Abstract
In this paper the problem of determination of the no arbitrage price of double barrier options in the case of stock prices is modelled on Lévy processes is considered. Under the assumption of existence of the Equivalent Martingale Measure this problem is reduced to the convolution equation on a finite interval with symbol generated by the characteristic function of the Lévy process. We work out a theory of unique solvability of the getting equation and stability of the solution under relatively small perturbations.
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Author acknowledges financial support by CONACYT project 046936-F.
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To I.B. Simonenko on the occasion of his 70th birthday
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Grudsky, S.M. (2006). Double Barrier Options Under Lévy Processes. In: Erusalimsky, Y.M., Gohberg, I., Grudsky, S.M., Rabinovich, V., Vasilevski, N. (eds) Modern Operator Theory and Applications. Operator Theory: Advances and Applications, vol 170. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7737-3_8
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