Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
978562 | Physica A: Statistical Mechanics and its Applications | 2011 | 11 Pages |
In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under this hybrid model. The core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term. Subsequently, a correction effect on the European option price is demonstrated both theoretically and numerically for a good agreement with practical results.
► A delayed geometric Brownian model is extended by a stochastic volatility term. ► A discounted option price is decomposed as a martingale plus a small term. ► Correction effects under our new hybrid model are demonstrated.