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A constraint-based notion of illiquidity

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  • Thomas Krabichler
  • Josef Teichmann

Abstract

This article introduces a new mathematical concept of illiquidity that goes hand in hand with credit risk. The concept is not volume- but constraint-based, i.e., certain assets cannot be shorted and are ineligible as num\'eraire. If those assets are still chosen as num\'eraire, we arrive at a two-price economy. We utilise Jarrow & Turnbull's foreign exchange analogy that interprets defaultable zero-coupon bonds as a conversion of non-defaultable foreign counterparts. In the language of structured derivatives, the impact of credit risk is disabled through quanto-ing. In a similar fashion, we look at bond prices as if perfect liquidity was given. This corresponds to asset pricing with respect to an ineligible num\'eraire and necessitates F\"ollmer measures.

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  • Thomas Krabichler & Josef Teichmann, 2020. "A constraint-based notion of illiquidity," Papers 2004.12394, arXiv.org.
    • Handle: RePEc:arx:papers:2004.12394
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    References listed on IDEAS

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    1. Charles-Albert Lehalle & Sophie Laruelle (ed.), 2013. "Market Microstructure in Practice," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8967, December.
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    3. Kardaras, Constantinos & Kreher, Dörte & Nikeghbali, Ashkan, 2015. "Strict local martingales and bubbles," LSE Research Online Documents on Economics 64967, London School of Economics and Political Science, LSE Library.
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    6. Irene Klein & Thorsten Schmidt & Josef Teichmann, 2013. "When roll-overs do not qualify as num\'eraire: bond markets beyond short rate paradigms," Papers 1310.0032, arXiv.org.
    7. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
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    9. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Stefan Tappe, 2022. "Invariant cones for jump-diffusions in infinite dimensions," Papers 2206.13913, arXiv.org, revised Nov 2023.

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