In this paper we introduce the so-called risk-exogenous measure and study the price of exogenous risks based on a fractional jump-diffusion financial market model. The option price equation indicates that the evaluation of risk-exogenous is consistent with that of the classical neutral risk. An empirical example shows that the risk-exogenous valuation is more suitable for practical financial markets by comparing the error between actual price of stocks and the price computed from BS formula and the option price equation under risk-exogenous measures respectively.
F. Black, M. Scholes, The pricing of options and corporate liabilities, Journal of Political
Economy 81 (1973) 122-155.
R. Elliott, J. Hoek, A General Fractional White Noise Theory and Applications to Finance,
Mathematical Finance 13 (2) (2003) 301-330.
T. Bjork, H. Hult, A note on Wick products and the fractional Black-Scholes model, Finance
and Stochastics 9 (2) (2005) 197-209.
P. Guasoni, No arbitrage under transaction costs with fractional Brownian motion and
beyond, Mathematical Finance 16 (3) (2006) 569-582.
H. Xue, Y. Sun, Pricing European Option under Fractional Jump-diffusion Ornstein-
Uhlenbeck Model, Conference Proceeding of 2009 International Institute of Applied
Statistics Studies, Aussino Academic Publishings House 164-169.
H. Xue, J. Lu, X. Wang, Fractional Jump-diffusion Pricing Model under Stochastic Interest
Rate, 2011 3rd International Conference on Information and Financial Engineering,
IACSIT Press 12(2011)428-432.
Pearce, D.K., Roley, Stock Prices and Economic News, Journal of Business 58 (1985)
Rigobon, R., B.P.Sac, Measure the Reaction of Monetary Policy to the Stock Market,
Quarterly Journal of Economics 118 (2) (2003) 639-669.
N. Ciprian, Option Pricing in a Fractional Brownian Motion Environment, Pure Mathematics
(1) (2002) 63-68.
Y. Hu, B. ?ksendal, Fractional white noise calculus and applications to finance, Infinite
Dimensional Analysis, Quantum Probability and Related Topics 6 (1) (2003) 1-32.