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 describes a simplified way to represent an active long volatility allocation discussed in a portfolio research paper. The proposed rule monitors the equity market over a rolling three-month window and buys options in the direction of a…
The document surveys ways to use QuantLib-backed analytics from Excel, motivated by spreadsheet workflows that combine pricing with data from market terminals. The options named include QuantLibXL, RExcel with RQuantLib, PyXLL with QuantLib-Python, a…
The document raises a question about replicating a variance swap fair strike from options when implied volatility is flat. The author expects the strike to equal implied volatility squared, but reports that a replication using constant volatility returns a…
This question examines whether a call option on a futures contract has the same theoretical value as a call option on the underlying stock. It compares the discounted futures-option pricing expression with the stock-option expression and uses the…
The document presents an attempt to infer implied volatility by minimizing the difference between observed option prices and Black–Scholes prices. The calculation uses spot, strike, time to expiry, interest rates, and dividend yield, with rates interpolated…
The document explains why different stocks may show different listed option expiration months. Historically, each stock belonged to a January, February, or March cycle, which determined which months in each quarter were available. Later rules ensured that…
The document derives a risk-neutral price for a payoff equal to the cube of a time-weighted integral of log stock prices in a zero-rate Black–Scholes model. Under the risk-neutral measure, the log price is a Brownian process with drift equal to minus one…
The document explains why an American digital put can be valued through the probability that the underlying asset reaches a specified minimum by expiry. The key reasoning is about exercise timing: when interest rates are nonnegative, the response says it is…
The document considers whether a practical option model can produce better delta hedges than Black–Scholes for equity options. One response says the Heston model is relatively quick to implement analytically, but may still miss important features of…
The document raises a question about a statement in a paper on variance swaps: a stock call option’s vega is greatest when the option is at the money. The author wonders whether this is because vanilla options are nearly linear in volatility at that point,…
The document asks how to automate daily retrieval of CDOR rates, swap rates, and options prices from Bloomberg into an Excel workflow. The answer recommends sending requests through Bloomberg's WAPI, which it says refreshes data when a request is sent,…
The document asks whether an option on a bond future can be represented using options on forward rates. It simplifies the contract to a European option on a zero-coupon cheapest-to-deliver bond and relates the forward bond price to the forward rate over the…
The discussion explains why a simulated delta hedge may retain tracking error and how to account for changing positions. In the Black–Scholes framework, hedge error should shrink as rehedging intervals become smaller when the simulated underlying follows the…
The document explains why a volatility-squared correction appears when expressing a stock price as an exponential Brownian process in the Black–Scholes framework. Under the risk-neutral measure, the discounted stock is modeled as a martingale. The answer…
The document explains the law of one price in a single-period trading model. Its central idea is that portfolios with identical payoffs should have identical current prices. This principle supports pricing a European option by constructing a portfolio of…
The document asks whether American and European puts should have the same value because they share the same terminal payoff, and what it means for an American option holder to exercise optimally. The replies clarify that matching terminal payoffs do not…
The document explains why a delta-gamma-theta estimate can differ from an option’s actual price change when the underlying price moves substantially. The approximation combines the first-order delta effect and second-order gamma effect of a stock-price move…
The document asks whether a one-factor Hull–White interest-rate model can price a European swaption that includes a floor on its floating leg while matching both swaption volatility and LIBOR volatility. The response says that fitting the floor or cap market…
The note explains how practitioners should choose finite-difference bumps when calculating time-sensitive option Greeks and related risk measures. A bump should be large enough to avoid numerical noise yet small enough to represent the sensitivity of…
The discussion considers whether tree and finite-difference methods can price convertible bonds whose call, put, or conversion-reset rules depend on past stock prices and allow early exercise. The central method is to add auxiliary state variables that…
The document asks why formulas connecting local volatility to implied volatility appear to give zero volatility when the underlying price equals the strike. That apparent result would make the equations seem unusable for at-the-money options, and values near…
The document addresses the sign of interest rate sensitivity, or rho, for call and put options. It identifies a likely typographical mistake in a cited book: under the standard setup discussed, call rho is positive and put rho is negative. The explanation…
The document considers whether buying a CADUSD put and selling a USDCAD call could create an arbitrage because their quoted premiums and payoffs appear to leave a net credit. The question highlights that the currencies are inversely related and argues that…
The answer shows how to price a European average-price call option using QuantLib’s continuous geometric averaging Asian option class. It sets up a call payoff and European exercise date, then supplies an initial asset value, constant volatility, and flat…