Interconnected balance sheets, market liquidity, and amplifi cation effects in a financial system
Nan Chen (The Chinese University of Hong Kong, Hong Kong)
Joint work with David Yao and Xin Liu

Thursday June 5, 14:00-14:30 | session 8.4 | Credit | room K

This paper investigates two amplification effects of a financial system in developing individual defaults to a systemic catastrophe. In our model, the financial institutions interconnect via two mutually stimulating channels: their balance sheets are linked directly by holding debt claims against each other; they share the market liquidity to liquidate assets to meet debt liabilities when they face distress. The liabilities network and market liquidity will amplify small and idiosyncratic shocks to a systemic impact, as evidenced by the recent financial crisis. We use optimization with equilibrium constraints to formulate our model of the above financial network to characterize analytically how the topological structures of the system and asset liquidation interact with each other to form the systemic risk. Two multipliers, network multiplier and liquidity multiplier, are identified to capture the above amplification effects. The model has a significant computational advantage and can be solved efficiently. It produces a natural metric for measuring financial institutions' systemic risk exposures. Furthermore, we examine some policy implications yielded from the numerical experiments on the data of European Banking Authority 2013 stress tests.

Consistent Valuation of Collateralized OTC Deals under Credit and Funding Risk
Qing Liu (Imperial College London, UK)
Joint work with Damiano Brigo, Andrea Pallavicini and David Sloth

Thursday June 5, 14:30-15:00 | session 8.4 | Credit | room K

We develop an arbitrage-free framework for consistent valuation of OTC derivative trades with collateralization, counterparty credit risk, and funding costs. Based on the risk-neutral pricing principle, we derive a general pricing equation where CVA, DVA, and FVA are introduced by simply modifying the payout cash-flows of the deal. Funding risk breaks the bilateral nature of the deal price and makes the pricing problem a highly non-linear and recursive one. This means that FVA is not generally an additive adjustment as commonly assumed by market participants. Our framework addresses common market practices of ISDA governed deals without restrictive assumptions on collateral margin payments and close-out netting rules. In particular, we allow for asymmetric collateral and funding rates. The pricing equation can be cast as a set of iterative equations that can be solved by least-squares Monte Carlo and we propose such a simulation algorithm. Our numerical results confirm that funding risk does have a non-trivial impact on the deal price.

About a class of counterparty risk related BSDEs
Stéphane Crépey (University of Evry, France)
Joint work with Shiqi Song

Thursday June 5, 15:00-15:30 | session 8.4 | Credit | room K

We study a class of BSDEs, key to the modeling of counterparty risk in finance, with terminal time $ T \wedge S,$ where $T$ is a positive constant and $S$ is a stopping time. When $S$ has an intensity and under a decomposability assumption, so-called condition (B), on the model filtration $\mathbb{G}$, we prove that this BSDE is equivalent to a simpler BSDE, relative to a reduced filtration $\mathbb{F}$ and with constant terminal time $T.$ To prove this result, we generalize several results in Jeulin's classical theory of enlargement of filtrations, using new arguments (the classical ones can no longer be used at this increased level of generality). In addition, assuming the existence of a changed probability measure $\mathbb{P}$ equivalent to the original probability measure $\mathbb{F}$ on $\mathcal{F}_T$ such that any $({\mathbb{F}},\mathbb{P})$-local martingale {stopped at ${S-}$} is a $(\mathbb{G},\mathbb{Q})$-local martingale, the so-called condition (A), we prove that the previous $({\mathbb{F}},\mathbb{Q})$ reduced BSDE is in turn equivalent to an $(\mathbb{F},\mathbb{P})$ BSDE that is essentially the original $(\mathbb{G},\mathbb{Q})$ BSDE, but with the constant terminal time $T$ --- an equivalence that we call the invariance principle. In order to interpret the condition (A) in a classical langage of enlargement of filtration, we establish a characterization of this condition in terms of the Azéma supermartingale of $S.$ Thus we can compare the setup offered by conditions (A) and (B) with other models, such as pseudo stopping times or density models. Finally, we show that the case of a predictable time $S$, important for application to the so-called cure period (which relates to gap risk) in counterparty risk modeling, is of a completely different nature from the above case where $S$ had an intensity --- an important message for financial practitioners. In order to deal with the predictable case, we propose a technique of desintegration of the BSDE with respect to an intermediate stopping time. In the end, as the last section illustrates, conditions (A) and (B) appear as the right framework for the study of the counterparty risk related BSDEs.