The Jarrow & Turnbull setting revisited

Abstract: We consider a financial market with zero-coupon bonds that are exposed to credit and liquidity risk. We revisit the famous Jarrow & Turnbull setting in order to account for these two intricately intertwined risk types. We utilise the foreign exchange analogy that interprets defaultable zero-coupon bonds as a conversion of non-defaultable foreign counterparts. The relevant exchange rate is only partially observable in the market filtration, which leads us naturally to an application of the concept of platonic financial markets. We provide an example of tractable term structure models that are driven by a two-dimensional affine jump diffusion. Furthermore, we derive explicit valuation formulae for marketable products, e.g., for credit default swaps.