Article ID Journal Published Year Pages File Type
978562 Physica A: Statistical Mechanics and its Applications 2011 11 Pages PDF
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.

► 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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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