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 why a Monte Carlo estimate of a European call price can differ from the Black–Scholes value even when the simulation is implemented correctly. With a path-independent payoff under geometric Brownian motion, the terminal stock price can…
The document examines whether dividends inferred from put-call parity can support a discounted cash flow model that is consistent with arbitrage-free, risk-neutral valuation. The central reply is that a list of implied dividend cash flows and a discount rate…
The document discusses extending QuantLib’s VanillaOption class to represent an option on a future whose expiry differs from the option’s exercise date. The proposed design adds a future-expiry field to a derived argument class and overrides argument setup…
The document describes an attempt to price from a market-implied distribution built from a linearly sloped normal-volatility smile. The author prices options with the Bachelier model across a strike grid, estimates the cumulative distribution from one-sided…
The document asks how to interpret the short-maturity result associated with Berestycki, Busca, and Florent: implied volatility is related to local volatility through a harmonic mean. It connects that result to a derivation of the half-slope rule and asks…
The document clarifies a partial derivative used in option pricing. Vega measures how an option’s value changes as volatility changes, while other inputs to the pricing function—including the current stock price—are held fixed. Under Black–Scholes…
The document offers several explanations for unusually high implied volatility in near-term options, including contracts on stocks without imminent earnings. One possibility is an upcoming sector-wide event that makes short-dated options useful as…
The document prices a European payoff equal to the square of the underlying asset price under a risk-neutral geometric Brownian motion. It writes the terminal asset value using a normally distributed Brownian increment, discounts the expected payoff, and…
The document asks how interest rates and dividends affect variance-swap pricing and delta when replication uses a finite set of options rather than a continuous strip. It contrasts this practical setting with a simplified, zero-rate framework in which…
This document asks how to interpret a quoted premium for an option on an index CDS series after constituent defaults have reduced the index factor. The example concerns a payer option with a stated notional, strike, expiry, and bid–ask quote, and asks…
The document describes calibrating the Heston stochastic volatility model to European call prices. It lists the model's mean-reverting variance process and the parameters to estimate: the variance reversion speed and long-run level, volatility of variance,…
The question asks how to gain exposure to an underlying asset touching a target level at any time before expiry, rather than finishing beyond that level. It considers whether an American vanilla option or spread could approximate a payoff that increases when…
The document asks whether one SABR parameter set can be fitted to an entire implied volatility surface, and whether the at-the-money volatility can still determine alpha when fitting across expiries. The accepted response says standard SABR describes one…
The document distinguishes a forward price of a zero-coupon bond from the bond’s future spot price, then applies that distinction to valuing a caplet whose payoff is fixed at the start of its interest period. A forward bond price is the expectation of the…
The document outlines the Heston stochastic volatility model, in which the asset price and variance are driven by correlated Brownian motions. It shows one way to express those motions using independent Brownian drivers, then applies a change of measure to…
The document examines how to transform the Black–Scholes pricing equation from log spot coordinates to log forward coordinates. It starts with the risk-neutral log-price process and the associated pricing PDE, then introduces a forward coordinate whose drift…
The document considers the volatility exposure of a long, delta-hedged at-the-money SPX call after the index falls. It explains that the option’s implied volatility can change because its fixed strike moves along the implied volatility skew, while…
The explanation uses put–call parity to clarify why early exercise of an American call on a non-dividend-paying stock is generally unattractive. When the stock price is above the strike, the call’s value while it remains alive is at least the value of the…
The document examines whether IPO buyers of SPAC units can sell the common shares at a guaranteed value while keeping the attached warrants. The accepted answer explains that units generally cannot be separated immediately; separation occurs after a waiting…
The document compares Monte Carlo option valuation under the risk-neutral measure with valuation under the real-world measure. Its central idea is that simulations generated using a different drift can still estimate a risk-neutral price if each payoff is…
The post asks why a combination of put and call prices at two strike prices can be valued at two thirds of a stated total. It is a question about interpreting an algebraic result obtained from put-call parity, rather than about an options trading strategy.…
The document considers how an investor might protect an equity holding against extreme losses, including buying far out-of-the-money puts. It describes purchasing equity index puts as a straightforward form of portfolio insurance, while emphasizing that…
The document asks how to express option sensitivities as dollar gains or losses for percentage changes in the underlying price and implied volatility. It focuses on delta and gamma for spot moves, vega and volga for volatility moves, and vanna when both…
The document asks how to extend a Monte Carlo portfolio Value at Risk calculation to holdings from different asset classes, using a stock, a Treasury bond, and an option as examples. It refers to a simulation approach involving correlated random returns and…