Option pricing in an investment risk-return setting. Issue 14 (22nd March 2022) - Stoyanov, Stoyan V.; Rachev, Svetlozar T.; Shirvani, Abootaleb; Fabozzi, Frank J.
ABSTRACT: In this paper, we combine modern portfolio theory and option pricing theory so that a trader taking a position in a European option contract, the underlying assets, and a risk-free bond can construct an optimal portfolio while ensuring that the option is perfectly hedged at maturity. 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 price dynamics in the underlying assets follow a discrete binomial model, and continuous diffusions, stochastic volatility, volatility-of-volatility, and Merton's jump-diffusion model are derived.