A delay financial model with stochastic volatility; Martingale method

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Abstract

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
Volume390
Issue number16
DOIs
Publication statusPublished - 2011 Aug 15

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

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