A Framework for Derivative Pricing in the Fractional Black-Scholes Market
AbstractThe aim of this paper is to develop a framework for evaluating derivatives if the underlying of the derivative contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. For this purpose we first prove some results regarding the quasi-conditional expectation, especially the behavior to a Girsanov transform. We obtain the risk-neutral valuation formula and the fundamental evaluation equation in the case of the fractional Black-Scholes market.
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Bibliographic InfoPaper provided by Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB in its series Advances in Economic and Financial Research - DOFIN Working Paper Series with number 19.
Date of creation: Oct 2008
Date of revision:
fractional Brownian motion; fractional Black-Scholes market; quasiconditional expectation; mathematical finance; contingent claim;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Alòs, Elisa & Mazet, Olivier & Nualart, David, 2000. "Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 121-139, March.
- Cipian Necula, 2008. "Barrier Options and a Reflection Principle of the Fractional Brownian Motion," Advances in Economic and Financial Research - DOFIN Working Paper Series 6, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
- L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
- Ciprian Necula, 2008. "Pricing European and Barrier Options in the Fractional Black-Scholes Market," Advances in Economic and Financial Research - DOFIN Working Paper Series 20, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
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