A delay financial model with stochastic volatility; Martingale method

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10 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2909-2919
Number of pages11
JournalPhysica A: Statistical Mechanics and its Applications
Issue number16
Publication statusPublished - 2011 Aug 15

Bibliographical note

Funding 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


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