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
This forum exchange addresses duplicate or misaligned intraday bars in an options strategy. A user reports that live indicator signals occur at different times from backtest signals and observes repeated minute-bar pushes from an option bar generator. The…
This market recap reviews Bitcoin and Ethereum options after an upside move. It reports rising realized volatility in both assets, with implied volatility lagging, and negative carry. The author links the demand for volatility to price moves exceeding…
The document clarifies dimensional consistency in the Black–Scholes stock price stochastic differential equation. If price is measured in currency and time in days, the drift coefficient has units of inverse time. To keep the diffusion term dimensionally…
The document asks how to interpret the Basel framework’s requirement to calculate equity vega “along one dimension.” It considers a two-year option whose theoretical vega depends on strike and maturity, then describes projecting the exposure to adjacent…
A calibrated implied volatility surface represents option volatility across strikes or deltas and maturities. It can interpolate prices for contracts without direct market quotes, support smooth inputs for calculations such as Dupire local volatility, and…
The document discusses ways to obtain option-chain information for a chosen underlying, including strikes, expirations, trading volume, and open interest. The responses distinguish freely viewable or scrapeable option-chain pages from historical tick-level…
The document prices a cash-or-nothing digital payoff that pays when the terminal stock price squared exceeds a threshold. Under the usual Black–Scholes assumptions with constant interest rate, dividend yield, and volatility, the key simplification is that…
The document asks how to convert an option-implied probability distribution into real-world probabilities, especially for downside market moves. It describes estimating an implied density from option prices across nearby strikes: interpolate missing prices…
The document explains rate inputs for pricing a one-year EUR/GBP option and distinguishes OTC options on spot FX from listed options on FX futures. For spot FX, it describes the Garman–Kohlhagen form of Black–Scholes, in which domestic and foreign rates both…
The note explains how to price a put option whose underlying is a European call, also called a compound option. At the put’s expiration, each node in the stock tree has a corresponding value for the still-live call. The put-on-call payoff at that node is the…
The document addresses how to describe a cap or spread attached to a monthly sum option. It asks whether these elements should be categorized as features or limits, highlighting that terminology may depend on the audience and the purpose of the description.…
The document poses a basic discrete-time finance problem: a savings account grows by a fixed factor, while a stock can move to one of two values. The stock’s initial value is normalized, and the two possible outcomes lie on opposite sides of the savings…
The document explains why a binomial option tree is evaluated backward from its terminal nodes. At expiration, the option payoff is determined by the underlying price in each scenario. Discounted risk-neutral expectations then propagate option values toward…
This document raises a sign-convention question about the current cost of a levered hedge in the Cox–Ross–Rubinstein option-pricing framework. The portfolio consists of written calls, purchased shares, and borrowed funds. Its payoff at expiration is…
The document compares Longstaff–Schwartz least-squares Monte Carlo with a forward Monte Carlo approach for pricing an American call. It explains that each method relies on an estimated exercise policy, so each reported price is a lower bound on the option’s…
The document explains how to derive past expiration dates for WTI options when a historical calendar is unavailable. It starts from the underlying futures contract: its final trading day falls three business days before the 25th calendar day of the month…
This note asks how to construct a security whose value responds to implied volatility by holding call options and managing the other risks embedded in them. Calls have positive vega, but also carry exposure to the underlying, time decay, interest rates, and…
This discussion considers boundary conditions for an implicit finite-difference solution of the Black–Scholes PDE after transforming spot into log-price. It compares fixing call values at finite grid edges with imposing slope conditions based on the call's…
This note interprets the ratio of the standard normal cumulative probabilities Φ(d₂) and Φ(d₁) in the Black–Scholes call formula. The call value is expressed as the stock holding value, S₀Φ(d₁), minus the discounted-strike cash amount, Ke⁻ʳᵀΦ(d₂). Thus Φ(d₁)…
This note examines whether a call option can be replicated in a one-period binomial market that admits arbitrage. It proposes a bond-and-stock portfolio and gives stock-price outcomes and a range of strikes and hedge positions for which the calculated…
The document examines whether rebalancing a delta hedge more often changes only the path and variance of profit and loss or can also change its expectation. A hypothetical long straddle example shows how frequent rebalancing can capture intraday round trips…
The document explains how to think about hedging a European option that pays the positive difference between two asset values. Its pricing expression uses both assets, their carry rates, and a combined volatility that depends on their individual volatilities…
The document explains how gamma and theta shape the profit and loss of a long call hedged by shorting the underlying. A local change in the hedged portfolio is approximated by theta decay over time plus a positive gamma contribution proportional to the…
The document sets up a pricing problem for a value function with geometric Brownian motion, a terminal put payoff, a constant running cost, and a constant intensity term that pulls the value toward a separate put-like payoff. It applies a Feynman–Kac…