TY - JOUR
T1 - Option pricing in an investment risk-return setting
AU - Stoyanov, Stoyan
AU - Rachev, Svetlozar
AU - Shirvani, Abootaleb
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.
M3 - Article
SP - 1
EP - 14
JO - American Economic Journal: Applied Economics
JF - American Economic Journal: Applied Economics
ER -