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.
10,263 documents
This document presents a Monte Carlo approach to pricing an up-and-out call option. It simulates geometric Brownian motion paths from an initial stock price, computes each path’s maximum, and discounts the terminal call payoff only for paths that stay below…
The question asks whether the square-root-of-time scaling associated with diffusion in the heat equation also appears in financial price models connected to Black–Scholes. The proposed quantity is the typical distance traveled over a time interval, which…
This document collects recommended books and papers across quantitative finance, including asset pricing, portfolio allocation, option theory, stochastic calculus, derivatives by asset class, risk management, statistics, machine learning, programming,…
The document explains a rule of thumb that relates an option's bid-ask spread to its vega. Vega measures how much the option price changes when implied volatility changes. Because of that sensitivity, a volatility bid-ask interval can be translated into a…
The document discusses ways to estimate a reference implied volatility (IV) for options at different moneyness levels, with the aim of identifying contracts whose market IV appears mispriced. For forward-looking average volatility, it points to variance swap…
The document explains why a portfolio of stock and a money market account is chosen to match a derivative’s payoff in a one-period, two-outcome binomial model. The derivative has specified payoffs for the up and down outcomes, and the investor selects the…
The exchange asks what conditions ensure that an equivalent pricing measure makes discounted asset prices true martingales, rather than only local martingales. Its answer distinguishes the setting in the fundamental theorem of asset pricing: under the stated…
The note derives a simple risk-neutral default probability for a zero-coupon bond using its current price, maturity payment, and assumed recovery value. It sets the probability-weighted payoff relative to the purchase price to zero, with one payoff for…
The document discusses how to obtain the two risk-free rates used in the CBOE VIX calculation for its near and next expirations. The cited methodology uses U.S. Treasury Constant Maturity Treasury yields and applies a cubic spline to estimate yields at the…
The document explains why a long put can sometimes have positive theta, meaning its value can rise as time passes. The sign depends on the relationship among the option price, intrinsic value, interest rates, and remaining maturity; it is not determined…
The document considers pricing an autocap, a cap-like contract that automatically exercises in-the-money caplets but limits how many can be exercised. Since its value depends on correlations among LIBOR rates, the author proposes calibrating a LIBOR Market…
The document discusses two securities driven by the same Brownian motion, each with drift expressed as the risk-free rate plus a shared market price of risk multiplied by its volatility. The question is whether choosing the parameter to match the second…
The question concerns the covariance between the exponential of a time integral of one Brownian motion and a time integral of a correlated Brownian motion. The answer rewrites each time integral as a stochastic integral with a deterministic weight. These…
The discussion asks whether Asian option prices reveal information about a stock’s stochastic process beyond what can be inferred from European options. In an idealized setting, a full set of European call prices across strikes can be differentiated with…
The document examines how to specify cross-correlations among Brownian drivers for two equity spots and their volatility processes. The question challenges an assumed cross-correlation between the first spot driver and the second volatility driver, proposing…
The document considers pricing a payoff that combines an upside payoff on one random variable with a downside payoff on another. It asks whether the joint expected value can be recovered from limited observations of individual cross-payoffs and marginal…
The document explains why a bond’s z-spread and asset-swap spread are often similar when its cash price is near par. The two measures reach a target price in different ways: an asset-swap spread adjusts cash flows, while a z-spread adjusts the discount rate…
The document asks how to express a defaultable bond’s credit spread when yields are quoted with semiannual compounding. It begins with the continuously compounded spread as the rate that relates the defaultable bond price to the default-free bond price over…
The document examines a proposed cash-and-stock replication of a call under the Black–Scholes model. It uses a Taylor expansion in the stock price to argue that the option’s convexity makes its value rise more than the local delta hedge when the stock moves,…
The document addresses why the sum of squared increments of a Wiener process approaches elapsed time as the time grid becomes finer. It includes an intuitive coin-toss analogy: symmetric zero-mean increments can have positive squared values, so their…
The document describes an attempt to model intraday price changes in SPX options that expire the same day. The goal is educational: to explore how option values respond to movements in the underlying index and volatility, especially near expiration, rather…
The document explains how time to maturity enters the Black–Scholes option pricing formula and why calculators often request days until expiration. The input unit itself is flexible: time must be expressed consistently with the units used for the risk-free…
The document derives the par fixed rate for a forward-starting swap by equating the present values of its fixed and floating legs. Under the stated setup, the floating leg can be expressed as a telescoping sum, giving a par rate determined by discount…
The document derives how premium-adjusted Greeks differ from Black–Scholes Greeks when an option is settled in a currency different from the underlying’s currency. In the example, the option value in the settlement currency is the value in the underlying…