Option pricing in an investment risk-return setting

Stoyan V. Stoyanov, Svetlozar T. Rachev, Abootaleb Shirvani, Frank J. Fabozzi

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
JournalApplied Economics
DOIs
StateAccepted/In press - 2021

Keywords

  • Merton jump diffusions
  • Option pricing
  • binomial pricing trees
  • mean-variance portfolio
  • stochastic continuous diffusions
  • stochastic volatility
  • volatility-of-volatility

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