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Pricing Model for Convertible Bonds: A Mixed Fractional Brownian Motion with Jumps

Published online by Cambridge University Press:  07 September 2015

Jie Miao  and
Xu Yang
Jie Miao*
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China Department of Mathematics, Changji College, Changji, Xinjiang 831100, China
Xu Yang
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China
*
*Corresponding author. Email addresses: [email protected] (J. Miao), [email protected] (X. Yang)
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Abstract

A mathematical model to price convertible bonds involving mixed fractional Brownian motion with jumps is presented. We obtain a general pricing formula using the risk neutral pricing principle and quasi-conditional expectation. The sensitivity of the price to changing various parameters is discussed. Theoretical prices from our jump mixed fractional Brownian motion model are compared with the prices predicted by traditional models. An empirical study shows that our new model is more acceptable.

Keywords

60J7560G2291G80Mixed fractional Brownian motionPoisson jumpconvertible bondempirical study
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 3 , August 2015 , pp. 222 - 237
Copyright
Copyright © Global-Science Press 2015 

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