Malliavin calculus in construction of hedging portfolio for the heston model of a financial market

• Autorzy: Janicki A. , Krajna Ł.
• Języki publikacji: EN

Abstrakty

EN

We present a method of theoretical and numerical construction of the hedging (replicating) portfolio for a given derivative financial instrument for the Heston model of a financial market. The stochastic Heston model is defined by an appropriate system oflto type stochastic differential equations. We use a methodology based on an application of the Clark-Ocone-Haussmann formula, leading to closed formulae for optimal replicating strategies. We show how to use it in computer oriented applications.

Słowa kluczowe

EN

hedging strategy; Heston model; stochastic model; financial market; Mallavin derivative

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 2
• Strony: 483--495
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Janicki A.

• Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

autor

Krajna Ł.

• Institute of Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Bibliografia

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• [2] S. Heston, A closed-form, solution for options with stochastic volatility with applications to bond and currency options, Rev. Financial Studies 6 (1993), 327-343.
• [3] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
• [4] A. Janicki, A. Weron, Simulation and Chaotic Behavior of α-stable Stochastic Processes, Marcel Dekker, New York, 1994, 2000.
• [5] I. Karatzas, S. E. Shreve, Methods of Mathematical Finance, Springer-Verlag, New York, 1998.
• [6] P. E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, New York, 1992, 1996, 1998.
• [7] M. Musiela, M. Rutkowski, Martingale Methods in Financial Modelling: Theory and Applications, Springer-Verlag, New York, 1997.
• [8] D. Nualart, The Malliavin Calculus and Related Topics, Springer-Verlag, New York, 1995.
• [9] D. L. Ocone, I. Karatzas, A generalized Clark representation formula, with application to optimal portfolios, Stochastics Stochastics Rep. 34 (1991), 187-220.