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 raises a question about two option sensitivities: dual delta, described as the derivative of option price with respect to strike, and epsilon, described as sensitivity to dividend yield. It asks whether these measures have practical uses and…
The document asks which implied volatility surface should serve as the target when calibrating the leverage function in a stochastic-local volatility model. It describes a two-stage setup: first calibrate pure Heston parameters, then fit the leverage…
The document explains how to value a European option whose payoff is determined at expiry but paid later. It distinguishes the option expiry date from the cash settlement date and expresses the value at expiry as the payoff multiplied by the price of a…
The document asks how quickly simulated asset paths converge under a Milstein discretization of the Heston stochastic volatility model. It gives the coupled stochastic differential equations for the asset price and variance, including mean reversion in…
The document presents Python code intended to value a European call or put using a time and asset-price grid. It sets the payoff at expiration, then attempts to step backward through the grid while estimating option sensitivities and applying boundary…
The discussion describes what makes options strategy backtesting more demanding than testing a simple underlying asset. A credible simulation needs historical option chains, including contract terms and market prices, alongside underlying prices used to…
The document compares Monte Carlo prices for a European call under constant volatility and under volatility sampled once per path from a lognormal distribution. It raises the question of why the random-volatility estimate is slightly below the…
The document raises a model-validation question: whether stochastic-volatility option models produce more accurate market-price estimates than the standard Black–Scholes–Merton model. It highlights two practical costs of more complex models: greater…
The question asks whether one can derive the Black–Scholes partial differential equation without invoking Girsanov’s theorem, and whether a stock with nonzero drift is a martingale. The answer distinguishes the original replication argument from later…
The document considers how to assess performance when an investor adds money at uneven intervals and holds a mix of securities, including ETFs and options, potentially with leverage. Its response separates investor cash flows from the return series used for…
The document challenges the claim that an option’s Black–Scholes price is the discounted expected payoff under real-world probabilities. The response recommends comparing this claim with risk-neutral valuation, which uses a pricing measure consistent with…
The document asks why a stock-price model with drift μ can be expressed under a different probability measure with drift equal to the risk-free rate r, while retaining the same volatility. This is the risk-neutral change of measure used in derivative…
The document raises a practical question about estimating spread option Greeks by applying finite differences to Kirk’s spread option approximation. The author reports that, for options with deltas between 0.45 and 0.6, the resulting gamma estimates fall…
The document considers the lower price bound for a claim in an incomplete market, where multiple risk-neutral measures may be consistent with observed prices. It asks whether sub-replication is the counterpart to super-replication: while the…
The document describes a general way to value a call option when the underlying’s terminal price distribution is known. The option value is the discounted expected payoff under a risk-neutral probability distribution: integrate the payoff above the strike…
The discussion considers whether an economics researcher who prices options and calibrates models should learn C++ to speed computationally intensive work, and how to connect it with higher-level languages. One respondent recommends a derivatives-pricing…
The document asks whether Black–Scholes call valuation should use a point estimate of variance from historical returns or average option values across the sampling distribution of that estimate. It describes treating the sample variance as uncertain, mapping…
The document examines how a rise in implied volatility for a short-expiry option may affect a longer-expiry option with the same strike, assuming the event driving the move occurs within the shorter option’s life. The answer models volatility across time…
The note distinguishes fitting an implied volatility surface at the current time from specifying how that surface changes as time passes and the underlying price moves. A cross section indexed by maturity and strike can be fitted to current market data, but…
The document asks how to include lags when applying least squares Monte Carlo to a timing real option. The project can be started at monthly decision dates over a five-year window, while revenue follows a non-Markov ARMA process sampled hourly over a…
The document works through an arbitrage-free valuation problem for a down-and-in claim paying the underlying stock value at maturity if a barrier is touched. The barrier equals the strike of a down-and-out call. The given market prices are for the…
The document asks what it means to say Black–Scholes overprices or underprices options when the option’s true value is not directly known. It presents research claims that the model can price deep in-the-money calls too high and deep out-of-the-money calls…
The document asks how to trade a violation of a stated no-arbitrage inequality involving three swaptions with the same strike and different option and swap maturities. The condition says the prices of two shorter-maturity swaptions, taken together, should be…
The document asks how to convert dollar P&L into percentage returns for a two-leg straddle strategy sized by vega notional. The strategy aims to stay vega neutral by balancing its legs, while positions are adjusted and delta hedged over time. The central…