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 exchange discusses whether least-squares Monte Carlo (LSM) for Bermudan options has numerical support and theoretical guarantees beyond a limited proof based on two exercise dates and a Markovian state on positive values. Mark Joshi replies that…
When a holder exercises a listed option, the exchange does not use identifying information attached to the contract to locate its original writer. Instead, the exchange randomly selects a clearing member to receive the assignment. The clearing member then…
The discussion considers how to price an American swaption, whose holder can exercise before expiry. It distinguishes the backward exercise decision—comparing immediate payoff with the discounted conditional value of continuing—from Black’s formula, which is…
The document considers what no-arbitrage principles constrain the pricing equation for European options. It models an option price as a function of the underlying price, time to maturity, and terminal payoff. A portfolio argument shows that the price of a…
The document asks how to calculate the expected positive difference between two correlated lognormal asset prices. It identifies the payoff as the positive part of the spread and connects the problem, when the assets are stocks, to a Margrabe exchange…
The document examines whether an option’s market price must always be at least its intrinsic value. The intuitive arbitrage argument is not universally sufficient: exercise rights, timing, financing, and trading frictions affect whether an apparent discount…
The document distinguishes derivative pricing from the profit and loss of a hedging strategy. Pricing a payoff as a risk-neutral expectation uses a model and market-implied volatility to produce a value and its sensitivities, such as delta and vega. To…
This discussion explains why owning one share does not automatically hedge a short call. The option’s value changes with the underlying price, and its exposure is generally different from one share. A covered position can therefore retain substantial…
The document describes a real-time pipeline for Bloomberg tick data covering many stocks and equity options. Multiple processing services publish updates through Redis pub/sub, Redis also holds intraday tick data, a separate process saves periodic snapshots…
The document considers how to estimate a volatility surface for illiquid daily options when the available market data consist only of at-the-money implied volatilities on quarterly futures. The options extend across a much longer horizon and include…
This question presents a one-period market with a stock and forward contracts, then asks how to replicate a call option using those traded instruments. The stock starts at 10, the forward price is 12, and the stock can finish at either 11 or 14; the call has…
The document uses a one-period stock and call option example to distinguish physical probabilities from risk-neutral pricing. Under the physical measure, the call has a higher expected payoff than its risk-neutral value, which prompts the question of whether…
The document considers using swaptions to estimate expected positive and negative exposure over the life of an interest-rate swap for credit and debit valuation adjustment calculations. It asks how this approach compares with interest-rate simulations and…
The document asks how to translate a large VIX increase into a volatility shock for single-stock options across expiries and strikes. Its proposed calibration starts by comparing the variability of the stock’s at-the-money implied volatility with VIX, while…
The document presents a no-arbitrage replication argument for a barrier option with strike equal to its barrier. Under continuous stock-price paths, zero rates, and no dividends, a forward struck at the barrier is worthless when the barrier is hit. The…
The document examines a derivation of option Greeks when implied volatility varies with moneyness. It compares the reported gamma and vanna expressions from a smile dynamics paper with calculations that treat the Black–Scholes price as depending on the…
The document investigates why a QuantLib implementation of Black-76 can produce option values that differ from online calculators. The accepted explanation identifies time-to-maturity resolution as the source of the discrepancy: by default, the relevant…
The document examines cross-gamma in a portfolio of options whose underlyings differ. It notes that when each option depends on only one underlying, shifting the other underlying does not affect its value, so a portfolio-level finite-difference calculation…
The document describes a practical problem in constructing an option volatility surface from implied volatilities quoted at different deltas. Direct interpolation in delta space can be awkward because call and put deltas fall on opposite sides of the axis,…
The note discusses which option prices to use when building an implied volatility surface. Its answer recommends using out-of-the-money options because they tend to have narrower bid–ask spreads than in-the-money options. For a more careful estimate, it…
The document raises a question about whether at-the-money or in-the-money and out-of-the-money options tend to attract more demand. It presents two competing explanations: at-the-money contracts may be favored for obtaining gamma and vega exposure with…
The discussion weighs the use of a zero percent discount rate in option and swaption models against discounting with an interest-rate curve. Whether the simplification is acceptable depends on rate exposure, product maturity, model accuracy, and the size of…
The document poses a mathematical question about using Malliavin calculus to construct hedges in a market model driven by a stochastic differential equation. It refers to a proof approach for obtaining an explicit delta-neutral hedge and asks whether a…
The document gives a concise checklist of core terms needed to describe an interest rate swaption. These include the option’s expiry date and time, whether it grants payer or receiver exposure (or is structured as a straddle), and the start and end dates of…