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Early exercise boundary and option prices in Levy driven models

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  • S. Z. Levendorski

Abstract

Pricing and hedging of European. American, barrier options and interest rate derivatives for wide classes of Levy driven models is consideref in situatins where qualitative and quantitative differences between gaussian and Levy modelling are most prominent, and the dependence on the choice of a family of Levy processes is analysed. Asymptotics of option prices near the barrier and expiry are calculated; for American options, two fast numerical methods are constructed. It is shown that for many classes of Levy processes, the early exercise boundary of the American put is separated from the strike by a non-vanishing margin, and as the riskless rate vanishes, the early exercise boundary tends to 0 uniformly over the interval [0, T). Implications for fitting of parameters are discussed.

Suggested Citation

  • S. Z. Levendorski, 2004. "Early exercise boundary and option prices in Levy driven models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 525-547.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:5:p:525-547
    DOI: 10.1080/14697680400000036
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    Cited by:

    1. Todorov, Viktor & Tauchen, George, 2010. "Activity signature functions for high-frequency data analysis," Journal of Econometrics, Elsevier, vol. 154(2), pages 125-138, February.
    2. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    3. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    4. Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models," Papers 2312.03915, arXiv.org.
    5. Chen, Son-Nan & Hsu, Pao-Peng, 2018. "Pricing and hedging barrier options under a Markov-modulated double exponential jump diffusion-CIR model," International Review of Economics & Finance, Elsevier, vol. 56(C), pages 330-346.
    6. Svetlana Boyarchenko & Sergei Levendorskii, 2023. "Simulation of a L\'evy process, its extremum, and hitting time of the extremum via characteristic functions," Papers 2312.03929, arXiv.org.
    7. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
    8. Z. Jiang & M. R. Pistorius, 2008. "On perpetual American put valuation and first-passage in a regime-switching model with jumps," Papers 0803.2302, arXiv.org.

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