Location of schweizer price in the range of European options prices for a diffusion with jumps model of the financial market

• Autorzy: Jach A.
• Konferencja: II Konferencja dla Młodych Matematyków. Zastosowania Matematyki -Lądek Zdrój 2001
• Języki publikacji: EN

Abstrakty

EN

Jump-diffusion models of financial market described by stochastic differential equations (SDEs) driven by a Brownian motion and Poisson processes are incomplete. Prices for contingent claims can not be determined in a unique way. For different equivalent martingale measures different values for options can be obtained. In the paper the theorems on the range of European options prices corresponding to the class of all such measures for jump-diffusion models of financiel market are presented. Equivalent martingale measures are explicitly described by appropriate linear stochastic differential equations, which can be solved with the use of general semimartingale Ito formula. In comparison with a content of the basic paper of N. Bellamy and M. Jeanblanc [1], the results are slightly more general (see Lemma 1) and proofs (presented in [4]) corrected and improved at some points. The price corresponding to the Schweizer minimal martingale measure is derived for a more general market model driven by Poisson random measures defined by Poisson processes with jumps of random size. The Schweizer price is located and compared with the Merton price in the range of prices corresponding to the class of all possible equivalent martingale measures for jump-diffusion models described by stochastic differential equations driven by a Brownian motion and a nnite number of Poisson processes. Results of computer experiments based on approximate construction of equivalent martingale measures provide a quantitative illustration of obtained results.

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Prace Naukowe Instytutu Matematyki Politechniki Wrocławskiej. Konferencje
• Rocznik: 2003
• Tom: Vol. 25, nr 4
• Strony: 29--40
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Jach A.

• Institute of Mathematics, Wrocław University of Technoloy, Poland.

Bibliografia

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