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Equivalent Martingale Measures and Lévy Processes. (2006). Fajardo, José.
In: Revista Brasileira de Economia - RBE.
RePEc:fgv:epgrbe:v:60:y:2006:i:4:a:961.

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  1. Aït-Sahalia, Y. (2004). Disentangling diffusion from jumps. Journal of Financial Economics, 74:487–528. Barndorff-Nielsen, O. E. (1998). Processes of normal inverse gaussian type. Finance and Stochastics, 2:41–68.
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  2. Carr, P. & Wu, L. (2004). Time-changed Lévy processes and option pricing. Journal of Financial Economics, 71:113–141.

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  6. Fajardo, J. & Farias, A. (2004). Generalized hyperbolic distributions and brazilian data. Brazilian Review of Econometrics, 24(2):249–271.

  7. fi(X1 t− , .., Xn t− )∆Xi t . where fi = ∂f ∂xi , fij = ∂2 f ∂xixj and [Xi , Xj ]c is the continuous part of the mutual variation8 of Xi and Xj 8For more details see Shiryaev (1999, Ch. III, 5C). RBE Rio de Janeiro v. 60 n. 4 / p. 353–361 Out-Dez
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  8. Huang, J. & Wu, L. (2004). Specification analysis of option pricing models based on time-changed lévy processes. Journal of Finance, LIX(3):1405–1440.

  9. Jacod, J. & Shiryaev, A. N. (1987). Limit Theorems for Stochastic Processes. Springer-Verlag, New York.
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  10. RBE Rio de Janeiro v. 60 n. 4 / p. 353–361 Out-Dez 361 Equivalent Martingale Measures and Lévy Processes Gerber, H. & Shiu, E. (1994). Option pricing by esscher transform. Transactions of the Society of Actuaries, 46:99–191.
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  11. Rydberg, T. (1997). Why financial data are interesting to statisticians. Technical Report 5, Centre for Analytical Finance, Aarhus University.
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  12. Sato, K.-I. (1999). Lévy processes and infinitely divisible distributions. Cambridge University Press, Cambridge.
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  13. Schoutens, W. (2003). Lévy Processes in Finance: Pricing Financial Derivatives. John Wiley and Sons.
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  14. Shiryaev, A. N. (1999). Essential of Stochastic Finance: Facts, Models and Theory. World Scientific Pub. Co.
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  15. Weron, R. (2001). Lévy-stable distributions revisited: Tail index does not exclude the Lévy-stable regime. International Journal of Modern Physics, C12:209–223. A. GENERALIZED ITO FORMULA For any measurable function f(t, x) we have X 0<s≤t f(s, ∆Ns) = t Z Z I R f(s, x)L(ds, dx), (11) and for any C2 function f, we have the Generalized Itô’s formula for cadlag semimartingales X1 , ..., Xn : df(X1 t , .., Xn t ) = X i fi(X1 t− , .., Xn t− )dXi t + X i,j fij(X1 t− , .., Xn t− )d[Xi , Xj ]c t +f(X1 t , .., Xn t ) − f(X1 t− , .., Xn t− ) − X i

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