Acta Mathematica Sinica, Chinese Series 2012, (2) 219-230 DOI:      ISSN: 0583-1431 CN: 11-2038/O1

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Keywords
fractional Brownian motion
fractional Vasicek model
zero coupon bond
option pricing
Authors
Wen Li HUANG
Xiang Xing TAO
Sheng Hong LI

Pricing Formulae for European Options under the Fractional Vasicek Interest Rate Model

Wen Li HUANG1, Xiang Xing TAO1, Sheng Hong LI2

1. Institute of Applied Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China;
2. Institute of Mathematical Finance, Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China

Abstract

Under the assuming of the stock price and interest rate obeying the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the risk hedge technique, fractional stochastic analysis and PDE method, we obtain the general pricing formula for the European option with stochastic interest rate. At the same time, we get the explicit expression for the European option price with stochastic interest rat and the call-put parity. The results in this paper extend as well as improve previously known results.

Keywords fractional Brownian motion   fractional Vasicek model   zero coupon bond   option pricing  
MSC2000 

O175.2, O211

Received 2010-09-01 Revised 2011-07-04 Online:  
DOI:
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Corresponding Authors:
Email: mathhuang@zju.edu.cn;xxtao@zust.edu.cn;shl@zju.edu.cn
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