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Continuously monitored barrier options under Markov processes

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  • Aleksandar Mijatovic
  • Martijn Pistorius

Abstract

In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given Markov model. We illustrate the method by implementing it for a range of models, including a local Levy process and a local volatility jump-diffusion. We also provide a convergence proof and error estimates for this algorithm.

Suggested Citation

  • Aleksandar Mijatovic & Martijn Pistorius, 2009. "Continuously monitored barrier options under Markov processes," Papers 0908.4028, arXiv.org, revised Dec 2010.
    • Handle: RePEc:arx:papers:0908.4028
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    File URL: http://arxiv.org/pdf/0908.4028
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    Cited by:

    1. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    2. Aleksandar Mijatovi'c & Martijn Pistorius, 2009. "Exotic derivatives under stochastic volatility models with jumps," Papers 0912.2595, arXiv.org, revised Oct 2010.
    3. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Lookback Option Pricing under Markov Models," Papers 2112.00439, arXiv.org.
    4. Dilip B. Madan, 2010. "Conserving Capital by Adjusting Deltas for Gamma in the Presence of Skewness," JRFM, MDPI, vol. 3(1), pages 1-25, December.

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