2020/01/03 by Abootaleb Shirvani, Frank J. Fabozzi, Shirvani, Abootaleb +3
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #q-fin.MF
paper · pdf · doi:10.48550/arxiv.2001.00737
arxiv created 2020/01/03 · openalex publication_date 2020/01/03 · arxiv updated 2020/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 follow discrete binomial price dynamics, continuous diffusions, stochastic volatility, volatility-of-volatility, and Merton-jump diffusion are derived.