A delay financial model with stochastic volatility; martingale method

Min-Ku Lee, Jeong-Hoon Kim and Joocheol Kim

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 16, 2909-2919

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.

Keywords: Black–Scholes formula; Delay; Stochastic volatility; Martingale; Option pricing (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:16:p:2909-2919

DOI: 10.1016/j.physa.2011.03.032

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