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Optional Defaultable Markets

Author

Listed:
  • Mohamed N. Abdelghani

    (Machine Learning, Morgan Stanley, New York City, NY 10019, USA
    The research is supported by the NSERC discovery grant 5901.)

  • Alexander V. Melnikov

    (Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada
    The research is supported by the NSERC discovery grant 5901.)

Abstract

The paper deals with defaultable markets, one of the main research areas of mathematical finance. It proposes a new approach to the theory of such markets using techniques from the calculus of optional stochastic processes on un usual probability spaces, which was not presented before. The paper is a foundation paper and contains a number of fundamental results on modeling of defaultable markets, pricing and hedging of defaultable claims and results on the probability of default under such conditions. Moreover, several important examples are presented: a new pricing formula for a defaultable bond and a new pricing formula for credit default swap. Furthermore, some results on the absence of arbitrage for markets on un usual probability spaces and markets with default are also provided.

Suggested Citation

  • Mohamed N. Abdelghani & Alexander V. Melnikov, 2017. "Optional Defaultable Markets," Risks, MDPI, vol. 5(4), pages 1-21, October.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:4:p:56-:d:115997
    as

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    References listed on IDEAS

    as
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