Option Pricing in an Investment Risk-Return Setting

25 Pages Posted: 1 Aug 2019

See all articles by Young Shin Kim

Young Shin Kim

State University of New York, SUNY at Stony Brook University, College of Business

Stoyan V. Stoyanov

Charles Schwab

Svetlozar Rachev

Texas Tech University

Frank J. Fabozzi

EDHEC Business School

Date Written: July 29, 2019

Abstract

In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the contract’s maturity the contract is perfectly hedged. We derive both the optimal holdings in the underlying assets for the trader’s optimal mean-variance portfolio and the amount of unhedged risk prior to maturity. Solutions assuming the cases where the price dynamics in the underlying assets follows discrete binomial price dynamics, continuous diffusions, stochastic volatility, volatility-of-volatility, and Merton-jump diffusion are derived.

Keywords: option pricing; mean-variance portfolio; binomial pricing trees; stochastic continuous diffusions

JEL Classification: G13, G12, G19

Suggested Citation

Kim, Young Shin and Stoyanov, Stoyan Veselinov and Rachev, Svetlozar and Fabozzi, Frank J., Option Pricing in an Investment Risk-Return Setting (July 29, 2019). Available at SSRN: https://ssrn.com/abstract=3428633 or http://dx.doi.org/10.2139/ssrn.3428633

Young Shin Kim (Contact Author)

State University of New York, SUNY at Stony Brook University, College of Business ( email )

306 Harriman Hall
Stony Brook, NY 11794
United States

Stoyan Veselinov Stoyanov

Charles Schwab ( email )

101 Montgomery Street (120K-15)
San Francisco, CA 94104
United States

Svetlozar Rachev

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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