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 poses a one-period binomial pricing question for a European call on a futures contract. It asks how to construct a replicating portfolio when the futures price can move up or down, and the underlying asset is itself a futures contract rather…
The note explains why a single option market price generally maps to different implied volatility values under Black-Scholes and Bachelier pricing. Each model uses its own pricing formula, so matching the same option terms and price requires a model-specific…
The discussion explains how to estimate a one-standard-deviation price move from annualized at-the-money implied volatility. Under the usual square-root-of-time approximation, volatility is multiplied by the square root of the fraction of a year in the…
The document addresses why standard option pricing models do not include a separate input for a company’s estimated economic growth, including for options with long maturities. Its central explanation is that expectations about growth are already reflected…
The document addresses how to hedge an option across multiple periods in a binomial stock-price model. Its central point is that the hedge must be recalculated at each node of the tree, since the appropriate holdings depend on the price path taken so far.…
The document shows how to represent straddle and strangle payoffs as combinations of European puts and calls, then add the component Black–Scholes prices and Greeks. A straddle combines a put and call at the same strike; a strangle combines them at different…
The document asks how to form a return series for strategies whose cumulative profit and loss can become negative, in the context of statistical strategy comparisons such as White's Bootstrap Reality Check. The issue is that conventional log returns cannot…
The document examines whether a recombining binomial option-pricing tree must use up and down factors whose product is one. One response says this condition is not necessary: recombination follows when the factors remain constant across steps, while…
The document raises practical questions about constructing a local volatility surface from call prices using Dupire’s formula. It considers a bounded region of strike and maturity values and asks whether interpolation should be performed on the derivatives…
The document asks where historical tulip mania prices can be obtained in a form suitable for statistical analysis. It describes the scarcity and uneven provenance of the surviving records: one compilation draws on sales across multiple varieties and market…
The document discusses a Python implementation of standard Monte Carlo valuation for an arithmetic average price Asian call. The method simulates asset-price paths with lognormal one-step growth, averages prices along each path, calculates discounted…
The document asks whether a stated put-call symmetry for calls has a corresponding form when starting from a put. It gives the call-side relationships in terms of spot and strike, then proposes swapping the call and put roles and exchanging the relevant spot…
The document addresses how to interpret the dividend-yield input when adapting a vanilla option delta or pricing framework to foreign exchange. Its answer explains that an FX option’s underlying is an exchange rate and that holding the foreign currency has…
The document considers writing a call against an existing long stock portfolio. The short call premium provides income and cushions some decline in the stock’s value, while the call obligation limits gains once the share price exceeds the strike. The…
The document explains the European put-call parity relation by comparing two portfolios: a call plus cash that grows to the strike, and the underlying asset plus a put. At expiry, both positions have the same payoff, so the law of one price implies equal…
The document examines whether a normal diffusion for a stock price, whose relative volatility falls as price rises, must produce a downward sloping lognormal implied volatility curve. It presents competing arguments based on vanilla option prices and on the…
The document points to the Litzenberger formula as a way to estimate risk-neutral probabilities from option prices. It identifies S&P 500 options as the example data and notes that their strikes are commonly spaced at five-point intervals. It also suggests…
The document derives a risk-neutral price for a European payoff that receives the asset value when the terminal price is at or below a strike and pays the negative strike when the price is above it. With zero interest rates and a lognormal terminal asset…
The document asks whether Longstaff–Schwartz Monte Carlo is generally the preferred method for Bermudan or American option pricing. The response favors a binomial tree for American-style options, based on a comparison with Longstaff–Schwartz. It describes…
The document considers whether an investor who owns a stock should sell it and use a futures contract to keep similar market exposure when the future trades below the stock. Its suggested method is to compare the expected cash flows and costs of each…
The document compares two common ways to calculate a put-call ratio from options open interest: puts divided by calls, and puts divided by the combined put and call total. It also notes that the ratio can instead use trading volume or a selected subset of an…
The document explores whether an underlying asset’s expected return should affect a Black–Scholes option premium through the dealer’s expected losses from dynamic delta hedging. It contrasts a call priced under a zero drift assumption with a hypothetical…
The document explains how to estimate a confidence interval for a European call price using Monte Carlo simulation. The recommended procedure is to calculate the option payoff in each scenario, including zero payoffs when the underlying finishes below the…
The document describes why the VIX often rises during stock-market declines. It emphasizes that VIX is calculated from a strip of options rather than directly from stock prices, with option contributions weighted by strike. When the market falls, realized…