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 surveys R packages for option pricing and related analysis. It names RQuantLib and NMOF for model implementations, including Black–Scholes–Merton, jump-diffusion, Heston, and characteristic-function approaches. It also points to RND for…
The document shows how to check that a Black-Scholes call price satisfies the Black-Scholes partial differential equation by substituting expressions for delta, gamma, and theta. The PDE relates the option value to its time sensitivity, underlying-price…
The document describes several uses of options pricing formulas even when markets are broadly efficient. Models can help traders assess possible mispricing, value contracts that are newly issued or lack a direct market quote, and infer quantities such as…
The document examines whether a European call can be replicated when the stock follows an arithmetic Brownian motion and the bank account grows at a constant rate. It outlines an argument for market completeness by finding a change of measure that makes the…
The document explains how to interpret the variance-rate assumption in the original Black–Scholes model. For a diffusion process, the instantaneous variance rate is the square of the coefficient multiplying the Brownian motion. In geometric Brownian motion…
The document explains how to derive an implied volatility surface for a currency pair from surfaces quoted for two related pairs. Its example combines EURUSD and USDJPY data to price EURJPY options. It first expresses the target option payoff in terms of the…
The document describes an implementation attempt for Haug’s double-barrier binary option formulas and explains why the asymmetric case produced incorrect results. The key correction is to treat the final term involving the asset’s position between the lower…
The document explains why binomial-tree formulas for the up factor can differ across constructions. In the Cox–Ross–Rubinstein tree, the up and down factors are set symmetrically around zero log drift, with volatility determining their size. The answer notes…
The document asks how to calculate the variance of integrated variance in the Heston stochastic-volatility model. It connects the problem to the closely related Cox-Ingersoll-Ross square-root process, whose integrated state variable has a known…
The document explains how to screen listed-option observations before calibrating a pricing model. It describes filters based on low average prices, wide bid-ask spreads, extreme moneyness, and very short or long times to expiry. These rules aim to remove…
The document asks how a market maker might hedge a short position in down-and-in Bitcoin puts. Its answer contrasts these barrier options with vanilla puts and gives two possible risk-management actions: use Bitcoin-dollar perpetual swaps or dated futures to…
The document rearranges European put-call parity to explain the components of put value when there are no dividends. It frames the put's intrinsic value as the strike minus the stock price, with time value reflecting both the call's upside protection and the…
The note explains that the share quantity attached to a call option is part of the contract terms. In the cited IBM example, the buyer may purchase a specified number of shares at the strike price during the option’s exercise period. For standardized…
The document presents Python code for pricing a European call or put with an implicit finite-difference grid. It asks why the coefficient matrix is modified at its first and last rows and why boundary grid values at each time step are extrapolated from…
The document asks when a fixed-strike arithmetic Asian call can be worth more than a vanilla call with the same maturity. Its answer compares their maturity payoffs: the Asian call pays on the average underlying price, while the vanilla call pays on the…
The document addresses implementing a characteristic function for option pricing in Excel VBA, where Excel's complex-number worksheet functions represent complex values as strings. The answer shows that these functions can be composed by passing their string…
The document explains how Markov Chain Monte Carlo can approximate an integral when a target density is known only up to a normalizing constant. In Metropolis–Hastings, a proposal distribution generates candidate states; moves toward higher target density…
The document raises a numerical boundary issue in the Avellaneda limit order book model: optimal bid and ask quotes use adjacent inventory-state values, so their formulas are defined only on reduced inventory ranges. A supplied response suggests handling…
The document derives the pricing relationship for a EUR-denominated option whose payoff is converted into COP. It applies the change-of-numéraire formula to the COP and EUR money-market accounts, accounting for the exchange rate that converts one EUR into…
The document discusses how to obtain historical data for European electricity futures and options, prompted by a researcher seeking EEX contract histories for a model. It describes several possible routes: ask the exchange whether it can provide data, seek…
The document suggests two routes for finding data to calibrate Lévy copula techniques. One is to consult research on dynamic copulas that uses credit default swap index products such as iTraxx and CDX. This points researchers toward multi-name credit…
The document explains the basic logic behind replicating an option in the Black–Scholes setting: when the underlying asset is the model’s sole source of uncertainty, a position in that asset and a risk-free account can hedge the option’s exposure. It…
This discussion explains why the constant-volatility assumption in Black-Scholes can be restrictive and outlines broader ways to extend the model. Stochastic-volatility models make volatility vary over time, with model dynamics linked to quantities such as…
The document presents a learner's attempt to derive a call option price by integrating the positive payoff over a lognormal terminal-price distribution, then substituting the risk-neutral expected price to determine the distribution's location parameter. The…