Option Profit and Loss Attribution and Pricing: A New Framework
63 Pages Posted: 25 Mar 2018 Last revised: 2 Nov 2019
Date Written: March 24, 2018
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.
Keywords: Profit and loss attribution; Local commonality; Risk-return trade-off; Statistical arbitrage; Delta; Vega; Vanna; Volga; Implied volatility term structure; Implied volatility smile
JEL Classification: C13; C51; G12; G13
Suggested Citation: Suggested Citation