From bid-ask credit default swap quotes to risk-neutral default probabilities using distorted expectations

TL;DR

This paper introduces a method to derive risk-neutral default probabilities directly from bid-ask CDS quotes using conic finance, accounting for market liquidity and providing unique calibration solutions.

Contribution

It formulates the CDS calibration as a conic finance problem to infer default probabilities from bid-ask quotes, incorporating liquidity considerations.

Findings

Unique calibration solutions under mild liquidity assumptions

Joint calculation of market-implied liquidity

Method applicable to bid-ask quotes without mid-quote approximation

Abstract

Risk-neutral default probabilities can be implied from credit default swap (CDS) market quotes. In practice, mid CDS quotes are used as inputs, as their risk-neutral counterparts are not observable. We show how to imply risk-neutral default probabilities from bid and ask quotes directly by means of formulating the CDS calibration problem to bid and ask market quotes within the conic finance framework. Assuming the risk-neutral distribution of the default time to be driven by a Poisson process we prove, under mild liquidity-related assumptions, that the calibration problem admits a unique solution that also allows to jointly calculate the implied liquidity of the market.