A delay financial model with stochastic volatility; Martingale method

Min Ku Lee; Jeong Hoon Kim; Joocheol Kim

doi:10.1016/j.physa.2011.03.032

A delay financial model with stochastic volatility; Martingale method

Min Ku Lee, Jeong Hoon Kim, Joocheol Kim

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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 language	English
Pages (from-to)	2909-2919
Number of pages	11
Journal	Physica A: Statistical Mechanics and its Applications
Volume	390
Issue number	16
DOIs	https://doi.org/10.1016/j.physa.2011.03.032
Publication status	Published - 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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10.1016/j.physa.2011.03.032

Cite this

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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.",

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AB - 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.

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A delay financial model with stochastic volatility; Martingale method

Abstract

Bibliographical note

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