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.
10,263 documents
This market recap reviews Bitcoin and Ethereum derivatives conditions, including realized and implied volatility, skew term structure, carry, and relative value. It reports that realized volatility had eased, front-end implied volatility softened before…
This document compares crypto spot, leveraged spot, and futures trading. It explains that spot positions are not subject to liquidation in the described framework, while borrowed margin positions and futures can be forcibly closed. It outlines long and short…
This document describes data structures for tracking option contracts, underlying instruments, and option chains in a portfolio. It updates positions from trades and holdings, derives mid prices from top of book quotes, and connects options with pricing…
The document describes an options volatility trading module built around live pricing, portfolio risk tracking, and execution. It outlines three pricing models for different exercise styles and underlyings, with routines to calculate theoretical prices and…
The document describes two portfolio analytics displays. The volatility chart plots call and put mid-implied volatilities against strike, alongside a pricing implied-volatility curve, and allows individual option chains to be shown or hidden. Curve data is…
The strategy compares a synthetic futures price, calculated from a call price minus a put price plus the strike, with the traded futures price. It measures the difference and opens a three-leg position when the spread crosses a configurable entry level: one…
The document derives an approximate single implied volatility for a portfolio of options whose components have different implied volatilities. It begins with the condition that the portfolio’s modeled value at the common volatility should equal the sum of…
The document explains how to estimate a bond’s value by discounting each scheduled coupon and principal payment. It adds the bond’s z-spread to the relevant spot rate, uses the resulting rates to calculate discount factors, and sums the discounted cash…
The document compares two martingale derivations of the Black–Scholes partial differential equation. With the bank account as numeraire, requiring the discounted option price to have zero drift yields the familiar PDE. The attempted stock-numeraire…
The document explains why the delta of a binary call becomes sharply concentrated around its strike as expiry approaches. Under Black–Scholes, the option value is expressed using the normal cumulative distribution function, and differentiating gives a delta…
The document derives an expression for the expected value of a process described by a stochastic differential equation with drift and diffusion terms. Rewriting the equation in integral form separates accumulated drift from the stochastic integral. Under the…
The document derives a European call pricing representation for an asset whose returns combine continuous Brownian movement with independent Poisson jumps. When jump sizes are lognormally distributed, conditioning on the number of jumps makes the terminal…
An implied volatility surface reflects option prices that vary by strike and maturity, unlike the constant volatility assumption in the basic Black–Scholes model. Looking at one maturity at a time, a steep downside wing means out-of-the-money puts are…
The document asks why an American put can have a different value from a European put when both are considered under the Black–Scholes framework. It contrasts the pricing inequality and payoff constraint for an American option with the familiar result that,…
The document asks how a short-term VIX futures index’s daily roll weights translate into the holdings and cash flows of an exchange-traded product. It uses a dated example with two adjacent futures prices to question how a roll handles a price difference,…
The document derives a closed-form price for a European payoff based on the positive part of one minus the strike divided by the terminal stock price, assuming the stock follows geometric Brownian motion under the money-market measure. Its key observation is…
The document explains how to simulate terminal prices for several assets whose returns are correlated, in order to value a multi-asset option by Monte Carlo. In a geometric Brownian motion model, dependence is specified through correlations among Brownian…
The document describes a backward path-integral scheme for pricing an American put on a log-price grid. At each time step, it discounts and integrates the next-step option value against a Gaussian propagator for log prices, then applies the early-exercise…
The document frames a model-selection problem for reinforcement-learning-based dynamic hedging of long-dated swaptions. The proposed application uses 2y2y and 4y2y swaptions, requiring simulated paths that update both a forward swap curve and an implied…
The document shows how to rewrite a European put’s discounted expected payoff as an integral of the underlying asset’s cumulative distribution function. Starting from the payoff integral over nonnegative asset prices, it extends the density’s support to the…
The document frames a research question about abrupt changes in index option prices near major expiration dates. It proposes systematic rebalancing by structured products as a possible source of price pressure and asks what other forces might contribute. The…
The document explains why a European put’s Black–Scholes–Merton value can fall below its immediate exercise payoff. A European option cannot be exercised before expiration, so when the underlying price is far below the strike, the eventual payoff is…
The document considers a weather-linked call whose daily payout depends on maximum temperature mapping to a quantity and a price index average exceeding a strike. The payoff also has daily and contract-wide payout limits, making a direct closed-form…
The document outlines a derivation of the Black–Scholes equation from the Capital Asset Pricing Model rather than from a risk-free portfolio formed by delta hedging. It starts from CAPM’s relation between expected return and covariance-based risk…