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Journal of Economic Interaction and Coordination

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26.08.2019 | Regular Article

A simulation analysis of systemic counterparty risk in over-the-counter derivatives markets

verfasst von: Yuji Sakurai, Tetsuo Kurosaki

Erschienen in: Journal of Economic Interaction and Coordination | Ausgabe 1/2020

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Abstract

In this paper, we propose a simulation framework to assess systemic risk in over-the-counter derivatives markets. We incorporate credit valuation adjustment (CVA), a mark-to-market estimate of counterparty credit risk booked on a bank’s balance sheet, into an otherwise standard structural model of credit risk. In this model, banks optimally hedge CVA by trading a credit default swap (CDS). The model aims to capture a possible adverse effect called “CDS–CVA feedback loop” from CVA hedging, which could increase CDS spreads due to a lack of liquidity in CDS markets and even further increase CVA because CVA is valued using the default probability extracted from CDS spreads. In order to measure systemic counterparty credit risk, we aggregate CVA across banks and examine how the distribution of systemic counterparty credit risk changes depending on underlying model parameters. We document that the tail risk of CVA increases nonlinearly when the liquidity of CDS markets declines. As an extension, we also model cost of posting collateral and discuss the trade-off between reducing systemic counterparty credit risk, stability of CDS markets and collateral cost.

Vorheriger Artikel Identifying financial instability conditions using high frequency data

Nächster Artikel Market microstructure, banks’ behaviour and interbank spreads: evidence after the crisis

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See Bank for International Settlements (2019) for reference.

An emerging strand of the literature aims at understanding the effect of introducing CCPs on financial markets: These papers include but are not limited to Duffie and Zhu (2011), Biais et al. (2016) and Hayakawa (2018). Different from these papers, this paper focuses on developing a theoretical model to capture the adverse feedback effects in the OTC derivatives markets.

Schubert (2011) discusses the accounting aspect of CVA. Prof. John Hull’s introductory textbook of risk management now has one chapter for CVA and related concepts. See the chapter 17 of Hull (2015). Several advanced textbooks of CVA were also published after the recent financial crisis. Cesari et al. (2009) and Gregory (2010) provide detailed discussions about CVA from the view of financial engineering.

See the first page of Basel Committee on Banking Supervision (2011).

See Basel Committee on Banking Supervision (2012) for the detail of the capital charge on value at risk of CVA.

For example, the Financial Times reports that the liquidity of “single” name CDS markets is declining (Rennison 2015). Note that a single-name CDS is CDS referenced to a specific firm. Furthermore, Risk.net reports a decline in CDS liquidity (Rega-Jones 2019). There are only a few academic studies focusing on the illiquidity component of single-name CDS spreads. Bongaerts et al. (2011) study CDS spreads on US firms during 2004–2008. They show that the liquidity effect is statistically significant but economically small.

Imperfect risk management means that the exposure is not fully collateralized and CVA is not perfectly hedged by CDS.

See Duffie (2001) for more details on the background history of CVA in the 1990.

Blavarg and Nimander (2002) empirically study Swedish banks’ counterparty credit risk exposure from the perspective of systemic risk. This paper’s focus is different: We are interested in developing a quantitative model to capture the adverse feedback effects due to CVA hedging in the OTC derivatives markets.

See Chapter 7 in Gregory (2010).

The last part of Sect. 3.2 explains the relationship between this simplified representation of CVA and the actual definition of CVA.

These approximate formulas are related to the work done by Cont and Wagalath (2016). They develop a tractable model to quantify the impact of loss-triggered fire sales on the risk of portfolio. They then derive analytical formulas for the impact of fire sales on the covariance matrix of asset returns. In the formula, realized volatility has two components: fundamental components and endogenous components.

This definition of CVA is consistent with the one defined in Pykhtin and Zhu (2007). In the equation (14) of their paper, the default probability from time t to $t+\varDelta t$ is denoted with $d\text {PD} (0,t)$. In our notation, $\mathrm{d}P^A (0,t)=\text {dPD}(0,t)$.

Specification for the dynamics of the value of underlying derivative trades as random walk is employed in Pykhtin and Rosen (2010). Our specification (4.9) includes random walk as a special case when $a^{ij}=1$.

Rigorously speaking, CDS spreads and credit spreads are two different concepts since the former is implied from CDS, while the latter is reverse engineered from the price of corporate bonds. In this paper, however, we use a structural credit risk model as a parsimonious way to associate credit risk with balance sheet information.

A negative sign of the first term in (4.16) comes from a discount factor. See, for instance, the following statement in page 4 of Sundaresan (2013): “Merton characterized credit spreads, $R(t)-r$, where the yield to maturity of the risky zero-coupon bond is defined as $D(t,T)\equiv B \mathrm{e}^{-R(\tau )\tau }$.” Let us map our notation to his notation, in such a way that $D(t,T)=\hbox {CB}(t,T), B=1, R(\tau )-r=c(t,T), \tau =T-t$. We obtain

$$\begin{aligned} \hbox {CB}(t,T)= \mathrm{e}^{-\left[ c(t,T)+r\right] (T-t)} \ \ \iff \ \ c(t,T) = -\frac{\log (\hbox {CB}(t,T))}{T-t}-r, \end{aligned}$$

which is Eq. (4.16). Equation (4.14) indicates that $\hbox {CB}(t,T)<\mathrm{e}^{-r(T-t)}$. Hence, c(t, T) is positive.

To be more precise, here we assume that CDS hedging is concentrated on a certain maturity and the hedging impact l(t) is extrapolated across other maturities T using the same number. We consider that this assumption is realistic as liquidity of single-name CDS is concentrated in 5 years. For example, Gregory (2012) is a popular and standard text book on CVA and he mentions that “We assume hedging with a 5-year CDS contract only, as this is likely to be the most liquid tenor available” in Section 16.4.2. Unfortunately, we do not have CDS transaction level data which allows us to investigate CDS illiquidity but CDS contracts with other maturities are even less liquid and thus the hedging impact should be even stronger if we capture the maturity-dependent hedging impact.

Recall that $\text {DVA}^{ij}$ does not depend on j’s CDS spreads. Hence, we have $\frac{ \partial \text {DVA}^{ij}}{ \partial s^j } =0$.

See page 27 in Deloitte (2013).

Huberman and Stanzl (2004) show that when price impact of trades is permanent and time-independent, only linear price impact functions rule out (quasi) arbitrage.

Both Avellaneda and Lipkin (2003) and Jeannin et al. (2008) assume the linear price impact with respect to the trading amount associated with dynamic hedging activity. The differences between our paper and their approach are (1) we are working on discrete-time framework while they model in continuous-time, and (2) in our model the impact is on absolute level of spread, while in their model the impact is on relative change in stock prices.

Precisely speaking, we have additional two time steps so that we have values for all variables. Recall that CVA requires CDS spreads as inputs but CDS depends on CVA in our model.

See Office of the Comptroller of the Currency (2018).

Recall that $\rho ^{ij}=-{\bar{\rho }}$ for $i>j$.

According to 2017 annual reports, the ratio of equity to total asset is as follows: 11.1 for Goldman Sachs, 10.9 for Morgan Stanley, 8.5 for Bank of America, 9.1 for Citibank, 9.9 for J.P.Morgan. Figure 3 in Beccalli et al. (2015) reports that leverage of US investment banks was around 20 during the 2005–2006 period and then jumped up to around 45 in 2008. After the crisis, the leverage declined to around 10.

In ISDA Standard Model Setting, the 40% recovery rate is used for most of categories except emerging markets: http://www.cdsmodel.com/cdsmodel/fee-computations.html.

We conducted sensitivity analysis with respect to these collateral-related parameters. Although not reported, we confirm that our main results in Section 5.3 remain qualitatively the same. The tipping point could change given the impact of collateral-related parameters on the exposure. For example, a higher haircut rate lowers the tipping point as it increases the exposure.

See the page 157 in Morgan (2012).

The skewness of the total CVA distribution represented with the black solid line in Fig. 9 is 0.2, while it is $-\,1.6$ in Fig. 10.

Here, $|V^{ij}(0)|$ is interpreted as the notional amount of the derivatives, as IM is often set to depend on the size of notional amount.

In Andersen et al. (2017), there is additional term for trade flows.

For example, IM requirement as percentage of notional exposure ranges from 1 to 4% for interest rate products, depending on maturity.

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Titel: A simulation analysis of systemic counterparty risk in over-the-counter derivatives markets
verfasst von: Yuji Sakurai
Tetsuo Kurosaki
Publikationsdatum: 26.08.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Economic Interaction and Coordination / Ausgabe 1/2020
Print ISSN: 1860-711X
Elektronische ISSN: 1860-7128
DOI: https://doi.org/10.1007/s11403-019-00260-7

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