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 note explains how to interpret the instantaneous forward variance quantity in a model of volatility smiles. It distinguishes that quantity from a forward-starting variance swap, whose fair strike is constructed from the variances of two maturities. The…
This discussion asks how to use volatility from an implied-volatility surface in Reiner-Rubinstein formulas for an up-and-out call, expressed as a vanilla call minus an up-and-in call. The vanilla component may reference the strike while another component…
This example compares delta-gamma and delta-vega hedging for a short call using another call and shares. It gives Black-Scholes Greeks for an in-the-money call and an at-the-money call, then solves for the option quantity that offsets gamma or vega and the…
This discussion frames Funding Valuation Adjustment (FVA) through an uncollateralized FX forward with a client, hedged by a bank under a Credit Support Annex. It asks what an FVA calculated from the trade’s expected exposure profile represents, given that…
The document discusses how to fit a Black-Scholes implied volatility surface when options trade with bid-ask spreads. It explains why separate arbitrage-free bid and ask surfaces are generally not useful for practical hedging, since trades and hedges can…
The document asks how to simulate stock paths under a Merton jump diffusion model, which combines continuous Brownian movement with jumps driven by a Poisson process. The response frames the task as Monte Carlo simulation: choose a time increment, draw a…
The document explains why delta-hedged option profits should not be confused with recovering the premium as trading revenue. Under Black–Scholes assumptions of zero rates, continuous hedging, and realized volatility equal to implied volatility, gamma gains…
The document explains that exchange options, whose payoff exchanges one asset for another, do appear in practice, though listed markets are limited and often less liquid than single-asset options. In commodity futures, a zero-strike spread option can have…
The document asks how to attribute stock-trading profit and loss to individual options in a delta-neutral portfolio when the stock is traded only to hedge those options. It compares allocating the hedge result in proportion to each option’s gamma with…
The document describes an attempt to infer a coherent zero-coupon discount curve from a quoted forward swap curve, with the aim of also producing a three-month LIBOR forward curve. The author recognizes that the available observations may not uniquely…
The document explains how to visualize Black–Scholes Vanna, the sensitivity of an option’s value to changes in both the underlying price and volatility. The central task is to evaluate Vanna over every pair drawn from two input ranges, rather than matching…
The document describes connections between actuarial science and quantitative finance, using insurance portfolios and life insurance contracts as examples. Its central distinction is that actuarial work often estimates future distributions from observed…
The document considers whether an American put calendar spread can have a negative price and examines an attempted no-arbitrage argument based on selling the shorter-maturity put and buying the longer-maturity put at the same strike. The key issue is…
The document discusses how a dealer might quote caps and floors in an emerging market with swaps but no traded interest-rate options. Without option quotes for calibration, the response recommends developing an indicative volatility cube using comparable…
The document asks how to construct term structures for ESTER and SOFR, daily reference rates that do not necessarily have established swap markets. It contrasts the usual curve-building approach with the limited instruments available for these newer…
The document distinguishes spot at-the-money options from at-the-money-forward options in foreign exchange. In the described convention, an ATM option has a strike equal to the current spot rate and its delta is hedged in the spot market. An ATMF option uses…
The document discusses difficulties fitting the Heston stochastic volatility model to vanilla option prices. Parameter dependence and flat regions in the calibration objective can make optimization unstable, especially for mean reversion. It considers…
The document examines the profit profile of a call writer who holds stock to offset the call’s delta. Because the stock position has no gamma while the short call has negative gamma, the combined portfolio retains negative gamma. The question is whether this…
The document raises a practical calibration question for a one-factor Hull–White interest-rate model used to price a structured note. The example note pays annual coupons based on the positive part of three-month EUR Libor plus a spread, then returns…
The note explains how to value a put whose premium is deferred until exercise. It rejects treating the arrangement as a standard put with a reduced strike, because that changes the payoff: a conventional option buyer can lose the upfront premium even when…
The document explains how to price a maturity claim that pays the larger of a deterministic money account and a dividend-paying stock. It decomposes the payoff into the money account plus a call option on the stock, with the money account value at maturity…
The document examines whether investment-grade bonds or junk bonds necessarily have greater duration. It distinguishes measures based on contractual cash flows from effective or risk-adjusted duration, which estimates interest-rate sensitivity using modeled…
The document introduces Emanuel Derman’s volatility approximation for a volatility swap under an assumed linear volatility skew. It describes the approximation as assuming a linear put skew and a flat call skew, with applicability focused on strikes…
The document explores whether an option-implied risk-neutral distribution can be checked by integrating its density twice and comparing the reconstructed call prices with observed option prices. It grounds the idea in the Breeden-Litzenberger relationship,…