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 explains how to assess completeness in a one-step trinomial stock model with a risk-free bond. An equivalent martingale measure assigns positive probabilities to all terminal states and makes the discounted stock price a martingale. The stock…
The document introduces basis-function selection in Longstaff–Schwartz least-squares Monte Carlo pricing for options on multiple underlyings. In this approach, continuation values are approximated with basis functions during backward induction, which…
The document asks how to express the value of a European call at an intermediate node of a Cox–Ross–Rubinstein binomial tree. It defines the node by the time step and the number of upward moves, and describes a backward-induction recurrence that discounts…
The document raises a theoretical question about a consistency property in the Vanna–Volga method. Starting from a price curve constructed by interpolation and extrapolation across strikes, the cited paper claims that selecting three different strikes on…
The document shows how to generate joint spot and variance paths from QuantLib's Heston process in Python. It constructs the process from initial variance, mean-reversion, long-run variance, volatility-of-variance, correlation, spot, and rate inputs, then…
The document asks whether information criteria or divergence measures can guide SABR calibration. The response describes a common rates-market workflow: preset beta, solve alpha to match the at-the-money volatility, then optimize rho and nu against smile…
The document examines why a bisection-style search for Black–Scholes implied volatility can fail for a put even when it works for a call. The key diagnosis is that the put price in the example is above the greatest value a European put can reach under the…
The response outlines a pricing approach for an FX-linked payoff when payment is made in a third, quanto currency. It defines the exchange rate with the foreign currency as the numerator and gives its drift under the quanto currency measure. The drift…
The document answers whether the standard European put-call parity relation also applies when the underlying is modeled with Heston stochastic volatility. Its central point is that parity follows from the option contracts and the ability to construct…
The document addresses how to summarize implied volatility across an option chain rather than relying only on the at-the-money option. It describes a model-free variance-swap approximation built from option prices over a range of strikes: calls above the…
The document outlines several ways to think about pricing options on a volatility index such as VIX. One approach starts from the option portfolio used to replicate variance and adds a convexity adjustment that accounts for the square root linking variance…
The document asks what changed in Monte Carlo methods for pricing American options between 2005 and 2016, following earlier machine-learning work on optimal stopping. One answer argues that the period brought few groundbreaking Monte Carlo advances and that…
The document considers a finite-difference approximation to the Black–Scholes equation and asks how coefficient sign conditions can establish a maximum-norm bound. The proposed argument rewrites each value at one time level using the neighboring values and…
The document considers how to recover FX option strikes from broker volatility quotes, forward points, deposit rates, and delta conventions. It explains that the ATM strike formula depends on the convention: a delta-neutral strike with premium-adjusted delta…
The document asks whether historical listed SPX options data from the CBOE data shop is reliable enough for backtesting, especially regarding missing or incorrect prices and Greeks. The response recommends checking a small sample of purchased contracts…
The discussion examines whether Black–Scholes–Merton derivations require an unproven self-financing condition. It describes replication arguments in which a portfolio holds stock and a money-market account, and its changes in value come from gains on those…
The document discusses a market maker who is assigned an in-the-money American call after the underlying market closes, creating stock delivery and delta exposure by the next open. Because the underlying cannot be traded during that interval, the direct…
The document asks how to interpret theta and gamma for a portfolio holding one call while dynamically hedging its delta with the underlying and financing trades. It gives the local P&L relationship in which theta contributes over time and gamma contributes…
This brief spreadsheet example shows how to make a Bloomberg BDP query use a strike stored in another cell instead of a fixed value. The method is to concatenate the ticker’s text components with the cell reference, while formatting the ticker with spaces as…
The discussion considers how to infer implied volatility from option bid and ask quotes across strikes, expiries, calls, and puts. It covers estimating forwards through put-call parity, choosing representative option prices, and fitting a consistent…
The question asks how to obtain the volatility input needed to calculate an option’s Black–Scholes delta. The replies explain that this input is commonly implied volatility: the volatility value consistent with the observed market price of the option and the…
The document discusses pricing a European exchange option that pays the positive difference between two stock prices at expiry. The assets follow correlated geometric Brownian motions. One answer changes to a measure using one asset as numeraire; under that…
The discussion considers why experience with poker may be relevant to equity and options trading. Its central analogy is that both activities involve decisions under uncertainty against other participants, where the quality of a choice depends on more than…
The document shows why European calls and puts with the same strike and maturity have equal gamma under put-call parity. It starts from the parity relation between the call, put, spot price, discounted strike, and interest rate. Differentiating once with…