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 examines an open foreign-exchange forward that lets its holder choose when to draw down or settle within a defined period, while requiring the full amount by maturity. The accepted response treats this flexibility as an option-like feature: at…
The document troubleshoots finding Black implied volatility from a cap price using a numerical root solver. It identifies two issues: the supplied cap prices use percentage-style values while the pricing formula expects decimal values, and the implementation…
The document explains the interpretation of two volatility measures: the SPX convexity spread, defined as variance swap volatility minus at-the-money implied volatility, and the convexity ratio, defined as variance swap volatility divided by at-the-money…
The document presents a Python attempt to reproduce results from Duan’s 1995 GARCH option pricing paper. It specifies GARCH parameters and a risk-neutral adjustment, simulates daily variance and innovations, evolves a stock price, and estimates a call price…
The document answers a request for an inexpensive source of current option-chain data for European stocks such as Bayer, Siemens, Volkswagen, and Daimler. It points to Eurex, where many of these companies’ options are listed, and says market information can…
The document asks how long a standard implementation of the Longstaff–Schwartz Monte Carlo method would need to price an American put under Black–Scholes to more than ten digits of accuracy. It gives one practitioner’s response: their C++ implementation did…
The document examines why a put option’s premium may rise by much less than its new intrinsic value plus its earlier out-of-the-money premium after the underlying falls through the strike. The explanation is that option Greeks describe changes in the total…
This note considers the costs of buying SPY options near the market open and selling later in the day. It highlights explicit transaction charges and the bid-ask spread as separate drags on a trade. It also warns that option spreads may widen around the open…
This note explains how to adapt QuantLib code after `DividendVanillaOption` was deprecated. The replacement is `VanillaOption`, constructed with the payoff and exercise terms alone; dividend information is supplied to the pricing engine instead. For a…
The document asks how a continuity correction for a discretely sampled diffusion’s minimum improves the weak convergence rate of a lookback option payoff. The approximation adjusts each simulated grid value by a term proportional to the local diffusion…
The document examines the relation between an option’s volatility, the underlying stock’s volatility, and the option’s elasticity. It asks whether this relation depends on the Black–Scholes model, referencing a textbook proof but supplying no derivation of…
The document explains why the undiscounted value of a European option can be a martingale, using the maturity bond as numeraire. Under the associated forward measure, the option value divided by the bond price equals the conditional expectation of the payoff…
The discussion explains how to implement the Black–Scholes vega formula by clarifying the notation for the derivative of the standard normal cumulative distribution function. By the fundamental theorem of calculus, that derivative is the standard normal…
The document derives an approximate mark-to-market value for a variance swap partway through its life. It splits total realized variance into the portion already observed and the expected variance over the remaining period, then weights each by its number of…
The document compares CME expiration language for serial options on several grain contracts. Most examples specify the last Friday that falls at least two business days before month-end, with a fallback to the preceding business day if that Friday is not a…
The document explains several apparent irregularities in historical SPX options data from 2008–2009. Traditional options can show Saturday expiration dates for historical reasons, although the practical settlement reference is Friday: the index close for…
The document asks how to choose a log-growth-maximizing allocation for a portfolio holding a stock and an option through expiration, without continuous hedging. It contrasts the familiar single-asset Kelly formula with the harder joint problem and describes…
The document frames a model selection question for calculating option Greeks from a fitted volatility surface. It compares a local volatility model that matches the observed vanilla surface closely with a stochastic volatility model that may better represent…
The document explains why Vibrato Monte Carlo can estimate sensitivities when a derivative has a discontinuous payoff and full valuation under the model is difficult. It contrasts pathwise sensitivities, which require differentiating the payoff, with the…
The document asks how to differentiate the risk-neutral value of a call option with respect to its strike. It starts from the discounted expected payoff and restricts the integral to terminal prices above the strike, then cites the familiar results: the…
The document compares analytic approximations for American option exercise boundaries, including Kim’s integral equation and the Whaley approximation, with numerical PDE methods. It argues that PDE solvers can be preferable when pricing requires reliable…
The document decodes a short market comment about a two-month Turkish lira put, describing an option with a five-delta level, a strike of 8, and a premium of 0.6%. In FX quoting terms, the position is a USD call and TRY put, with the strike expressed as…
The document contrasts the standard Black–Scholes pricing equation, which uses the risk-free rate r in both the underlying-price drift term and the option discount term, with a modified equation that uses a separate rate r′ to discount the payoff. It invokes…
The document derives a European call price when the forward price follows a lognormal process with volatility that changes deterministically over time. The option expires at an earlier date than the forward's delivery date. Integrating the instantaneous…