2015/06/04 by Takuji Arai, Arai, Takuji
Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1506.01477
openalex publication_date 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive representations of local risk-minimization of call and put options for Barndorff-Nielsen and Shephard models: jump type stochastic volatility models whose squared volatility process is given by a non-Gaussian rnstein-Uhlenbeck process. The general form of Barndorff-Nielsen and Shephard models includes two parameters: volatility risk premium β and leverage effect ρ. Arai and Suzuki (2015, arxiv:1503.08589) dealt with the same problem under constraint β=-(1)/(2). In this paper, we relax the restriction on β; and restrict ρ to 0 instead. We introduce a Malliavin calculus under the minimal martingale measure to solve the problem.