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 explains why the premium of an at-the-money straddle is not generally equal to the dollar amount of a one-standard-deviation move. At expiry, a straddle pays the absolute distance between the underlying price and the strike. With the strike at…
The note asks how Hanson’s logarithmic market scoring rule (LMSR) produces quoted outcome prices and whether trading pressure shifts prices in a see-saw pattern. The response says that this effect can be moderated by charging a wider spread, with the…
The question describes a path-dependent contract with one payoff if the underlying stays above a barrier and a different payoff if it crosses below it. It asks how to balance the component instruments to give the contract zero initial value and how to solve…
The exchange concerns pricing an EUR/GBP option when EURIBOR is negative and asks whether converting quoted rates to continuously compounded rates requires taking a logarithm. The answer clarifies that the relevant transformation is the logarithm of one plus…
The document asks how to derive a European call price from its terminal payoff, beginning with the positive part of the difference between terminal asset value and strike. The questioner attempts to reduce the calculation to the probability that the terminal…
The document raises a question about how volatility affects the value of an in-the-money European call when the underlying return distribution is negatively skewed. The author observes that, under a variance-gamma pricing formula, increasing the volatility…
The document examines Black’s approximation for an American call on a stock with a known discrete dividend. The approximation takes the larger of two European call values: one calculated using the stock price reduced by the dividend’s present value, and…
The note explains how to select strikes for a costless collar using gold options. A collar pairs a long put with a short call whose premium offsets the put’s cost. There is an unlimited set of such strike pairs: for each positive put strike, a call strike…
The note outlines how to price a European put in a four-month binomial stock model where the share price changes by a fixed amount each month. The stock starts at 100, moves up or down by 10 per step, and the riskless bond compounds at a 5% annual rate. The…
The document presents Black-76 formulas for European payer and receiver swaptions, scaling the option payoff by the present value of the underlying swap’s fixed-leg annuity. It defines the forward swap rate, strike, expiry, volatility, compounding frequency,…
The document asks whether the stock-and-bond portfolio used to interpret the Black–Scholes call formula remains self-financing as time passes. The proposed hedge holds a quantity of stock linked to the call’s delta and finances part of that position by…
The document considers whether futures options volatility behaves as sticky strike or sticky delta, and why intraday tick data can make the distinction difficult. Options and futures quotes may update at different times, while illiquid markets may not…
The document considers whether two call options can hedge a short call so that the resulting portfolio is both gamma-neutral and vega-neutral. It expresses the hedge as a two-equation linear system, with the other options’ vegas and gammas forming a…
This exchange examines whether implied volatility can be used to estimate the range of future stock prices. The question raises three concerns: log returns may be modeled as normal while prices are lognormal, the expected return affects longer-horizon…
The question asks how to model daily SPX implied volatilities across several maturities and moneyness levels, preserving their correlations and incorporating jumps linked to recurring events such as economic releases and dividends. The proposed goal is to…
The document explains how to obtain the terminal asset-price density from the second derivative of a European call price with respect to strike. It starts from the discounted payoff integral and its first strike derivative, which is minus the discounted…
The document considers filling missing market-maker bid and ask values across strikes and maturities when historical option prices are available for all liquid contracts and fair quotes exist for only some. It covers both European options, for which the…
The document explains why co-terminal European swaptions are often used to calibrate the Hull–White interest-rate model when the intended application is pricing Bermudan swaptions. Each Bermudan exercise date is associated with a European swaption whose swap…
The document explains a claim about how weekly options may change trading around options expiration. When traders can take short-term positions in several weekly contracts as well as the front-month monthly contract, their activity is spread across…
The document investigates an apparent increase in call-option gamma when a Black-Scholes routine is used to represent options on futures. The setup discounts the futures price before passing it as the underlying, then compares options with the same spot and…
The document explains why hedging an option on one asset with a correlated second asset can require a sensitivity that differs from the ordinary OLS slope between their price levels. Under a bivariate geometric Brownian motion, the instantaneous changes in…
The document discusses a question about Gatheral’s derivation connecting local variance to the conditional expectation of instantaneous variance. The central issue is why a stochastic differential term involving the underlying price and a strike disappears,…
The document asks how to price an option on a long-duration coupon bond whose payoff depends on the bond’s value at option maturity relative to its initial value. It proposes simulating short-rate paths with a model such as Hull–White, deriving discount…
The question compares a stated reference value for SPY with a lower quoted value for deeply in-the-money FLEX calls and asks why the contracts appear to have been purchased at a discount. One answer offers expected dividends as an explanation: when a call…