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The Absence of Arbitrage on the Complete Black-Scholes-Merton Regime-Switching Lévy Market

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  • Sulima Anna

    (Wroclaw University of Economics and Business, Wroclaw, Poland, Department of Econometrics and Operational Research, Faculty of Economics and Finance)

Abstract

The main aim of the paper was to prove that the complete Black-Scholes-Merton regime-switching Lévy market is characterized by an absence of arbitrage. In the considered model, the prices of financial assets are described by the Lévy process in which the coefficients depend on the states of the Markov chain. Such a market is incomplete; in order to complete this market, jump financial instruments and power-jump assets were added. Then, an equivalent martingale measure was indicated and the conditions were determined so that the above model is characterized by the absence of arbitrage. Arbitrage is a trade that profits by exploiting the price differences of identical or similar financial instruments in different markets or in different forms. Thus arbitrage can be understood as risk-free profit for the trader.

Suggested Citation

  • Sulima Anna, 2021. "The Absence of Arbitrage on the Complete Black-Scholes-Merton Regime-Switching Lévy Market," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(3), pages 72-84, September.
    • Handle: RePEc:vrs:eaiada:v:25:y:2021:i:3:p:72-84:n:1
    DOI: 10.15611/eada.2021.3.04
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    References listed on IDEAS

    as
    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Zbigniew Palmowski & Łukasz Stettner & Anna Sulima, 2019. "Optimal Portfolio Selection in an Itô–Markov Additive Market," Risks, MDPI, vol. 7(1), pages 1-32, March.
    3. Naik, Vasanttilak, 1993. "Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-1984, December.
    4. José Manuel Corcuera & David Nualart & Wim Schoutens, 2005. "Completion of a Lévy market by power-jump assets," Finance and Stochastics, Springer, vol. 9(1), pages 109-127, January.
    5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    6. Philippe Artzner & David Heath, 1995. "Approximate Completeness With Multiple Martingale Measures," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 1-11, January.
    7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    More about this item

    Keywords

    Lévy process; regime-switching; arbitrage; martingale measure;
    All these keywords.

    JEL classification:

    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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