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
The document explains how the Carr-Madan decomposition represents a European payoff as a bond position, a call-minus-put position at a chosen strike, and integrals of puts and calls weighted by the payoff’s second derivative. In a complete market with…
The discussion explains that an issuer can create a contract whose payoff tracks an asset such as gold by promising clients a cash settlement tied to a defined reference price. This is primarily a contractual arrangement. An exchange traded fund, product, or…
The document raises two modeling issues when applying stochastic quanto pricing formulas to crypto futures and perpetual swaps. First, it questions what domestic discount rate to use when the contract is settled in bitcoin, given the absence of a…
The note evaluates whether a bond index price can be approximated by dividing average coupon yield by yield to maturity. It explains that this ratio is appropriate in the limiting case of a bond with infinite maturity, where price is tied to coupon divided…
The note explains how to estimate fair value for a futures contract using the cost-of-carry relationship. For an index future, it relates the spot index level to financing over the contract term, adjusted for income such as dividends. The same idea can be…
The discussion explains a common source of discontinuities when building return series for standardized contracts such as IMM swaps or credit default swaps. A fixed-maturity CDS quote can remain stable across a roll date, while its label as an on-the-run…
The discussion addresses why a Chilean peso swap valuation built from flat discount and projection curves may differ substantially from market valuations. The response recommends constructing a curve from market quotes for the relevant CLP overnight indexed…
The discussion explains why Black–Scholes remains useful even though it cannot establish a uniquely fair option price. Its broader contribution is the dynamic hedging framework: under suitable assumptions, an option payoff can be replicated by adjusting…
The document asks how to show that a power of a Black–Scholes stock price, normalized by its initial value, is a positive martingale under the risk-neutral measure. It assumes the stock follows the standard risk-neutral diffusion and sets the power using the…
The answer distinguishes equality of option Greeks from equality of option prices. Greeks describe sensitivities, so two positions can have the same sensitivities while differing by a constant price offset. A replicating or hedging argument can support a…
The answer explains that the Black–Scholes formula follows from the terminal-price distribution of a geometric Brownian motion (GBM). A Monte Carlo method simulates terminal prices under that process, applies the option payoff, averages the payoffs, and…
The document examines a European call with a lower strike and a put with a higher strike, both expiring at the same time. It asks whether a condition linking their premiums to the gap between strikes could create a portfolio with a non-negative payoff and…
The document examines whether asset-level absolute risk contribution limits can be added to a return-maximizing portfolio optimization problem with a volatility cap. It defines portfolio volatility from the covariance matrix and weights, then derives…
The document describes the exposure a broker takes on when a customer buys a contract for difference (CFD). Because a CFD passes through the underlying asset’s price change, the broker is short that exposure and may need to acquire a corresponding long…
The document explains why an option skew measure based on volatility differences divided by log-strike distance, with a square-root-of-maturity adjustment, can remain similar across listed expiries. The key comparison uses strikes set at a fixed number of…
The document poses a conceptual question about pricing contingent claims under an equivalent martingale measure. It asks whether taking a conditional expectation requires specifying the underlying stochastic process or terminal distribution, or whether a…
The document examines integrability conditions for a cumulative income process in a mathematical finance framework. It asks how an expectation under a risk-adjusted measure, involving the finite-variation component divided by a numeraire, relates to an…
The document asks whether forward rates derived from one compounding convention can be used to calculate discount factors under ACT/360. It presents a method for deriving a forward rate from two spot rates and maturities, then proposes a discount-factor…
The document raises implementation questions about valuing an interest rate swap in QuantLib. It asks how a piecewise log-cubic discount curve uses dates and rates supplied through rate helpers, including whether the curve interpolates between those inputs.…
The document considers whether options can reveal volatility over a specific upcoming interval, such as a trading day containing a scheduled central-bank announcement. It notes that implied volatility is only directly observable for horizons with liquid…
The document asks how to build a forward six-month LIBOR curve in a multi-curve framework from three market inputs: par OIS rates, a fixed six-month LIBOR rate, and par swap rates on swaps with semiannual floating payments and annual fixed payments. It…
Co-terminal, or diagonal, swaptions share a common final maturity while their expiries step forward and their underlying swap tenors shorten. The document illustrates the structure with a callable bond that can be redeemed at regular intervals before…
The document explains why a futures contract’s implied repo rate may be higher when the short delivers on the last eligible date rather than the first. The key detail is that the invoice price includes accrued interest in addition to the futures price…
The document compares a portfolio of call options on individual assets with a call option written on a weighted portfolio of those assets. For nonnegative weights summing to one, the payoff of a call is a convex function of its underlying value. Convexity…