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
The discussion separates two ideas that are often conflated: a normal distribution need not have a zero mean, and observed equity returns need not follow a normal distribution. A normal distribution is described by its mean and standard deviation; the…
The document asks how node values for an American option on a small stock-price tree translate into a hedge. The accepted reply identifies the commenter’s suggested stock position as delta hedging: adjusting exposure to the underlying so that small price…
The document addresses pricing a positive-part payoff built from weighted prices of two assets observed at multiple dates. It asks whether a closed-form formula exists when a spread involves more than two prices. The response proposes moment matching:…
The discussion asks whether MACD and its fast and slow exponential moving averages should be calculated from an option’s market price or its underlying. One response argues that smoothing the underlying before using it to calculate an option premium would…
The document explains how least-squares Monte Carlo (LSM) estimates the value of callable derivatives and exposure measures without repeatedly running costly nested simulations. It simulates model states and their discounted future cash flows, then fits a…
The discussion considers whether factor models and momentum strategies used in equities have equivalents in options. It identifies the underlying price, underlying volatility, time to expiration, and interest rates as major influences on option prices. It…
The document addresses whether an option-implied distribution for a stock’s log return must be symmetric because Brownian motion is symmetric. The response clarifies that symmetry is not a general property of option-implied distributions and points to models…
The document examines numerical difficulties in pricing European calls under the stochastic volatility with correlated jumps (SVCJ) model. The original MATLAB implementation produces integration warnings and NaN values while attempting to recover prices from…
The document discusses how to check an option-adjusted spread (OAS) produced by an external calculator. Because OAS results depend on the calculation method and model, verification begins by identifying the stochastic model behind the utility. One can then…
The document considers whether Lévy processes and related academic techniques are used on options market-making desks. Its answer argues that Lévy models are a poor practical choice for pricing derivatives under the risk-neutral measure, warning that using…
The document explains why delta neutrality does not guarantee a break-even result or a profit. Delta measures a portfolio’s local sensitivity to the underlying price; it does not eliminate all sources of return or risk. The response distinguishes the claim…
The document derives the instantaneous volatility of the product of two correlated assets modeled with lognormal diffusion dynamics. Applying Itô’s product rule produces a return shock with contributions from both assets, including their correlation.…
The document discusses stopping a Monte Carlo valuation of a European option when the estimate is sufficiently precise. The proposed criterion compares a confidence-interval half-width, estimated as a normal critical value times the sample standard error,…
The document examines whether probability belongs in explanations of option Greeks. Its response distinguishes uncertainty in future price paths, given fixed model parameters, from uncertainty in the parameters themselves. Under the fixed-parameter…
The document asks how to find the time horizon at which the expected change in a derivative payoff reaches zero. It models two underlying quantities as drifting diffusion processes, with one carrying Brownian variance, and expresses the expected payoff…
The document derives a condition for a vanilla option’s implied volatility curve to have zero slope with respect to strike at a given maturity. Differentiating the Black–Scholes call price, expressed using strike-dependent implied volatility, and comparing…
The document examines how to replicate the square of a European call’s value across time. It distinguishes a terminal payoff from a value process: the squared call price does not generally have discounted-martingale dynamics, so a terminal claim alone cannot…
The document considers why a long 7Y1Y payer swaption might show gamma with different signs at the 7-year and 8-year points on a par yield curve. The answer suggests that the reported bucketed exposures may come from repricing after a parallel curve bump,…
The document examines an attempted derivation connecting bond convexity with squared modified duration. It defines modified duration as the negative price sensitivity to yield, scaled by bond value, and convexity as the similarly scaled second derivative.…
The answer argues that implied volatility need not be extracted only from the Black–Scholes lognormal model. It describes constructing option valuation formulas under alternative distributions, including log-hyperbolic-secant, log-Cauchy, log-t, and…
The discussion describes how to represent a complex payoff as a weighted combination of simpler instruments, such as the underlying, zero-coupon bonds, calls, and puts. It frames the task as minimizing the difference between the target payoff and the…
The document asks how to value a tracker certificate linked to a basket of index futures. It compares this with a proposed approach for an equity-index tracker: project the underlying using a forward curve, then discount using a discount curve. The question…
The note clarifies that a credit default swap (CDS) spread and a bid–ask spread use the word “spread” for different concepts. A CDS spread is described as the cost of credit protection and, in the answer, as the difference between a credit-risky interest…
The discussion distinguishes the role of two conditions used when building a trinomial pricing tree. The conditional expected stock price is set to grow at the risk-free rate under the tree’s transition probabilities. This is the no-arbitrage condition: it…