A constraint-based notion of illiquidity

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 numéraire. If those assets are still chosen as numéraire, 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 numéraire and necessitates Föllmer measures.

References in corpus (5)

• Strict local martingales and bubbles
• Supermartingales as Radon-Nikodym densities and related measure extensions
• Filtration shrinkage, strict local martingales and the Föllmer measure
• When roll-overs do not qualify as numéraire: bond markets beyond short rate paradigms
• The Jarrow & Turnbull setting revisited