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A constraint-based notion of illiquidity

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.