Option Profit and Loss Attribution and Pricing: A New Framework

63 Pages Posted: 25 Mar 2018 Last revised: 2 Nov 2019

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Liuren Wu

City University of New York, CUNY Baruch College - Zicklin School of Business

Date Written: March 24, 2018

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.

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

Carr, Peter P. and Wu, Liuren, Option Profit and Loss Attribution and Pricing: A New Framework (March 24, 2018). Journal of Finance, Forthcoming, Baruch College Zicklin School of Business Research Paper No. 2018-04-01, Available at SSRN: https://ssrn.com/abstract=3148796 or http://dx.doi.org/10.2139/ssrn.3148796

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Liuren Wu (Contact Author)

City University of New York, CUNY Baruch College - Zicklin School of Business ( email )

One Bernard Baruch Way
Box B10-247
New York, NY 10010
United States
646-312-3509 (Phone)
646-312-3451 (Fax)

HOME PAGE: http://faculty.baruch.cuny.edu/lwu/

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