Ebook Derivative Pricing with Liquidity Risk: Theory and Evidence from the Credit Default Swap Market
The relation between liquidity and asset prices has received considerable attention recently. However, much less is known about liquidity effects in derivative markets. This paper provides a theoretical model of liquidity effects in derivative markets and estimates this model for the credit default swap market. Recent market developments suggest that the credit default swap (CDS) market is subject to shocks in liquidity. In the subprime crisis of summer 2007, not only credit spreads increased substantially, but liquidity also dropped dramatically.
Our paper makes three contributions. Our first contribution is a theoretical asset pricing model for derivatives that incorporates liquidity risk. This model extends the ‘Liquidity-CAPM’ of Acharya and Pedersen (2005), who only consider investors with long positions in assets that are in positive net supply, in which case illiquidity always leads to lower asset prices. For derivative securities, which are in zero net supply, the effect of liquidity is much more complicated and can be zero, positive or negative. We propose an equilibrium framework where heterogenous investors use derivatives to hedge a fixed (credit) risk exposure. Transaction costs for derivatives vary systematically over time. We derive that under fairly mild conditions, the expected return on the derivative asset can be decomposed into market risk premia, an expected liquidity component, and one liquidity risk premium. This result differs from the result for a positive net supply market as in Acharya and Pedersen (2005) where there are three liquidity risk premia. In particular, our model predicts that the liquidity exposure of a derivative to derivative-market liquidity is not priced. We show that sign of the liquidity effects depends on heterogeneity in investors’ risk exposures, risk aversion and wealth. Our model is related to work on hedging pressures in futures markets (De Roon, Nijman and Veld, 2000) and option markets (Garleanu, Pedersen and Poteshman, 2006).
Our second contribution is an empirical test of this theoretical framework for an important class of derivative assets, credit default swaps (CDS). By now, the market for CDS contracts is one of the largest derivative markets (approximately 45.5 trillion USD around June 2007 according to Baird (2007)). The CDS market has become much more liquid than the corporate bond market. This has induced researchers and practitioners to use CDS spreads as pure measures of default risk (for example, Longstaff, Mithal and Neis (2005) and Blanco, Brennan and Marsh (2005)). However, using a standard two-pass regression approach to estimate the asset pricing model, our empirical results show that part of the CDS spread reflects a compensation for expected liquidity. Sellers of credit protection thus receive an illiquidity compensation on top of the compensation for default risk. There is no strong evidence for an effect of market-wide CDS liquidity risk on expected CDS returns, which is line with predictions from our theoretical model.
Third, we make several methodological contributions. We derive expressions for realized and expected excess returns on CDS positions. In particular, we show how to construct the expected excess returns from the CDS spread level, corrected for the expected loss. As argued by Campello, Chen and Zhang (2008) and De Jong and Driessen (2005), this procedure gives much more precise estimates of expected returns than averaged realized returns. On the econometric side, we use a repeated sales methodology to construct portfolio CDS returns and bid-ask spreads from the unbalanced panel of individual CDS quotes. Since our data are rather sparse, and because the sample composition varies substantially from one day to another, a repeated sales methodology makes much more efficient use of the information in the data than simple averaging of quotes over daily or weekly intervals.
For the empirical analysis we use a representative dataset of CDS bid and ask quote data for US firms and banks over a relatively long period (2000-2006). We only rely on the most standard and most liquid 5-year contracts. By taking raw quote data we avoid the use of pre-manipulated data. Applying the repeated sales method to these data, we construct excess CDS returns and bid-ask spreads for portfolios sorted on rating and quote activity. The level and variation of the bid-ask spreads is used to measure liquidity and liquidity risk.
We estimate the asset pricing model in two steps. In the first stage, realized CDS excess returns and unexpected liquidity shocks are regressed on market risk factors. In the second stage, expected excess returns are regressed on a measure of expected liquidity and on the risk exposure coefficients obtained in the first step. As discussed above, the expected excess returns are obtained from CDS spread levels, corrected for expected loss. Here, including both portfolios sorted on rating and quote activity helps to disentangle the effects of credit risk and liquidity.
The first-step time series regressions provide evidence for systematic equity risk and credit risk exposure of CDS returns. Moreover liquidity shocks also seem to exhibit a factor structure, but to a systematic liquidity factor rather than to a systematic market risk factors. In the second stage, we find a significant premium on expected liquidity, earned by the protection seller. Survey data for the CDS market in 2006 from the British Bankers Asscoiation1 show that long-term investors such as insurance companies and hedge funds are net protection sellers, while banks are net buyers. The expected liquidity premium for the protection sellers is in line with the theoretical model if protection sellers (long-term funds) are less risk averse and/or have more wealth than protection buyers (banks).
Specification tests on the empirical model reveal that the effect of liquidity on CDS prices feeds through the channel of expected liquidity and that the systematic liquidity factor does not play a role in CDS pricing, which is in line with the theoretical predictions.
Two recent papers estimate the impact of liquidity on CDS spreads, Tang and Yan (2006) and Chen, Cheng and Wu (2005). Our paper contributes to this work by developing a theoretical framework for liquidity effects on derivative prices and by explicitly estimating an asset pricing model for expected CDS returns. The asset pricing model allows for an immediate interpretation of our results as liquidity and liquidity risk premia. Tang and Yan (2006) regress CDS spreads on variables that capture expected liquidity and liquidity risk, and find that illiquidity leads to higher spreads. Chen et al. (2005) estimate the impact of liquidity and other factors on CDS spreads using a term structure approach. For estimation, they use term structures of CDS spreads over a sample period of slightly less than one year, much shorter than our sample period. They find that premia for liquidity risk and expected liquidity premium are earned by the CDS buyer. The identification of the liquidity risk premium comes from the term structure of CDS spreads, whereas our method follows the standard procedure of identifying risk premia from expected excess returns. Another recent paper by Das and Hanouna (2007) develops a framework in which lower equity market liquidity leads to higher CDS prices and confirms this mechanism empirically.
More generally, our paper builds on the literature on asset pricing and liquidity.2 For derivative markets, the literature on liquidity is very scarce and often starts from a some what different viewpoint, see for example C¸etin, Jarrow, Protter and Warachka (2006) who add liquidity to the standard Black Scholes framework and Brenner and Eldor (2001) who investigate the effect of non-tradability on currency derivatives. Deuskar, Gupta and Subrahmanyam (2006) find empirically that illiquid interest rate options trade at higher prices than liquid options, and also find evidence for commonality in liquidity of different options.
The remainder of this paper is structured as follows. In section 2 we introduce our theoretical model. In section 3 we discuss the definition and construction of our model variables in detail. A brief description of the data and the filters applied to these data is presented in Section 4. The results of the empirical analysis are presented in Section 5. Section 6 concludes.
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