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 raises a valuation question about a convertible bond: how to derive yield to maturity from a value calculated with an option valuation model. It considers treating the difference between the calculated value and the bond’s issue value as…
The document asks whether an options gamma exposure index can help forecast realized volatility and how to turn gamma exposure into an implied-move curve across underlying prices. It describes GEX as an aggregate of call and put gamma exposure, calculated…
The document asks for research on whether options open interest is related to implied volatility, proposing that heavy market-maker short positioning at a strike might lower implied volatility. The response highlights a basic identification issue: each open…
The document considers pricing a European put when the underlying follows geometric Brownian motion multiplied by a compound Poisson jump process. It proposes conditioning on the number of jumps over the option’s remaining life, then summing the conditional…
The discussion compares Bloomberg’s BGN and CMPN sources for EUR/USD FX option volatility quotes, especially butterfly quotes used in strategies that trade convexity. The answer describes BGN as a generic daily close and CMPN as a composite of contributor…
The document asks how to adapt a Heston European call formula for an FX pair, where pricing involves both a domestic rate and a foreign rate. It supplies a stock-option integral formula, a characteristic function, and proposed asset and variance dynamics,…
The answer shows how to test a laddered option payoff for mispricing by expressing it as a portfolio of simpler calls. It first represents the payoff across strike-defined regions, then rewrites it using call payoffs that activate above each strike. For the…
The discussion addresses how to estimate an option’s vega, volga, and vanna by repricing after perturbing the volatility input. When a product depends on an entire Black variance surface, replacing it with a single constant volatility can be unsuitable for…
A call option on a forward gives its holder the right to enter a forward contract at the option’s expiry. Whether exercise is worthwhile depends on the forward price at that time relative to the strike. The resulting exposure is to the forward contract; it…
The note outlines a model-based route to backtesting variance and volatility swaps when direct swap data is unavailable. It uses a one-factor Bergomi setup in which instantaneous variance follows a lognormal process correlated with the asset return. In this…
The document derives a replication for a European chooser option, which lets its holder decide at an intermediate date whether to receive a call or a put, both expiring later. At the choice date, put–call parity expresses the put payoff as the call payoff…
The document describes an option-pricing problem in which volatility changes when the underlying crosses a specified barrier. It suggests this setup may represent a post-crash environment where near-term option volatility is elevated and expected to move…
The document asks why a futures price is not simply the expected future spot price, and contrasts this intuition with cost-of-carry pricing. Its answer frames futures and forwards through arbitrage-free pricing: if an asset can be bought and financed until…
The document considers how to estimate daily value-at-risk for a long option and asks whether the estimate can reflect the fact that the position cannot lose more than its premium. It contrasts a rough premium-based rule with delta-gamma VaR, which…
The document examines a chart of equity index implied skew and spot–volatility beta across option maturities. It describes implied skew as related to how implied volatility changes as the forward or spot level moves, while emphasizing that the relationship…
The document explores how financial variables can be dependent without having linear correlation. It begins with the mathematical example of a normally distributed variable and its square, then considers financial analogies where the relationship can be…
The document introduces Black–Scholes as a model for calculating a theoretical option price and asks how to interpret its d1 and d2 terms. The response says the model gives an appropriate price only if its assumptions hold. It does not explain d1 or d2…
The document describes a method for estimating an ETF’s implied funding or borrowing spread from option prices. It first adjusts American option prices toward European equivalents using the American–European price difference from a fitted volatility model.…
The document asks how to value commodity futures options when an investor has a specific view about the future return distribution: a substantial oil price spike is considered possible over a stated horizon, with the move expected to be brief. The goal is to…
The document asks whether a weighted mixture of two local-volatility models can provide an implied density for path-dependent options, including barrier and touch products. It presents the mixture as a weighted average of the component models’ vanilla option…
The note explains how the option portfolio’s gamma contribution to price change follows from the second-order term in Itô’s lemma. It distinguishes the instantaneous variance term in the pricing equation from realized movement in the underlying price. Using…
The document gives intuition for the variable changes used to transform the Black–Scholes partial differential equation into the heat equation. The response breaks the spatial transformation into two steps: first express the underlying price in…
The document discusses how to include swaps, FX forwards, and other non-equity derivatives in Monte Carlo Value at Risk simulations. It contrasts sensitivity-based approximations with full revaluation under simulated market scenarios. Sensitivity methods…
The document clarifies an ambiguous claim that spot price and variance have correlation near negative one. One response explains that the leverage effect concerns negative association between stock returns and volatility, rather than between the price level…