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.
|Number of pages||11|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 2011 Aug 15|
Bibliographical noteFunding Information:
The authors acknowledge helpful suggestions from the anonymous referees. This work was supported by the Korea Research Foundation Grant funded by the Korean Government ( KRF-2008-314-C00045 ) and in part by the Ministry of Knowledge Economy and Korea Institute for Advancement in Technology through the Workforce Development Program in Strategic Technology.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics