Josep Perelló et al J. Stat. Mech. (2008) P06010 doi:10.1088/1742-5468/2008/06/P06010
Josep Perelló1, Ronnie Sircar2 and Jaume Masoliver1
Show affiliationsWe study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein–Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein–Uhlenbeck subordinated process describing the randomness of the log-volatility. We derive an approximate option price that is valid when (i) the fluctuations of the volatility are larger than its normal level, (ii) the volatility presents a slow driving force, toward its normal level and, finally, (iii) the market price of risk is a linear function of the log-volatility. We study the resulting European call price and its implied volatility for a range of parameters consistent with daily Dow Jones index data.
E-print Number: 0804.2589
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05.40.Fb Random walks and Levy flights
89.65.Gh Economics; econophysics, financial markets, business and management
60J65 Brownian motion (See also 58J65)
91B24 Price theory and market structure
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
91B26 Market models (auctions, bargaining, bidding, selling, etc.)
Issue 06 (June 2008)
Received 17 April 2008, accepted for publication 20 May 2008
Published 19 June 2008
Josep Perelló et al J. Stat. Mech. (2008) P06010
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