Ebook The Delivery Option in Credit Default Swaps
The pace at which the credit derivatives market has been growing since its inception about ten years ago topped all projections1, increasingly calling for the development of more and more accurate pricing tools for these products since market reality often reveals that the assumptions underlying the prevalent models are inadequate and misleading.
The instrument this paper focuses on is a credit default swap (CDS). This is a bilateral contract aimed at transferring the credit risk of a (corporate or sovereign) borrower from one market participant (the protection buyer) to another (the protection seller). The CDS buyer pays a periodical premium for the assurance that the CDS seller will compensate him for the loss in case the borrower defaults during the term of the contract. If so, the protection seller pays the notional amount of the contract to the protection buyer as compensation for the loss incurred. The latter, in turn, must deliver obligations (usually bonds) of the defaulted borrower with total principal equal to the notional amount of the CDS contract.
Since the CDS is a derivative instrument based on defaultable debt as the underlying asset, it is natural to enquire about the relation between the prices of credit risk in the bond and derivatives markets charged for resp. to a particular borrower. Such a relation is of crucial importance for pricing and hedging credit exposures. Duffie shows that it is only under highly restrictive and simplifying assumptions that the intuitive equality between the premium on a CDS and the yield spread of a bond over its risk-free counterpart (written on resp. issued by the same corporate borrower) holds. In a static setting, taking merely no-arbitrage arguments into account, the equivalence is valid for par floating-rate notes rather than for par fixed-rate notes. As expected, applying this argument to observable CDS and bond yield spreads, pricing discrepancies are uncovered.
The differences do not vanish even if one actually models the credit risk by employing standard pricing models (cf. e.g. Schönbucher) instead of simply replicating cash flows. Not even complex credit risk models are presently able to price in the observed differences. In the market this differential between CDS and bond spreads (of equal maturities, usually 5 years) has become known as the CDS basis. Precisely this divergence in the pricing of instruments in the bond and derivatives markets for corporate debt is the topic of our research.
This paper explores the relation between the prices in the bond and derivatives markets on a representative and diverse cross-section of euro-denominated corporate bonds and CDS. Using standard assumptions we quantify the above mentioned mispricing when employing a deterministic reduced-form framework. In an extensive comparison of the pricing properties in the bond market for several parameterizations of the default intensity the Nelson-Siegel specification turns out to be optimal. This parametrization is subsequently used to price CDS, resulting in model CDS spreads up to 50% lower on average than observed in the market.
A model extension is therefore proposed which explicitly incorporates the delivery option implicit in CDS contracts: Since in settlement the protection buyer is entitled to choose from a basket of pari passu deliverable obligations (bonds), she will prefer to deliver the cheapest bond in the market at default. Our extension thus models the implied recovery value of the cheapest-to-deliver bond. Applying the extension to the data, the new recovery parameter considerably improves the pricing properties in the CDS market, as expected. The average implied recovery rates range from 8% to 47% and strongly vary across obligors and within individual ratings and industries. Analyzing the implied recovery rates a cross-sectional regression reveals a statistically and economically significant dependence on delivery option proxies. Our paper thus points out the necessity for incorporating the random structure of recovery rates into credit risk models in order to accurately price credit-risky instruments.
Considering the academic literature, there are several papers dealing with the pricing difference, as measured by the CDS basis, from a wholly descriptive point of view, i.e. not attempting to model, but simply to present and discuss possible explanatory approaches. Hjort et al. and O’Kane and McAdie distinguish between fundamental and technical (market) factors, describing their likely effects on the relative valuation in the two markets. According to their reasoning, factors such as legal and regulatory risk, new bond issuance, difficulties in shorting corporate bonds, the embedded delivery option for the CDS buyer, the positivity of CDS spreads, and exotic bond features (e.g. coupon step-ups, convertibility) drive CDS spreads higher, whereas funding costs of bonds, counterparty risk, and leveraging opportunities constitute factors reducing CDS spreads, while liquidity is identified as having an ambiguous pricing effect. To the best of our knowledge, due largely to their complexity there have only been very few attempts to include some of the above stated factors in an actual valuation.
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