Optional Defaultable Markets

Mohamed N. Abdelghani and Alexander V. Melnikov
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Mohamed N. Abdelghani: Machine Learning, Morgan Stanley, New York City, NY 10019, USA
Alexander V. Melnikov: Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2R3, Canada

Risks, 2017, vol. 5, issue 4, 1-21

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.

Keywords: defaultable claims; hazard process; martingale deflators; optional processes; hedging (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2017
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