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 considers pricing a path-dependent option linked to a stock index and an interest-rate index. The proposed setup uses a Hull–White short-rate process and a local-volatility stock model, with correlated Brownian shocks. The question is whether…
The note examines why a delta-neutral call ratio backspread, with more calls bought than sold, may open for a credit under a traditional theoretical pricing model. Its example sells one lower-strike call and buys two higher-strike calls. Setting the…
The question asks how to size a variance swap as an imperfect hedge for an asset return that tends to weaken when its variance rises. It proposes modeling returns with a GARCH-in-mean relationship and setting swap notional to offset the estimated sensitivity…
The document addresses whether a multi-leg options position can have a net delta or other Greeks. When the derivatives share a common underlying, their deltas and most other Greeks can be added to estimate the position’s combined sensitivity. For a call…
The document explains how a call option’s payoff distribution follows from the distribution of its underlying asset. For a European call with strike K, the payoff is zero whenever the underlying finishes at or below K; above the strike, the payoff is the…
The document explains the analogy between the Black–Scholes partial differential equation and the heat equation. In the heat equation, temperature spreads through a material over time; in the option-pricing equation, option value evolves over time across…
The document describes the market action for settling an exercised call on EUR, quoted in USD, when the call writer does not already hold the currency to deliver. In its example, the strike is below the expiry spot rate. The writer can buy EUR in the spot…
The document explains how changing from a bank account numéraire to a spot asset numéraire can be represented as an Esscher transform for certain one-period return distributions. It focuses on skew Laplace returns, rewriting their density as a weighted…
Implied volatility is inferred from an option’s market price, so without an options market there is no market-implied volatility to observe directly. With sparse but available quotes, the response suggests using the implied volatility of an out-of-the-money…
The document points readers seeking payoff formulas for non-path-dependent options toward standard references. For plain vanilla options, it recommends learning the payoff diagrams for long and short calls and puts, then combining those building blocks to…
The document considers a one-year contract on two stocks, each initially priced at 100, that pays the higher stock price at maturity. It explains that the issue price cannot be determined from the initial prices and maturity alone: asset volatilities and…
The document discusses a bullish LEAPS call spread: buy an out-of-the-money call and sell a call at a higher strike, with both options expiring more than a year away. The proposed plan is to close the short call partway through the trade if the outlook…
This discussion asks how to estimate the chance that a non-defined-risk options combination, such as a straddle or strangle, will be profitable at expiration. It contrasts using delta as a rough probability proxy for an individual option with inferring…
This discussion examines whether gamma exposure (GEX), calculated from option gamma and open interest, can help predict hedging flows and market behavior. The author applies the call-positive, put-negative convention from a published framework to Nifty 50…
The note considers which Treasury maturity to use as an interest-rate input when pricing options. Responses suggest matching the rate tenor to the option’s maturity, while also distinguishing the role of rates in different parts of a derivatives valuation.…
This note asks how to solve a differential equation relating implied volatility across log-moneyness to local volatility in the short-maturity limit. It states the proposed relationship and a claimed solution: implied volatility at a given log-moneyness is…
The document examines an attempt to infer risk-free rates from put-call parity using DAX index option settlement prices. The proposed calculation compares put and call prices at two strikes with the same maturity, eliminating the underlying index level and…
The document explains why option theta differentiates the pricing function with respect to calendar time while holding the stock-price input fixed, even though the stock price itself evolves over time. It distinguishes the deterministic pricing function…
The document works through how an FX call strike can be recovered from a quoted delta for a risk reversal. Its accepted answer applies the Garman–Kohlhagen model, using the currency pair’s forward rate, interest rates, volatility, and separate expiry and…
The document distinguishes risk neutrality in utility theory from risk-neutral valuation in derivatives pricing. In utility theory, a risk-neutral investor has an affine utility function, so expected utility is linear in wealth. The post considers a buyer’s…
The document asks how forward delta relates to the vega ratio of out-of-the-money options and to the vega of in-the-money options. It describes a proposed interpretation in which the underlying forward price is used to calculate delta for an option with the…
The document raises how to assess moneyness for a cancellable interest rate swap. The example is a position paying a fixed contract rate with the right to cancel, and it compares that contract rate with a quoted par coupon rate. The example supplies both…
The document examines when a European call under stochastic interest rates can be valued by averaging Black–Scholes prices using the path’s average short rate. It explains that this conditioning argument works when the stock and rate processes are…
The document examines how a derivative’s hedge changes when implied volatility depends on the underlying price. It states that the total sensitivity to the underlying combines the usual partial delta with a vega contribution that depends on how volatility…