Option Profit and Loss Attribution and Pricing: A New Framework

Abstract

This paper develops a new top-down valuation framework that links the pricing of an option investment to its daily profit and loss attribution. The framework uses the Black-Merton-Scholes option pricing formula to attribute the short-term option investment risk to variations in the underlying security price and the option's implied volatility. Taking risk-neutral expectation and demanding no dynamic arbitrage results in a pricing relation that links an option's fair implied volatility level to the underlying's volatility level with corrections for the implied volatility's own expected direction of movement, its variance, and its covariance with the underlying security return.