TY - JOUR
T1 - Option pricing in an investment risk-return setting
AU - Stoyanov, Stoyan V.
AU - Rachev, Svetlozar T.
AU - Shirvani, Abootaleb
AU - Fabozzi, Frank J.
N1 - Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - binomial pricing trees
KW - mean-variance portfolio
KW - Merton jump diffusions
KW - Option pricing
KW - stochastic continuous diffusions
KW - stochastic volatility
KW - volatility-of-volatility
UR - http://www.scopus.com/inward/record.url?scp=85116562012&partnerID=8YFLogxK
U2 - 10.1080/00036846.2021.1980490
DO - 10.1080/00036846.2021.1980490
M3 - Article
AN - SCOPUS:85116562012
SN - 0003-6846
VL - 54
SP - 1625
EP - 1638
JO - Applied Economics
JF - Applied Economics
IS - 14
ER -