Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion

The pricing problem of a kind of European vulnerable option was studied. The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. The closed-form solution to European option pricing was obtained by applying martingale measure transformation m...

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Main Authors: Yanmin Ouyang, Jingyuan Yang, Shengwu Zhou
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2018/4047350
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author Yanmin Ouyang
Jingyuan Yang
Shengwu Zhou
author_facet Yanmin Ouyang
Jingyuan Yang
Shengwu Zhou
author_sort Yanmin Ouyang
collection DOAJ
description The pricing problem of a kind of European vulnerable option was studied. The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. The closed-form solution to European option pricing was obtained by applying martingale measure transformation method. At the end of this paper, some numerical experiments were adopted to compare the new pricing formula introduced in this paper with the classical Black-Scholes pricing formula. The result showed that the new pricing formula conformed to the actual financial market. In fact, the option value is positively correlated with the underlying asset price and the company’s asset price and the jump process has significant influence on the value of option.
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institution Kabale University
issn 1026-0226
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publishDate 2018-01-01
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series Discrete Dynamics in Nature and Society
spelling doaj-art-dee796dbc69f427b95bdc9267a1569632025-02-03T07:26:05ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/40473504047350Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian MotionYanmin Ouyang0Jingyuan Yang1Shengwu Zhou2School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, ChinaSchool of Management, China University of Mining and Technology, Xuzhou, 221116, ChinaSchool of Mathematics, China University of Mining and Technology, Xuzhou, 221116, ChinaThe pricing problem of a kind of European vulnerable option was studied. The mixed fractional Brownian motion and the jump process were used to characterize the evolution of stock prices. The closed-form solution to European option pricing was obtained by applying martingale measure transformation method. At the end of this paper, some numerical experiments were adopted to compare the new pricing formula introduced in this paper with the classical Black-Scholes pricing formula. The result showed that the new pricing formula conformed to the actual financial market. In fact, the option value is positively correlated with the underlying asset price and the company’s asset price and the jump process has significant influence on the value of option.http://dx.doi.org/10.1155/2018/4047350
spellingShingle Yanmin Ouyang
Jingyuan Yang
Shengwu Zhou
Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion
Discrete Dynamics in Nature and Society
title Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion
title_full Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion
title_fullStr Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion
title_full_unstemmed Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion
title_short Valuation of the Vulnerable Option Price Based on Mixed Fractional Brownian Motion
title_sort valuation of the vulnerable option price based on mixed fractional brownian motion
url http://dx.doi.org/10.1155/2018/4047350
work_keys_str_mv AT yanminouyang valuationofthevulnerableoptionpricebasedonmixedfractionalbrownianmotion
AT jingyuanyang valuationofthevulnerableoptionpricebasedonmixedfractionalbrownianmotion
AT shengwuzhou valuationofthevulnerableoptionpricebasedonmixedfractionalbrownianmotion