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 asks how to handle the negative rate-times-value term in a Heston–Hull–White partial differential equation discretized with an alternating direction implicit (ADI) scheme. The paper described by the question allocates this term evenly among the…
The document clarifies how to calculate profit and loss for a continuously delta-hedged option position. Its central distinction is between the gains from holding a changing number of shares and the change in the market value of the final share position.…
The document explains why converting an FX option delta into a strike requires the market’s quoting conventions and the correct definition of at-the-money. In the example, the pair uses unadjusted deltas, and the at-the-money strike is delta-neutral: the…
The document addresses the expected value of an asset's time average when the price follows geometric Brownian motion, in the context of arithmetic Asian option pricing. The response derives the risk-neutral expected asset price at each future time as its…
The document considers an asset-backed security with a long legal maturity and an earlier anticipated repayment date. Missing that date triggers a higher interest rate and a full cash sweep. It asks how to interpret those terms when valuing the debt,…
The document describes estimating a risk-neutral density as a weighted mixture of normal kernels centered on a strike grid. The weights are constrained to be nonnegative and sum to one, and are fitted to observed put prices by minimizing pricing errors. It…
The document offers career-development advice to a mathematics PhD with derivatives valuation experience who wants demonstrable C++ work implementing financial models. The answer suggests exploring public repositories focused on topics such as option pricing…
The note proposes a market-mechanics hypothesis about how options open interest could relate to underlying price moves. It suggests that large put positions might behave like support and large call positions like resistance, and that some short option…
This note motivates bivariate time-series models for quarterly stock returns and dividends. It highlights features a model may need to capture: managers have discretion over payouts, dividends tend to remain stable or rise modestly, and cuts are often…
The document considers an exchange-traded product combining a butterfly payoff with a double no-touch condition: the payoff follows a butterfly profile if the underlying stays between two barriers until maturity, and becomes zero if either barrier is…
The document addresses poor Monte Carlo pricing accuracy for deep out-of-the-money options under a stochastic volatility model. The question focuses on Euler simulation of the Heston process and asks whether importance sampling can reduce variance and speed…
The discussion examines option price changes near expiration that appear larger than delta and theta alone would suggest. It explains that gamma exposure is most pronounced near at-the-money strikes and presents gamma scalping as a way to manage a long gamma…
The document describes how to turn a piecewise linear profit-and-loss graph at expiration into a portfolio of calls, puts, and possibly cash or the underlying. It proposes placing option strikes at the graph’s breakpoints, then solving a linear system whose…
The document clarifies what a mid-curve swaption measures and how it can help infer forward volatility. A mid-curve swaption measures volatility of a forward-starting swap rate, but that is not itself the forward volatility of an option whose strike will be…
The document explains why an in-the-money call generally cannot trade below the underlying stock price minus the strike, using a no-arbitrage argument. If it did, an investor could sell the stock, buy the underpriced call, and invest the strike amount. The…
The document addresses how to value American options on SPY when dividends are present. It challenges the proposed shortcut of taking the maximum of two European option values, one tied to the ex-dividend date and one to final expiry. An American option can…
The document considers an optimal stopping problem in which the payoff depends on an Ornstein–Uhlenbeck process, then asks whether that process can represent a stock price. The response argues that under a risk-neutral, arbitrage-free model, discounted…
The document poses an implied-volatility problem for an American call when a known dividend is paid before expiration and interest rates are zero. Because early exercise may be optimal immediately before the ex-dividend date, the contract can be viewed as…
The document raises a practical issue in constructing an implied volatility curve for ETF options during high-frequency intraday trading. Its premise is that option quotes may update faster than the ETF cash price, so calculating implied volatility from the…
The document considers whether recent historical bond-price volatility is suitable as the volatility input for pricing a bond option with the Black 76 model. The preferred input, when available, is implied volatility: the value that reproduces the option’s…
For sparse, illiquid index option chains, the response recommends cleaning and fitting prices or total variance rather than removing implied-volatility outliers and interpolating the remaining points. In option-price space, useful restrictions are clearer:…
This exchange examines a numerical discrepancy in a paper’s purported exact formula for pricing an arithmetic-average Asian option. The questioner reports difficulty reproducing a stated value and asks whether the paper or their Monte Carlo implementation is…
The document presents a replication problem involving the conversion of an implied volatility surface into a local volatility surface using Dupire’s formula. The author builds a smooth implied surface by parameterizing total implied variance against time and…
The document asks how to value the asset return leg of a total return swap referencing a convertible bond when a convertible bond mark-to-market pricer is available. It proposes decomposing the leg into coupon cash flows, the change in bond value at swap…