The objective is to provide an Al\`os type decomposition formula and an approximate option pricing formula for the Barndorff-Nielsen and Shephard model: an Ornstein-Uhlenbeck type stochastic volatility model driven by a subordinator without drift. Al\`os (2012) introduced a decomposition expression of the call option prices for the Heston model by using Ito's formula. In this paper, we extend it to the Barndorff-Nielsen and Shephard model. As far as we know, this is the first result on the Al\`os type decomposition formula for models with infinite active jumps . Moreover, investigating the rate of convergence as the time to maturity tends to 0 for each term in the obtained decomposition formula, we shall present an approximate option pricing formula, and implement numerical experiments, which show that our approximation formula is effective for in-the-money options .
The objective is to provide an Al\`os type decomposition formula of call option prices for the Barndorff-Nielsen and Shephard model: an Ornstein-Uhlenbeck type stochastic volatility model driven by a subordinator without drift. Al\`os (2012) introduced a decomposition expression for the Heston model by using Ito's formula. In this paper, we extend it to the Barndorff-Nielsen and Shephard model. As far as we know, this is the first result on the Al\`os type decomposition formula for models with infinite active jumps .
R
and an approximate option pricing formula
of call option prices
D
of the call option prices
D
. Moreover, investigating the rate of convergence as the time to maturity tends to 0 for each term in the obtained decomposition formula, we shall present an approximate option pricing formula, and implement numerical experiments, which show that our approximation formula is effective for in-the-money options