Robust Option Pricing: Hannan and Blackwell Meet Black and Scholes

37 Pages Posted: 20 Mar 2006 Last revised: 28 Jan 2016

See all articles by Peter M. DeMarzo

Peter M. DeMarzo

Stanford Graduate School of Business; National Bureau of Economic Research (NBER)

Ilan Kremer

University of Warwick; Hebrew University of Jerusalem

Yishay Mansour

Tel Aviv University

Date Written: January 12, 2016

Abstract

We apply gradient strategy methods, developed in the literature on robust optimization, approachability and calibration, to develop new bounds for option prices. While this literature focuses on asymptotic performance, we provide a financial interpretation of these methods by demonstrating how the gradient strategies developed by Hannan and Blackwell to minimize asymptotic regret imply trading strategies that yield arbitrage-based bounds for option prices. These bounds are both new and robust in that they do not depend on the continuity of the stock price process, complete markets, or an assumed pricing kernel. Rather, they depend only on the realized quadratic variation of the stock price process, which can be measured and, more importantly, hedged in financial markets using existing securities. We then argue that the Hannan–Blackwell strategy is path dependent and therefore suboptimal with a finite horizon. We solve for the optimal path-independent strategy, and compare the bounds achieved with Black-Scholes.

Keywords: Option Pricing, Replication, No arbitrage pricing, approachability, calibration, robust optimization, online algorithms

JEL Classification: C70, G13

Suggested Citation

DeMarzo, Peter M. and Kremer, Ilan and Kremer, Ilan and Mansour, Yishay, Robust Option Pricing: Hannan and Blackwell Meet Black and Scholes (January 12, 2016). Available at SSRN: https://ssrn.com/abstract=891626 or http://dx.doi.org/10.2139/ssrn.891626

Peter M. DeMarzo

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States
650-736-1082 (Phone)
650-725-7979 (Fax)

HOME PAGE: http://www.stanford.edu/people/pdemarzo

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Ilan Kremer (Contact Author)

Hebrew University of Jerusalem ( email )

20 Lila Street
Re'ut
Jerusalem
Israel

University of Warwick ( email )

Gibbet Hill Rd.
Coventry, West Midlands CV4 8UW
United Kingdom

Yishay Mansour

Tel Aviv University ( email )

Ramat Aviv
Tel Aviv 69978, 6997801
Israel

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