about one half does not match the full payoff change in a large, single-step move. Delta is a local sensitivity: in the theoretical continuous-time setting, it approximates how an option’s…
The document explains why a stochastic local volatility model can combine features of local volatility and stochastic volatility. It writes the asset’s instantaneous volatility as a stochastic factor multiplied by a state- and time-dependent local factor.…
The document addresses whether CME options on one-month SOFR futures continue trading during the month when the underlying SOFR rate is measured. This matters for implied volatility modeling: if trading overlaps the averaging period, remaining uncertainty…
The document presents an arbitrage argument for convexity of European call option prices as a function of strike. If the price at a middle strike were at least as high as the average prices of two equally spaced neighboring strikes, a trader could buy the…
The document explains why option delta is generally tied to a particular underlying asset, so a portfolio containing options on different stocks does not have a single ordinary delta obtained by simply adding the component deltas. For a portfolio whose value…
The document asks how to assign equal risk contributions across asset classes in a portfolio that includes nonlinear instruments such as options. One response recommends first converting each instrument into a return stream, estimating risk parameters from…
The document explains calibration as choosing a model’s parameters so its prices fit observed prices for selected liquid options. A common formulation minimizes the aggregate pricing error across instruments with specified characteristics such as strike and…
The document outlines the usual discrete-time Black–Scholes delta hedge for a European call on a stock. It sells the option, offsets its delta with a stock position, and places the residual value in a risk-free account. At each step, the stock price is…
The note evaluates a proposed way to choose an expiration for uncovered puts: maximize option premium divided by days to expiration. It argues that this ratio tends to mechanically favor shorter-dated contracts, because option value generally does not rise…
The note asks how to obtain the first, second, and fourth cumulants of the variance gamma with stochastic arrival model for use in Fourier-cosine option pricing. It defines the model through a characteristic function built from a variance gamma process with…
The note explains why multiplying an option’s current theta by the days remaining can imply more decay than its current time value. It uses a deep in-the-money call as an example: most of its price is intrinsic value, while the quoted time value is small and…
The document questions an apparent U-shaped implied-volatility pattern in SPX options, especially at far out-of-the-money strikes. A response compares the displayed pattern with a snapshot of implied volatilities for weekly options, reporting generally…
The document examines how to estimate expiration probabilities and expected value for a two-leg put credit spread. It divides outcomes into three price regions: above the short strike, between the strikes, and below the long strike. The author asks whether…
The document explores how to derive a variational or weak formulation for the Black–Scholes partial differential equation. Its central issue is integration by parts in the diffusion term, where the coefficient depends on the underlying price variable.…
The document addresses how to construct an implied volatility smile from US equity options when no traded option has a strike exactly equal to the underlying price. It asks how to estimate at-the-money volatility and connect out-of-the-money put and call…
The document considers how to turn over-the-counter FX option quotes, reported at different strikes and maturities, into a usable volatility surface. One proposed workflow starts from standard delta quotes, converts each maturity’s deltas to strikes using…
The document investigates a negative value appearing in a plotted down-and-out call price when the underlying starts below the barrier. It presents a Black–Scholes barrier pricing expression, defines its parameters, and compares that expression with an…
The document examines how credit risk and contract terms affect the Black-76 valuation of options on corporate bonds. It highlights that the forward bond price must reflect the bond’s risky market value and financing or discounting assumptions; treating a…
The question seeks a way to estimate the risk-neutral variance of an underlying stock’s gross return and considers option-implied distributions alongside estimates made from data under the physical measure. One reply assumes geometric Brownian motion under…
The note addresses why implied volatilities calculated from option prices differ across strikes. It explains that Black–Scholes implied volatility is the volatility input that reproduces a given market price under the model; when the model assumes a single…
The document asks why a strongly path-dependent option’s value is written as a function of the asset price, time, and an accumulated quantity. The payoff depends on a path summary defined as the time integral of a function of the asset price and time. Since…
The question describes using QuantLib to price options from a dataset containing contract start dates, expirations, and strikes. The proposed workflow groups contracts by expiration, supplies implied volatilities and market inputs to Heston model helpers,…
The document considers ways to hedge a long SPY position against a substantial decline: a volatility-linked ETF, an inverse leveraged ETF, and put options. It sketches possible gains and costs for each, but the proposed payoff estimates are uncertain and are…