Credit Default Swaps and Risk-Neutral Default Probabilities

We propose a method to extract the risk-neutral distribution of firm-specific stock returns using both options and credit default swaps (CDS). Options and CDS provide information about the central part and the left tail of the distribution, respectively. Taken together, but not in isolation, options and CDS span the intermediate part of the distribution, which is driven by exposure to the risk of large, but not extreme, returns. Through a series of asset-pricing tests, we show that this intermediate-return risk carries a premium, particularly at times of heightened market stress. This paper was accepted by David Simchi-Levi, finance.

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xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024920500065 ◽

2020 ◽

Vol 23 (01) ◽

pp. 2050006

Author(s):

LIXIN WU ◽

DAWEI ZHANG

Keyword(s):

Risk Management ◽

Interest Rate ◽

Liquidity Risk ◽

Credit Default Swaps ◽

Interest Rate Swap ◽

Funding Liquidity ◽

Credit Default ◽

Risk Neutral ◽

Default Risks ◽

Rate Swap

xVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This paper is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on bilateral replication pricing using shares and credit default swaps, we attribute the P&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks, can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties. We call for the adoption of VaR or CVaR methodologies for managing funding risks. The pricing of xVA of an interest-rate swap is presented.

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