Option Profit and Loss Attribution and Pricing: A New Framework

54 Pages Posted: 25 Mar 2018 Last revised: 27 Apr 2018

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

Marking to market dictates that investors worry not only about terminal payoffs, but also about daily price fluctuations. This paper develops a new valuation framework that links the pricing of an option investment to its daily profit and loss attribution. The new framework uses the explicit Black-Merton-Scholes option pricing formula to attribute the short term investment risk of the option to variations in the underlying security price and in the option's implied volatility. This attribution highlights the key risk drivers affecting the short term investment return distribution and provides a basis for determining what risks to dynamically hedge and what risks to take exposure on. Taking risk-neutral expectation and applying dynamic no-arbitrage constraints results in a pricing relation that links the option's fair implied volatility level to the underlying's short term volatility level as well as corrections for the implied volatility's own expected direction of movement, its variance, and its covariance with the underlying security return. Commonality assumptions on the implied volatility co-movements across strike price, maturity date, and the underlying security allow one to generate cross-sectional pricing implications for a selected number or range of option contracts underlying the same security or across many different names.

Keywords: Profit and Loss Attribution; 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). 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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